CN118171201A - A multidimensional data modeling and analysis method and system based on subspace sequence - Google Patents

Abstract

The invention discloses a multi-dimensional data modeling and analyzing method and system based on subspace sequences, which realize multi-angle analysis, dynamic evolution prediction and correlation effect analysis of a complex system through abstract representation and dynamic modeling of subspace sequences, and are innovative in that sequence dimensions are introduced, dependency relations among subspaces based on a graph model are constructed, and sequence dependence and topology constraint are combined; thus, the modeling accuracy can be enhanced, and the accuracy of system analysis is improved; meanwhile, the method does not need to rely on training data and historical parameters marked on a large scale, so that the method is very suitable for analysis of nonlinear complex systems; in addition, the topological relation among the nodes in the map is further mined through data mining, and the subspace association network map is updated according to the topological relation; based on the method, the deep analysis of the whole structure of the subspace network can be realized, and the modeling precision can be further increased, so that the accuracy of system analysis is improved.

Description

A multidimensional data modeling and analysis method and system based on subspace sequence

Technical Field

The present invention belongs to the technical field of multi-source heterogeneous data modeling and analysis for complex systems, and specifically relates to a multidimensional data modeling and analysis method and system based on subspace sequences.

Background technique

At present, the analysis of complex systems is based on system modeling and analysis methods, such as time series prediction based on vector autoregression (VAR) model, probabilistic graphical model based on Bayesian network, etc. The above methods are mainly based on statistical modeling ideas, which rely on a large amount of historical data for parameter training and are sensitive to data quality and quantity. Therefore, these methods are mostly limited to linear modeling, and have weak modeling capabilities for nonlinear complex systems and low analysis accuracy. In addition, nonlinear modeling methods such as neural networks rely on large-scale annotated training data and cannot make good use of the existing structural knowledge in modeling, which will lead to poor modeling interpretability. Based on the above explanation, in general, the existing technology for modeling and analysis of complex dynamic systems still has obvious defects and cannot accurately analyze complex dynamic systems. Therefore, how to provide a multidimensional data modeling and analysis method that can be applied to nonlinear complex systems and has high analysis accuracy has become a problem that needs to be solved urgently.

Summary of the invention

The purpose of the present invention is to provide a multidimensional data modeling and analysis method and system based on subspace sequences, so as to solve the problem that the prior art cannot accurately analyze complex dynamic systems.

In order to achieve the above object, the present invention adopts the following technical solutions:

In a first aspect, a multidimensional data modeling and analysis method based on subspace sequences is provided, comprising:

Acquire a data set of a target to be analyzed, wherein the data set includes data of a plurality of first dimensions of the target to be analyzed, wherein the target to be analyzed includes a target city, and the first dimension is used to characterize a data type;

Selecting a plurality of data of a specified first dimension from the data set, and constructing a subspace corresponding to each data of the specified first dimension based on each data of the specified first dimension;

Constructing a subspace sequence common to all subspaces, wherein the subspace sequence is used to represent the logical order of data;

Based on the subspace sequence, a dual relationship mapping process is performed on the subspace sequence and each subspace to establish a sequence number for each subspace instance in each subspace, wherein the subspace instance in any subspace is used to represent a data in the any subspace;

By using each subspace with established serial numbers, a subspace association network graph containing all subspaces is constructed, wherein the subspace association network graph is represented by G={V,E,g}, V is a node set, E is a node edge set, g is a graph attribute set, each node in the node set is a subspace instance in each subspace, and any node is represented by a serial number corresponding to the subspace instance;

Performing data mining processing on the subspace association network graph to obtain an updated subspace association network graph;

The updated subspace association network diagram is used to obtain the analysis results of the target to be analyzed, wherein the analysis results include the city status prediction results of the target city, and the city status prediction results include traffic flow prediction results, air quality prediction results and/or crowd distribution prediction results.

Based on the above disclosed content, the present invention first obtains a data set (i.e., a multidimensional data space) of a target to be analyzed (such as a target city), and then selects data of a specified first dimension (i.e., selects data of a key type) to construct a corresponding subspace; then, a subspace sequence that can reflect the logical order of the data is introduced to number each subspace instance in each subspace, so as to use the subspace sequence to track the dynamic evolution trajectory of each subspace state; after completing the numbering of the instances in each subspace, each subspace with a sequence number can be used to construct a subspace association network diagram; in this way, it is equivalent to constructing a relationship map of each subspace, and clarifying the dependency and constraint relationship between each subspace node; then, data mining is performed on the subspace association network diagram to further mine the topological relationship between each node in the map, thereby improving the subspace association network diagram; finally, using the improved subspace association network diagram, the state analysis of the target city can be completed, thereby obtaining the prediction results of indicators such as traffic flow, air quality and/or passenger flow distribution of the target city in different states.

Through the above design, the present invention provides a general process modeling method based on subspace sequence, which aims to support the representation modeling and association analysis of complex dynamic processes using multi-source heterogeneous data. The method realizes multi-angle analysis, dynamic evolution prediction and association effect analysis of complex systems through abstract representation and dynamic modeling of subspace sequences. Its innovation lies in the introduction of sequence dimension, the construction of dependency relationship between subspaces based on graph model, and the combination of sequence dependency and topological constraint at the same time; in this way, the accuracy of modeling can be enhanced, thereby improving the accuracy of system analysis; at the same time, the method does not need to rely on large-scale annotated training data and historical parameters, and is therefore very suitable for the analysis of nonlinear complex systems; in addition, the topological relationship between nodes in the graph is further mined through data mining, and the subspace association network diagram is updated accordingly; based on this, an in-depth analysis of the overall structure of the subspace network can be achieved, so that the global association pattern and important nodes can be determined, and the modeling accuracy can be further increased, thereby improving the accuracy of system analysis (i.e., prediction of the target city state); therefore, the present invention is very suitable for large-scale application and promotion in the field of complex system analysis.

In a possible design, the data set further includes data of multiple second dimensions, wherein the second dimension is used to represent a data logical dimension, and the data logical dimension includes a time dimension and/or an event dimension;

Among them, the subspace sequence common to all subspaces is constructed, including:

Selecting all or some of the data of the second dimension from the data set;

Based on the selected data of the second dimension, a subspace sequence common to all subspaces is constructed, wherein the subspace sequence includes a time sequence and/or an event occurrence sequence.

In a possible design, data mining is performed on the subspace association network graph to obtain an updated subspace association network graph, including:

Acquire feature description information of each subspace, wherein the feature description information of each subspace has the same representation form, and the feature description information of any subspace includes one or more of vector representation information, tensor representation information, graph representation information, depth representation information, and semantic representation information;

Based on the characteristic description information of each subspace and using a data mining algorithm, data mining processing is performed on the subspace association network diagram to obtain the updated subspace association network diagram after data mining.

In a possible design, feature description information of each subspace is obtained, including:

The feature description information corresponding to each subspace is extracted by using a feature representation algorithm, wherein the feature representation algorithm includes one or more of a vector representation algorithm, a tensor representation algorithm, a graph representation algorithm, a depth representation algorithm, and a semantic representation algorithm.

In one possible design, the data mining algorithm includes a graph convolutional network algorithm, a network embedding algorithm, a network dynamic modeling algorithm, a multi-granularity semantic learning algorithm, a reinforcement learning algorithm and/or a wavelet network algorithm.

In a possible design, the updated subspace association network diagram is used to obtain the analysis result of the target to be analyzed, including:

Using an incremental learning algorithm or a transfer learning algorithm, a local state prediction process is performed on each subspace in the updated subspace association network diagram to obtain a local state prediction result of each subspace;

The analysis result of the target to be analyzed is obtained by using the local state prediction results of each subspace.

In a possible design, after obtaining the analysis result of the target to be analyzed, the method further includes:

Based on the analysis result of the target to be analyzed, the subspace association network diagram is adjusted to achieve feedback learning of the subspace association network diagram.

In a second aspect, a multidimensional data modeling and analysis system based on subspace sequences is provided, comprising:

An acquisition unit, configured to acquire a data set of a target to be analyzed, wherein the data set includes data of a plurality of first dimensions of the target to be analyzed, wherein the target to be analyzed includes a target city, and the first dimension is used to characterize a data type;

A subspace construction unit, configured to select a plurality of data of a specified first dimension from the data set, and construct a subspace corresponding to each data of the specified first dimension based on each data of the specified first dimension;

A subspace sequence unit, used to construct a subspace sequence common to all subspaces, wherein the subspace sequence is used to represent the logical order of data;

A mapping unit, configured to perform dual relationship mapping processing on the subspace sequence and each subspace based on the subspace sequence, so as to establish a sequence number for each subspace instance in each subspace, wherein the subspace instance in any subspace is used to represent a data in the any subspace;

A subspace association network graph construction unit is used to construct a subspace association network graph containing all subspaces by using each subspace with established serial numbers, wherein the subspace association network graph is represented by G={V,E,g}, V is a node set, E is a node edge set, g is a graph attribute set, each node in the node set is a subspace instance in each subspace, and any node is represented by a serial number corresponding to the subspace instance;

A data mining unit, used for performing data mining processing on the subspace association network graph to obtain an updated subspace association network graph;

An analysis unit is used to use the updated subspace association network diagram to obtain analysis results of the target to be analyzed, wherein the analysis results include the city status prediction results of the target city, and the city status prediction results include traffic flow prediction results, air quality prediction results and/or crowd distribution prediction results.

In the third aspect, a multidimensional data modeling and analysis device based on subspace sequences is provided. Taking the device as an electronic device as an example, the device includes a memory, a processor and a transceiver which are communicatively connected in sequence, wherein the memory is used to store computer programs, the transceiver is used to send and receive messages, and the processor is used to read the computer program to execute the multidimensional data modeling and analysis method based on subspace sequences as described in the first aspect or any possible design of the first aspect.

In a fourth aspect, a storage medium is provided, on which instructions are stored. When the instructions are executed on a computer, the multidimensional data modeling and analysis method based on subspace sequences as described in the first aspect or any possible design of the first aspect is executed.

In a fifth aspect, a computer program product comprising instructions is provided, which, when executed on a computer, enables the computer to execute the multidimensional data modeling and analysis method based on subspace sequences as described in the first aspect or any possible design of the first aspect.

Beneficial effects:

(1) The present invention provides a general process modeling method based on subspace sequences, which aims to support the representation modeling and correlation analysis of complex dynamic processes using multi-source heterogeneous data. The method realizes multi-angle analysis, dynamic evolution prediction and correlation effect analysis of complex systems through abstract representation and dynamic modeling of subspace sequences. Its innovation lies in the introduction of sequence dimensions, the construction of dependencies between subspaces based on graph models, and the combination of sequence dependencies and topological constraints. In this way, the accuracy of modeling can be enhanced, thereby improving the accuracy of system analysis. At the same time, the method does not need to rely on large-scale annotated training data and historical parameters, so it is very suitable for the analysis of nonlinear complex systems. In addition, the topological relationship between nodes in the graph is further mined through data mining, and the subspace correlation network diagram is updated accordingly. Based on this, an in-depth analysis of the overall structure of the subspace network can be achieved, so that the global correlation pattern and important nodes can be determined, which can further increase the modeling accuracy, thereby improving the accuracy of system analysis (i.e., the prediction of the target city state). Therefore, the present invention is very suitable for large-scale application and promotion in the field of complex system analysis.

(2) In the data mining process, the present invention introduces graph neural networks to achieve end-to-end joint representation learning of subspace sequences, so as to unify the feature descriptions of each subspace, and based on this, to mine the subspace association network graph; in this way, the present invention does not require manual feature engineering, and improves the automation and generalization capabilities of modeling.

(3) Feedback learning is introduced in the entire model construction process, that is, the prediction results are fed back to the previous network construction and feature learning to form a closed loop. In this way, the subspace association network diagram can be adjusted during use, thereby continuously improving the model accuracy and further improving the accuracy of complex system analysis.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a schematic diagram of the steps of a multidimensional data modeling and analysis method based on subspace sequences provided by an embodiment of the present invention;

FIG2 is a flowchart of a multidimensional data modeling and analysis method based on subspace sequences provided by an embodiment of the present invention;

FIG3 is an example diagram of an object model provided by an embodiment of the present invention;

FIG4 is a schematic diagram of a field model provided by an embodiment of the present invention;

FIG5 is a schematic diagram of a spatial network model provided by an embodiment of the present invention;

FIG6 is a schematic diagram of a traffic subspace with a sequence number provided by an embodiment of the present invention;

FIG7 is a schematic diagram of a city thermal channel effect subspace with serial numbers provided by an embodiment of the present invention;

FIG8 is a schematic diagram of a commercial district distribution subspace with serial numbers provided by an embodiment of the present invention;

FIG9 is a diagram showing an example of subspace representation provided by an embodiment of the present invention;

FIG10 is an example diagram of an overall graph force-directed layout provided by an embodiment of the present invention;

FIG11 is an example diagram of a step-by-step timing diagram provided by an embodiment of the present invention;

FIG12 is an example diagram of state prediction and impact propagation provided by an embodiment of the present invention;

FIG13 is a schematic diagram of the structure of a multidimensional data modeling and analysis system based on subspace sequences provided in an embodiment of the present invention.

Detailed ways

In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the present invention will be briefly introduced below in combination with the drawings and the description of the embodiments or the prior art. Obviously, the following description of the structure of the drawings is only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work. It should be noted that the description of these embodiments is used to help understand the present invention, but does not constitute a limitation of the present invention.

Example:

As shown in Figure 1, the multidimensional data modeling and analysis method based on subspace sequences provided in this embodiment realizes multi-angle analysis, dynamic evolution prediction and correlation effect analysis of complex systems through abstract representation and dynamic modeling of subspace sequences; among them, for example, this method can be but not limited to running on the analysis end side, optionally, the analysis end can be but not limited to a personal computer (personal computer, PC), a tablet computer or a smart phone. It can be understood that the aforementioned execution subject does not constitute a limitation on the embodiments of the present application. Accordingly, the operation steps of this method can be but not limited to the following steps S1 to S7.

S1. Obtain a data set of a target to be analyzed, wherein the data set includes data of multiple first dimensions of the target to be analyzed, wherein the target to be analyzed includes a target city, and the first dimension is used to characterize the data type; in this embodiment, the target to be analyzed may be but is not limited to the target city, that is, a multi-dimensional collaborative analysis of a smart city is performed on the target city; of course, specific settings may also be made according to other usage scenarios, such as life cycle analysis of industrial products, etc., which are not limited to the aforementioned examples; at the same time, the data set of the target to be analyzed is essentially its corresponding multi-dimensional data space, which contains data of the first dimension and data of the second dimension; specifically, the first dimension The first dimension is used to characterize the data type, such as the traffic data of the target city (including vehicle flow, road conditions and other data), air quality data, population distribution data, etc., while the second dimension is used to characterize the data logic dimension, and the data logic dimension may include but is not limited to the time dimension and/or event dimension (the dimension may be specifically set according to different application scenarios and data types, such as the stage dimension (data changes in a multi-stage process) and the behavior dimension (data changes caused by different behaviors)); in this way, data modeling of the target to be analyzed may be performed based on the data set, so as to facilitate subsequent data analysis; optionally, the modeling process may be but is not limited to the following steps S2 to S5.

S2. Select a number of data of the specified first dimension from the data set, and construct a subspace corresponding to each data of the specified first dimension based on the data of each specified first dimension; in this embodiment, selecting a number of data of the specified first dimension is equivalent to extracting key types of data. For example, taking the target city as an example, traffic data, air quality data, population distribution data, etc. can be extracted. Of course, for different analysis targets, the corresponding data of the specified first dimension are different, which can be determined according to actual use; at the same time, when constructing the subspace, domain knowledge or a priori can be used to determine the constituent dimensions of the subspace, and then based on this, subspaces corresponding to data of different specified first dimensions are constructed.

In this way, through the above design, by constructing an abstract representation of the subspace, multiple key reflection dimensions (such as traffic, air quality, population distribution, etc.) can be extracted from the complex system. At the same time, focusing on modeling each key subspace can shield other complex components of the system, thereby reducing the difficulty of modeling and obtaining a multi-angle analysis view to improve the accuracy of modeling.

In specific implementation, subspace creation is a common technology for multidimensional data modeling, and its principle is not repeated here. After obtaining the subspace corresponding to each specified first dimension of data, this embodiment constructs a subspace sequence for characterizing the logical order of the data to number each data in each subspace in order to describe the topological relationship between subspace instances. The construction structure of the subspace sequence can be but is not limited to that shown in the following step S3.

S3. Construct a subspace sequence common to all subspaces, wherein the subspace sequence is used to characterize the logical order of data; in specific implementation, the example may include but is not limited to selecting all second dimensional data or several second dimensional data from the data set; then, based on the selected second dimensional data, construct a subspace sequence common to all subspaces; in this embodiment, the subspace sequence may include but is not limited to time series and/or event occurrence sequence.

Specifically, the aforementioned step S3 actually uses the data of the selected second dimension to form an ordered sequence. This sequence can represent a time series, an event sequence or other sequence relationships, and can be sorted by timestamps or other indicators; such as sorting in chronological order and/or in the order of event occurrence; for example, taking chronological order as an example, the subspace sequence is a time series, and each element in the sequence is a moment; for example, if sorting is performed in the order of event occurrence, the aforementioned subspace sequence is an event occurrence sequence, and the sequence contains each event; in this way, based on combining the aforementioned subspace sequence with each subspace, sequence dimensions such as time can be added on the basis of subspace modeling, so as to continuously track the dynamic evolution trajectory of each subspace state and reveal the laws of collaborative dynamic evolution between subspaces.

Optionally, the specific process of using the subspace sequence to serially number each subspace may be, but is not limited to, as shown in the following step S4.

S4. Based on the subspace sequence, a dual relationship mapping process is performed on the subspace sequence and each subspace to establish a serial number for each subspace instance in each subspace, wherein the subspace instance in any subspace is used to represent a data in the any subspace; in specific applications, it is equivalent to using the dual space composed of the subspace sequence to serially number the subspace instances in each subspace; in this embodiment, the dual space is a space composed of the sequence dimension generated in step S3, and a dual relationship mapping is established with the selected subspace. Specifically, the dual space provides an external, independent coordinate system to describe the topological relationship between subspace instances; wherein the serial number of the subspace instance is composed of the subspace and the sequence space, such as {Sn, (Dij)}, which is interpreted as the instance in the nth subspace can be uniquely determined by the subspace type Sn, the sequence dimension i and the sequence number j; if the subspace sequence is a time series, {S1, (Di1)}, can represent the data in the first subspace at the first moment; of course, the above example is only for illustration and is not limited to this, and its subspace sequence dimension can be specifically set according to actual use.

After completing the serial numbering of each subspace instance in each subspace based on step S4, the subspaces with established serial numbers can be used to establish a relationship graph of each subspace (i.e., the subspace association network graph below), so as to clarify the dependency and constraint relationship between each subspace node; wherein, the process of constructing the relationship graph can be but is not limited to as shown in the following step S5.

S5. Using the subspaces with established serial numbers, a subspace association network diagram including all subspaces is constructed, wherein the subspace association network diagram is represented as G={V,E,g}, V is a node set, E is a node edge set, g is a graph attribute set, each node in the node set is a subspace instance in each subspace, and any node is represented by the serial number of the corresponding subspace instance; in this embodiment, it is equivalent to using the serial numbers in different subspaces as nodes in the model, and then connecting the nodes with association relationships with edges, so that a subspace association network diagram including all subspaces can be constructed.

Optionally, each node in the node set is recorded as v{S _n ,(D _ij )}, and each edge in the node edge set can be recorded as: e{(S _m ,(D _pq )),(S _n ,(D _ij ))}, wherein the edge represents the connection edge between the node with sequence number (S _m ,(D _pq )) and the node with sequence number (S _n ,(D _ij )); in this way, the association between the nodes in all subspaces can be realized, thereby forming a relationship graph between the nodes; further, the aforementioned graph attribute set represents a set of properties or structures of the graph, which may include but is not limited to the topological structure and weight information of the graph; initially, the set may be empty, but as the deep graph neural network technology learns, this set will gradually become richer; in the continuous learning process, the properties and structure of the graph will be dynamically adjusted and optimized to more accurately reflect the association and topological structure between the subspaces.

After completing the construction of the subspace association network diagram, data mining processing can be performed to mine the topological relationship between nodes and discover global patterns, thereby improving the subspace association network diagram; wherein the data mining process can be but is not limited to as shown in the following step S6.

S6. Perform data mining on the subspace association network diagram to obtain an updated subspace association network diagram; in specific applications, for example, it can be but not limited to first performing subspace feature learning, and then using the learned subspace features to perform data mining; wherein the aforementioned process can be but not limited to as shown in the following steps S61 and S62.

S61. Obtain feature description information of each subspace, wherein the feature description information of each subspace has the same representation form, and the feature description information of any subspace includes one or more of vector representation information, tensor representation information, graph representation information, depth representation information and semantic representation information; in this embodiment, step S61 utilizes various feature expression techniques to learn the feature representation of the subspace to capture the intrinsic properties of the subspace, and the representation integrates the information of all subspaces to support subsequent global pattern discovery and local state prediction.

Optionally, for example, but not limited to, feature representation algorithms can be used to extract feature description information corresponding to each subspace, where the feature representation algorithms include vector representation algorithms (the algorithm learns a low-dimensional vector for each subspace to represent its numerical features), tensor representation algorithms (which use tensors to express the multi-dimensional features of the subspace, perform tensor decomposition and other operations to obtain tensor expressions), graph representation algorithms (essentially using graph structures to represent the intrinsic topological structure of the subspace, thereby obtaining corresponding topological representation information), deep representation algorithms (using autoencoders, manifold learning and other methods to learn the deep nonlinear features of the subspace) and semantic representation algorithms (using NLP technology to learn word vectors or sentence vectors that express subspace attributes) One or more; specifically, the integrated features of subspaces learned by different technologies can also be combined to serve as feature description information of the subspace.

In this embodiment, the vector representation algorithm may adopt: Word2Vec or GloVe (a word vector representation algorithm); the tensor representation algorithm may adopt: TensorRNN or CP decomposition (Canonical Polyadic Decomposition) and other algorithm models; the graph representation algorithm may adopt: Graph Convolutional Networks (GCNs) or Graph Attention Networks (GATs), etc.; the depth representation algorithm may adopt Variational Autoencoders (VAEs) or Generative Adversarial Networks (GANs); the semantic representation algorithm may adopt, but is not limited to: BERT (Bidirectional Encoder Representations from Transformers, language description model) or GPT (Generative Pre-Training Transformer, generative pre-training Transformer model); and the integrated representation algorithm of integrated features may adopt, but is not limited to: multimodal fusion based on graph neural network or adversarial multi-view autoencoder (Adversarial Multi-view Autoencoder); of course, the above examples are only for illustration, and the specific selection of various representation algorithms is not limited to this.

For example, but not limited to, the following steps S61a and S61b may be used to obtain the aforementioned feature description information.

In this embodiment, the feature description information of any subspace may be, but is not limited to, represented as: Among them, F(·) represents the feature learning function in the aforementioned feature representation algorithms, _Sn , ( _Dxi , _Dyj , _Dzk ) represents the nodes in any subspace. Of course, in this formula, the subspace sequence is three-dimensional.

In this way, based on the aforementioned step S61, a more representative feature description of the subspace can be obtained through learning of feature expression, thereby reducing dependence on original data and improving the generalization ability and adaptability of the model.

After obtaining the feature description information of each subspace, the topological relationship and global pattern mining of the subspace association network graph can be performed based on this; wherein, the data mining process can be but is not limited to the step S62 shown below.

S62. Based on the feature description information of each subspace and the subspace association network diagram, the subspace association network diagram is subjected to data mining processing by using a data mining algorithm, so as to obtain the updated subspace association network diagram after data mining. In this embodiment, it is equivalent to using the subspace features learned in the aforementioned step S61 and the subspace association network constructed in the aforementioned step S5, using graph neural network and other technologies to mine the intrinsic topological relationship between nodes and discover the global link pattern of the network, so as to reveal the deeper intrinsic dependency relationship between subspaces, thereby further optimizing and improving the network topological structure. Optionally, the data mining algorithm includes but is not limited to a graph convolutional network algorithm (using convolution operations to directly extract and aggregate features on the graph structure, such as GCN, GAT, etc., which can be used for node classification and node discovery), a network embedding algorithm (learning the vectorized representation of the subspace through network random walks and language model embedding and other technologies, such as Node2Vec, DeepWalk (which is a random walk (random walk) and word2vec), network dynamic modeling algorithms (i.e., using continuous-time dynamic network models to learn the dynamic evolution of network topology, such as EvolveGCN (parameter evolution graph convolutional network of dynamic graphs)), multi-granularity semantic learning algorithms (using semantic embedding and knowledge graph technology to learn the semantic representation of subspaces and build conceptual associations at a higher level of abstraction, rather than just statistical associations), reinforcement learning algorithms (which are used to construct Markov decision processes for subspace associations and use reinforcement learning to discover more complex nonlinear dependencies) and/or wavelet network algorithms (such as GWNN, which can represent the global topology of the network).

In this embodiment, the main connections and differences between the updated subspace association network diagram obtained in this step and the initial subspace association network diagram in the aforementioned step S5 are as follows:

(1) The initial subspace network constructed in step S5 is connected based on the basic associations between subspaces; this step constructs a global network graph with deeper topological relationships. Based on step S5, it uses deep graph neural network technology to learn the intrinsic associations and topological structures between subspaces.

(2) The model in step S5 is more basic, while the model in this step can reflect deeper internal dependencies.

(3) Step S5 provides the original structure, and this step abstracts and infers on this basis to obtain a higher-level network topology representation.

(4) The model diagram in this step optimizes and strengthens the initial network, and there is a progressive relationship between the two.

Optionally, the topological relationship between the mined nodes may include: the closeness of the connection (whether it is direct or multi-step association); the directionality of the connection (one-way or two-way influence); the weight of the connection (the strength of the influence); the type of connection (different types of connections such as physical, information, semantic, etc.). In this way, the integration of these topological information can provide a deeper understanding of the intrinsic connections between subspaces.

Therefore, through the aforementioned steps S61 and S62, the topological relationship between nodes can be mined and global patterns can be discovered; this step focuses more on the in-depth analysis of the overall structure of the subspace network, emphasizing the discovery of global association patterns and important nodes; in this way, after obtaining the updated subspace association network diagram, the analysis of the target to be analyzed can be carried out, and the analysis process can be but is not limited to as shown in the following step S7.

S7. Utilize the updated subspace association network diagram to obtain the analysis result of the target to be analyzed, wherein the analysis result includes the city state prediction result of the target city, and the city state prediction result includes the traffic flow prediction result, the air quality prediction result and/or the crowd distribution prediction result; in this embodiment, for example, it can be but not limited to utilizing an incremental learning algorithm or a transfer learning algorithm to perform local state prediction processing on each subspace in the updated subspace association network diagram to obtain the local state prediction result of each subspace; then, the local state prediction result of each subspace can be utilized to obtain the analysis result of the target to be analyzed; for example, based on the subspace corresponding to the aforementioned traffic data, a local state prediction is performed to obtain the traffic flow data at different times in the future; based on the subspace corresponding to the air quality, a local state prediction is performed to obtain the air quality at different times in the future, and so on.

In specific implementation, the incremental learning method enables the model to continuously learn and absorb newly emerging subspace state data, thereby gradually refining the understanding of the state evolution laws; secondly, by identifying the relationship between new subspaces and existing subspaces, cross-subspace knowledge transfer is carried out to accelerate the learning process of new subspace state laws; finally, reinforcement learning technology enables the entire prediction system to be optimized and adjusted online. With the continuous acquisition of new knowledge, the prediction ability of the model can be continuously improved.

Optionally, the state prediction can be achieved by using, but not limited to, the following methods: (1) constructing a meta-learner based on a memory-enhanced network structure, continuously absorbing new state samples of the subspace, saving them to the associated knowledge base, and selecting related memories through an internal attention mechanism, incrementally adjusting model parameters, and achieving adaptive learning; (2) pre-training the state prediction model of the source task, and using parameter migration and fine-tuning for the new subspace to quickly obtain the target prediction capability, and being able to identify the semantic and topological similarities of the subspace, thereby achieving better transfer learning effects; (3) using algorithms such as DDPG and A3C to build an enhanced learning agent, modeling and predicting the environment state, and continuously improving the strategy through a reward mechanism, and generating new samples through self-simulation in the agent process to assist model training; (4) considering the local temporal structure, analyzing the subspace state time evolution sequence, and establishing a dynamic time association model such as LSTM for local modeling of the temporal connection between states; (5) incrementally adjusting the time association model parameters after the arrival of new state data to ensure continuous capture of the state evolution law.

In this way, the essence of realizing local state prediction is: using the knowledge of subspace association network and global pattern mining constructed in the previous steps, and using appropriate models or algorithms to predict the local state of each subspace. This prediction process can be based on historical data, global state evolution trends and other relevant information; of course, the method used for local prediction is a common method, and its principle will not be repeated.

In addition, in order to further improve the model accuracy and thus increase the accuracy of the analysis, the present embodiment is further provided with a feedback learning step, that is, after obtaining the analysis result of the target to be analyzed, the subspace association network diagram is adjusted based on the analysis result of the target to be analyzed to realize feedback learning of the subspace association network diagram; thus, referring to FIG2 , the entire closed-loop process is as follows: first, the association network of the subspace is constructed to express the topological relationship between the subspaces; then, feature learning is used to obtain a characteristic expression of the state of each subspace, and on this basis, the association pattern between the subspaces and the global evolution law are further explored; then, the prediction and analysis of the local subspace state are guided; finally, the prediction result is fed back to the previous network construction and feature learning to form a closed loop, thereby, the adjustment of the subspace association network diagram can be realized during use, thereby continuously improving the model accuracy to further improve the accuracy of the analysis of complex systems.

In summary, the present invention has the following beneficial effects:

(1) Abstract representation of complex systems from multiple perspectives in subspaces. By constructing an abstract representation of subspaces, multiple key reflection dimensions can be extracted from complex systems. At the same time, focusing on modeling each key subspace can shield other complex components of the system, thereby reducing the difficulty of modeling and obtaining a multi-angle analysis view.

(2) The sequence dimension is introduced for dynamic subspace modeling. By adding sequence dimensions such as time to subspace modeling, the dynamic evolution trajectory of each subspace state can be continuously tracked, revealing the laws of coordinated dynamic evolution between subspaces and supporting process optimization.

(3) Define the dependency relationship between subspaces based on the graphical model; by constructing a relationship graph based on subspaces, the dependency and constraint relationship between subspace nodes is clearly expressed, and on this basis, joint modeling and reasoning are carried out to analyze the interaction mechanism of different components in the system.

(4) Based on the constructed subspace dependency graph, the propagation analysis of causal effects can be carried out to evaluate the chain reaction that a change in a subspace state will cause within the system, thereby achieving the prediction of state evolution and risk assessment.

(5) The sequential dependency constraints in sequence modeling and the topological dependency constraints in the graph model are integrated to form a subspace modeling framework with both sequential dependency and spatial constraints. This can enhance the accuracy of state evolution prediction.

(6) The present invention supports cluster combination by introducing more regional subspaces, so that cross-regional large-scale joint modeling can be established, which can be applied to large system analysis and decision optimization that require local fine-grained control.

(7) The joint representation of subspaces is realized based on graph neural networks. The present invention uses graph neural networks to realize the joint representation learning of subspace sequences, so that the model can autonomously extract the complex feature representation of state evolution without the need for manual feature engineering, thereby expanding the automation and generalization capabilities of modeling.

(8) It supports the expansion from microscopic single subspace modeling to macroscopic unified modeling of the entire subspace set, and can realize system dynamic modeling and scenario prediction from local to global. In this way, it can provide theoretical support for the strategic planning and decision optimization of complex systems.

In a possible design, the second aspect of this embodiment provides an application example, that is, using the method provided in the first aspect of the embodiment to perform multi-dimensional collaborative evolution of a smart city, and the process is as follows.

Step 1: Subspace construction; from the multi-dimensional heterogeneous data of the city, six key subspaces are selected, including transportation network, urban heat island, commercial area distribution, air quality, population distribution, and energy utilization, to focus on the analytical perspective of coordinated and sustainable development of the city; the above six key subspaces are: transportation network (spatial network model), modeling the urban transportation network, including vehicle flow, road conditions, public transportation system, etc.; urban heat island effect simulation (field model), using the field model to model the urban heat island effect, considering factors such as meteorological data and urban building density; commercial area distribution (object model), using the object model to represent the location, scale, type and other information of the commercial area; air quality (field model), using the field model to model the air quality of different areas of the city, including particulate matter concentration, nitrogen oxides, etc.; population distribution (object model), using the object model to represent the population distribution of different areas of the city, including population density, residential area, etc.; energy utilization (field model), establishing an energy utilization model, considering the city’s energy consumption, renewable energy utilization, etc.

In this embodiment, although it is considered as 6 sub-spaces, the form is spatial data, which can basically be expressed by three spatial models to establish object models, field models and spatial network models; the detailed description is as follows:

Object Model: It is used to represent specific objects in space, including points, lines, and surfaces. This model uses geometric expression to present entities in space by describing the geometric shape, position, and other related attributes of the object. For example, in smart city modeling, the object model can be used to represent buildings, roads, or other geographic features. See Figure 3, which shows a schematic diagram of the object model, where the left picture in Figure 3 is an abstract expression of the right picture.

Field Model: It is used to represent continuous variables or attributes related to location, which are continuously distributed in space. The field model uses functional expression to describe the attribute values at each point in space, such as temperature, humidity, or other environmental factors. In the example of smart cities, the field model can be used to simulate the urban heat island effect, taking into account factors such as meteorological data and building density. An example diagram can be seen in Figure 4.

Spatial Network Model: The spatial network model is used to represent the connection relationship and attributes between entities in geographic space. This model uses a network diagram to depict the association and interaction between entities. In the multidimensional data of smart cities, the spatial network model can be used to model traffic networks, including vehicle flow, road conditions, etc. Nodes represent entities, and edges represent the connection relationship between them. They can also carry certain attribute information. The schematic diagram can be seen in Figure 5.

After the subspace is created, the subspace sequence can be constructed, as shown in the following step 2.

Step 2: Subspace sequence generation: Use time series as the sequence dimension to establish a time series model for the above six subspaces to form a sequence expression of the subspace; select a time series model that matches the characteristics of the subspace, such as the field model-time change, which represents the evolution of the continuous field over time, which means that the incremental changes of the spatial state over time can be captured through the field model; for example, the object model-event/process is used to represent the stability of the entity's temporal attributes, which observes the events and processes of the entity in the time series; for example, the spatial network model-time snapshot is selected to express the spatiotemporal network such as the time expansion graph and the time aggregation graph, which captures the spatiotemporal changes of the network connection relationship.

Here, we take six subspaces as examples to illustrate how to match them with different time series models to better capture the spatiotemporal dynamic changes of multidimensional data: (1) Traffic network (spatial network model): Use the time snapshot model to model the urban traffic network, which can sample the state of the traffic network at different time points, including changes in vehicle flow, road conditions, public transportation systems, etc.; (2) Use the time variation model to model the urban heat island effect. The field model considers factors such as meteorological data and urban building density, while the time variation model captures the evolution of the urban heat island effect over time; (3) Use the event/process model and use the object model to represent the location, scale, type and other information of the commercial district. In this way, we can observe the events and processes of the commercial district in the time series, such as the expansion or change of the commercial district; (4) Use the time snapshot model to model the air quality in different areas of the city. The field model can consider the distribution of particulate matter concentration, nitrogen oxides, etc., while the time snapshot model captures the changes in air quality at different time points; (5) Use the time variation model and the event/process model to represent the population distribution in different areas of the city through the object model. This helps to observe the stability of population changes and related events, such as population density and the evolution of residential areas; (6) Using field models and time-varying models, an energy utilization model is established. Considering the city's energy consumption, renewable energy utilization, etc., to capture the evolution of energy utilization over time.

After the subspace sequence is constructed, the subspace sequence can be numbered based on it, as shown in the following step three.

Step 3: Dual space and sequence numbering; During the sequence generation process, a one-dimensional time series space is simultaneously constructed as the dual structure of the above subspace sequence. On this dual sequence space, a subspace state numbering method is defined: {ID, time}, and a unique identifier is given to the subspace state at each moment to establish a mapping relationship between the subspace and a specific moment. For example, {S1, T1} represents the traffic network subspace with ID S1 at moment T1; this numbering system provides a basis for the subsequent analysis of the synergistic association between subspaces on the time axis; optionally, the schematic diagrams of the three key subspaces of traffic, heat island, and commercial distribution after serial numbering can be seen in Figures 6-8 respectively. Since the remaining three key subspace types are the same as those mentioned above, they will not be elaborated here.

After completing the serial numbering of the subspace instances in each subspace, the subspace association network diagram can be constructed, as shown in the following step 4.

Step 4: Subspace association network construction: According to the time sequence number of the subspace, it is used as a network node, and the connection relationship between the nodes represents the association and mutual restriction between different subspaces. Construct a mesh topological structure that reflects the complex association of the urban system.

Step 5: Subspace feature learning; that is, in order to process different types of subspaces, such as spatial networks, fields and object models, this embodiment can use a unified representation method, such as using a graph neural network (GNN). GNN is a type of deep learning model specifically used to process graph structured data, which can effectively capture spatial relationships, dynamic evolution and multi-dimensional features.

For each subspace, we can represent it as a graph; in the spatial network model, each traffic node can be represented as a node, which contains the node's geometric information (coordinates) and other attributes related to the node, such as traffic flow, etc.; road connections can be represented by edges in the graph, each edge connects two nodes, representing the road between two intersections or traffic nodes; in the field model, each raster can be represented as a node, containing the raster's location information and field values (for example, temperature, air quality, etc.), and the edges can represent the spatial relationship between rasters, such as the connection between adjacent rasters; in this way, such edges can reflect the changes in the field in space; similarly, in the object model, each spatial object (such as a commercial area, an area with high population density, etc.) can be represented as a node, containing the object's geometric information, and the edges can represent the spatial relationship between objects, such as the connection between adjacent areas; in this way, this unified representation method can facilitate network modeling, and its corresponding subspace representation example diagram can be, but is not limited to, as shown in Figure 9.

After feature learning is completed, data mining can be performed, as shown in step six below.

Step 6: Topological relations and global pattern mining: For the construction of the entire network, all subspaces have been represented as graphs in the fifth step. In this step, a large graph (i.e., global graph representation) can be constructed, in which 18 subspaces are nodes and edges represent certain relationships. There are two ways to construct this large graph:

The overall picture spans time and subspace:

Fully connected graph: The simplest way is to construct a fully connected graph, where each subspace is connected to all other subspaces by edges. Such a graph indicates that all subspaces are connected, but it may be too dense.

Connection based on association strength/subspace similarity: Use graph neural networks, such as GraphSAGE, GCN, GAT, etc., to learn representations of subspaces. In this process, the model learns the associations and similarities between subspaces. Calculate weights for each edge in the graph. These weights can take into account association strength and similarity; a threshold can be set based on association strength/similarity, and associations/similarity above the threshold will be retained, and associations/similarity below the threshold will be discarded; thus, through the above design, a sparser network can be constructed, which emphasizes key associations/similarity.

Force-directed layout: Force-directed layout is applied in the node-link graph to show the topological structure more clearly. Force-directed layout considers the attraction and repulsion between nodes, so that highly interconnected nodes are close to each other and unrelated nodes are separated; an example diagram of the overall graph force-directed layout can be seen in Figure 10.

Step-by-step timing diagram:

Time series modeling: The set of 6 subspaces at each moment constitutes a slice (which can be a vector or graph representation data), which is input into a sequence model, such as a recurrent neural network (RNN) or a long short-term memory network (LSTM), to learn the temporal evolution of the global state.

Evolution of global state: The global state representation learned by the sequence model can be used to understand the changes and evolution of the overall system in time sequence. An example of a step-by-step timing diagram can be seen in Figure 11.

In this embodiment, the two can be combined, that is, first construct a distribution time series diagram to understand the basic rules; then construct a global dynamic diagram to discover deep topological knowledge; in this way, the mined topological relationships and global patterns can provide contextual information for local state prediction, and by understanding the global evolution laws of the entire system, the state of a specific subspace at a future moment can be more accurately predicted; at the same time, the mined topological relationships may imply some key nodes or subspaces, which may play an important role in the evolution.

After completing the mining of the subspace association network graph, system analysis can be performed, as shown in step seven below.

Step 7: Local state prediction and evolution analysis aims to deeply understand the evolution laws of each subspace in the system at different times through the prediction and evolution analysis of local states, and evaluate the robustness of the system in terms of local dynamic changes. The specific description is as follows:

Local state prediction: Using the knowledge of subspace association network and global pattern mining constructed in the previous steps, a suitable model or algorithm is used to predict the local state of each subspace; this prediction process can be based on historical data, global state evolution trends, and other relevant information.

Under the constraints of network topology: In the prediction process, the influence of the topological structure of the subspace associated network on the system dynamics is taken into account. That is, under the constraints of the network topology, the local state changes of each subspace are predicted.

Evolutionary relationship analysis under different circumstances: Analyze how the local state of each subspace evolves under different circumstances. This can include local dynamic responses under system disturbances or changes. Through this analysis, key subspaces in the system can be identified, as well as their changing patterns under different circumstances.

Propagation of the impact of network disturbances on the system: Evaluate the propagation of the impact of network disturbances on the local state of the system. Through the prediction and evolution analysis of local states, it can reveal how network disturbances propagate in the system and affect the evolution of related subspaces.

Iterative prediction and dynamic update of propagation paths: In the entire closed-loop analysis framework (see step 8), the states of the six subspaces can influence each other through iterative prediction; each time a prediction is made, the state of the subspace is updated, and the updated state information is propagated to the associated subspace. The propagation path is dynamically updated so that the weight and association strength of the path can be adjusted with time and changes in prediction, better reflecting the dynamic relationship between subspaces; an example diagram of state prediction and influence propagation can be shown in Figure 12.

In actual scenarios, when making local state predictions, not only the topological constraints of the subspace association network are considered, but also more complex factors such as traffic flow, commercial activities, and climate environment are combined to analyze their co-evolution with the traffic network subspace. This makes traffic flow predictions more accurate.

In the evolutionary analysis under different scenarios, we considered in detail how traffic pressure during peak hours affects the city's air quality and energy utilization, and how it causes a more serious urban heat island effect; this complex correlation modeling can help us evaluate the layered impact of traffic network anomalies on the entire urban system.

When evaluating the propagation of network disturbances, such as traffic disruptions caused by road repairs or traffic accidents, we not only analyze their impact on the transportation network itself, but also explicitly explore how such disturbances propagate through multiple related subspaces of traffic-air quality-commercial activities, causing impacts on the larger urban system.

In iterative prediction and updating, we also consider more socio-economic factors such as urban planning and population distribution, and the deep dynamic connections with other subspaces. This helps us to make more intelligent urban regulation suggestions as a whole and achieve coordinated optimization of subspaces.

Step 8: Feedback Learning Feedback learning is a key step in the whole process, which continuously optimizes the model and prediction by understanding the dynamic evolution of the system in real time. The following is an example of feedback learning:

In the previous step, the future state of the traffic network subspace was predicted based on the association network between the subspaces; assuming that the prediction results have a certain deviation from the actual traffic conditions, the following measures can be taken in feedback learning:

Analyze the source of deviation in traffic network prediction and whether other subspaces have an important impact on it; for example, the urban heat island effect causes abnormal deterioration of traffic conditions; then adjust the association network structure between subspaces based on the analysis; increase the degree of association between the heat island effect and the traffic network; re-learn subspace features on the adjusted network and use heat island data to enhance the state expression of the traffic network; then, based on the updated subspace expression, re-predict the future state of the traffic network; finally, verify the improved prediction results and repeat this feedback optimization process to gradually improve the representation ability of the association network and the state prediction accuracy of each dimensional subspace.

In a possible design, the third aspect of this embodiment provides another application example, which constructs a multidimensional dynamic life cycle assessment correlation analysis model (Multidimensional Dynamic LCA Correlation Analysis Model, MDLCCAM), which realizes dynamic, nonlinear and correlation modeling of the overall life cycle performance of products and processes.

The technical core of MDLCCAM is high-dimensional subspace abstract representation and association network modeling. First, a high-dimensional state space is constructed by defining subspaces that reflect the diversity of the system. Then, the subspaces form a complex network topology based on rich associations. The subspace sequence has built-in time and event identifiers, which can dynamically track the state evolution process.

Based on the subspace network, machine learning technology can be used to model the nonlinear characteristic relationships contained therein, and potential influencing mechanisms can be discovered through association rule mining; based on this high-dimensional dynamic network, MDLCCAM can support online decision-making in environmental management and realize functions such as anomaly detection, path construction, system prediction, and process optimization. Through dynamic, nonlinear, and correlation modeling, it expands and enhances traditional LCA analysis and provides strong technical support for sustainable development.

In this embodiment, the construction steps are consistent with the second aspect of the aforementioned embodiment; among them, in terms of the selection of key dimensions, environmental impact indicators (reflecting the potential impact on the environment); resource utilization indicators (reflecting resource usage); emission indicators (assessing the degree of pollution); economic indicators (reflecting economic impact); social impact indicators (reflecting social effects); each specific dimension of the subspace corresponds to an LCA calculation indicator; that is, the subspace is a comprehensive space that includes all LCA core indicators.

In the subspace sequence construction step: this model constructs a two-dimensional dynamic sequence structure by introducing two dimensions, time series and event series, to reflect the evolution network of subspace states; the time series describes the changes of subspace states over time with a unified benchmark; the event sequence represents the evolution path of the subspace driven by different conditions; in this way, each point of the two-dimensional sequence corresponds to a state of the subspace under the event at that moment, and finally a two-dimensional dynamic sequence network can be formed. By analyzing this network, the dynamic laws of subspace state changes under multiple conditions can be interpreted, that is, the evolution mechanism of the environmental impact assessment results of products or processes under different circumstances.

In the two-dimensional dynamic sequence network constructed by this model, the subspace state corresponding to each node needs to be uniquely identified and numbered. For this purpose, the concept of dual space of subspace sequence is introduced; the general expression of sequence number is: {ID, (time, event)}, for example: {S1, (T0, E1)} represents the corresponding network node of subspace S1 under time T0 and event condition E1; this number forms a one-to-one mapping relationship with the sequence network node; the sequence numbering enables the node to be quickly searched and indexed by number after the network is built, and the subspace and its state value information carried can be read. This provides important support for network analysis and state evolution law mining.

In the process of constructing the subspace association network graph, this embodiment integrates the subspace evolution paths of multiple event-driven scenarios into one graph, thereby realizing a comprehensive analysis of the evolution of subspace indicators over time and events; each node has the following numbering format: {Sn, (Tx, Ey)}, where Sn represents the subspace, Tx represents the time point, and Ey represents the event-driven condition; wherein, the subspace evolution paths under different scenarios are horizontally integrated (e.g., the X-axis represents time, and the subspace evolution paths under the same scenario can be integrated along the time axis to reveal the evolution law of the subspace under the same scenario over time; this helps to identify the differences in subspace performance under the same conditions. Dynamic trend, because the indicators reflected by the dimensions in the subspace have time evolution requirements, that is, it is necessary to observe the dynamic changes of the indicator values of a certain process in the time flow); and longitudinally compare the evolution differences of the subspace at the same time point under different scenarios (such as the Y-axis represents different scenarios/event driving conditions, and the subspace evolution paths at the same time point are compared longitudinally. This helps to identify the performance differences between subspaces under different scenarios at a specific time point); thus, the two-dimensional network constructed in this way comprehensively simulates this dual evolution mechanism, which includes both the state changes of the subspace itself over time and the relative differences in various events on the time section.

For subspace feature learning: Since the subspace constructed in step 1 is a single entity that integrates the overall life cycle performance of a product or process, it covers LCA indicators in multiple dimensions such as environment, resources, and emissions; in the dynamic subspace network constructed in step 4, each node carries the mapping of these multidimensional LCA indicators, thus forming the characteristics of the subspace under a certain state; thus, when the subspace data is sufficient, deep learning and other methods are preferred to automatically learn the expression of the intrinsic characteristics of the subspace, so as to model its complex multidimensional indicator structure and nonlinear relationship. When faced with insufficient data constraints, alternative methods such as statistical learning can be used for feature engineering as a supplement to the graph neural network method, making the model's learning of subspace representation more reliable and stable.

After completing the subspace feature learning, step six (i.e., topological relationship and global pattern mining) can be carried out; among them, on the basis of the constructed two-dimensional dynamic subspace network, the intrinsic topological relationship between nodes can be mined through association analysis, relationship reasoning and other technologies, and the weight index of the edge can be introduced in the mining process to quantify the strength of the association between nodes; specifically, the association analysis can assign weights to the edges according to the similarity between the subspaces or the degree of association of each evaluation indicator, reflecting the coupling strength between nodes; subspaces with more similarity or stronger correlation will obtain higher weights. If the network expresses the co-evolution of indicators, the edge weight represents the evolution consistency, and the subspace spans multiple dimensions, the weight contribution of each dimension can be integrated; and for time series networks, the weight can also be determined according to the consistency of the subspace change trend on the time axis. When the association is difficult to quantify, expert evaluation can also be introduced to assign edge weights.

Assume that the subspace state node {Sn, (Tx, Ey)} in the network is simplified to Si, and the edge is e(Si, Sj). Then the edge weight can be expressed as: similarity weight: w_sim(e(Si, Sj)) = sim(Si, Sj); association weight: w_corr(e(Si, Sj)) = corr(Si, Sj); co-evolution weight: w_coe(e(Si, Sj)) = corr(delta(Si), delta(Sj))(delta is the time difference); dimension comprehensive weight: w(e(Si, Sj)) = αw1+βw2+...(α, β are dimension weight coefficients); expert evaluation weight: w_exp(e(Si, Sj)) = E(re l(Si, Sj))(E is the expert evaluation function, re l is the qualitative association type, and the possible values include: strong positive correlation, positive correlation, independence, negative correlation, and strong negative correlation).

Through the weighted association network, a network topology that reflects the real binding relationship of nodes can be constructed; the association strength between nodes, network density, and internal and external structures of the network may change, so that the initial grid-like topology gradually evolves into a network with complex irregular connections; the introduction of weights enhances the quantitative characterization of the intrinsic association of indicators. On such a weighted network, pattern recognition and cluster analysis techniques can be used based on edge weights to discover the global pattern structure in the network; therefore, the identified network pattern can accurately reflect the coupling mechanism between the evaluation indicators of the product process and its coordinated evolution characteristics; compared with the traditional binary network, the weighted network makes the pattern and mechanism abstraction more refined and explanatory, and it provides a three-dimensional perspective to deeply understand and optimize the life cycle performance of the product process. The generation of complex networks lays an information foundation for state prediction and process optimization decisions. This lays an information foundation for the state prediction and process optimization decisions of the subsequent network.

After completing data mining, local state prediction and evolution analysis can be performed, that is, the global pattern reflects the main characteristic types and dynamic evolution mechanisms of the multi-index co-evolution of the entire product or process; this provides a more global background for the definition and analysis of local states, and helps to make more targeted local state predictions; among them, the change in network topology introduces new paths or relationships, which may reveal the connection between subspaces that were not originally considered. These new paths may have an impact on the prediction of local states, because new associations may lead to the formation of new local states or affect the evolution of existing states; specifically, it can be divided into node distance adjustment and the emergence of new paths.

In the actual scenario, taking the life cycle of the steel industry as an example, there are two related event sequences: "market steel production adjustment" and "inter-enterprise carbon emissions trading"; in the "market steel production adjustment" event sequence, it is predicted that a new future state X will appear in the overall "greenhouse gas emissions" assessment node of the steel industry; to explain the formation mechanism of state X, we constructed a new path to associate it with a related historical state node Y under the second event sequence "inter-enterprise carbon emissions trading"; this reflects that the exogenous carbon trading policy will affect the industry's future total greenhouse gas emissions through the endogenous emission quota adjustment mechanism between steel companies. This new path identification across event sequences allows the model to more accurately predict the impact of carbon trading policies on the emission trend of the steel industry.

After completing the local state prediction and evolution analysis, feedback learning can be performed. The principle is the same as the above example and will not be repeated here.

As shown in FIG. 13 , the fourth aspect of this embodiment provides a hardware system for implementing the multidimensional data modeling and analysis method based on subspace sequence described in the first aspect of the embodiment, including:

An acquisition unit, configured to acquire a data set of a target to be analyzed, wherein the data set includes data of a plurality of first dimensions of the target to be analyzed, wherein the target to be analyzed includes a target city, and the first dimension is used to characterize a data type;

A subspace construction unit, configured to select a plurality of data of a specified first dimension from the data set, and construct a subspace corresponding to each data of the specified first dimension based on each data of the specified first dimension;

A subspace sequence unit, used to construct a subspace sequence common to all subspaces, wherein the subspace sequence is used to represent the logical order of data;

A mapping unit, configured to perform dual relationship mapping processing on the subspace sequence and each subspace based on the subspace sequence, so as to establish a sequence number for each subspace instance in each subspace, wherein the subspace instance in any subspace is used to represent a data in the any subspace;

A subspace association network graph construction unit is used to construct a subspace association network graph containing all subspaces by using each subspace with established serial numbers, wherein the subspace association network graph is represented by G={V,E,g}, V is a node set, E is a node edge set, g is a graph attribute set, each node in the node set is a subspace instance in each subspace, and any node is represented by a serial number corresponding to the subspace instance;

A data mining unit, used for performing data mining processing on the subspace association network graph to obtain an updated subspace association network graph;

An analysis unit is used to use the updated subspace association network diagram to obtain analysis results of the target to be analyzed, wherein the analysis results include the city status prediction results of the target city, and the city status prediction results include traffic flow prediction results, air quality prediction results and/or crowd distribution prediction results.

The working process, working details and technical effects of the device provided in this embodiment can be found in the first aspect of the embodiment and will not be described in detail here.

The fifth aspect of this embodiment provides a multidimensional data modeling and analysis device based on subspace sequences. Taking the device as an electronic device as an example, it includes: a memory, a processor and a transceiver that are communicatively connected in sequence, wherein the memory is used to store computer programs, the transceiver is used to send and receive messages, and the processor is used to read the computer program to execute the multidimensional data modeling and analysis method based on subspace sequences as described in the first aspect of the embodiment.

The working process, working details and technical effects of the electronic device provided in this embodiment can be found in the first aspect of the embodiment and will not be described in detail here.

The sixth aspect of this embodiment provides a storage medium that stores instructions for the multidimensional data modeling and analysis method based on subspace sequences as described in the first aspect of the embodiment, that is, the storage medium stores instructions, and when the instructions are run on a computer, the multidimensional data modeling and analysis method based on subspace sequences as described in the first aspect of the embodiment is executed.

The working process, working details and technical effects of the storage medium provided in this embodiment can be found in the first aspect of the embodiment and will not be described in detail here.

A seventh aspect of the present embodiment provides a computer program product comprising instructions, which, when executed on a computer, enables the computer to execute the multidimensional data modeling and analysis method based on subspace sequences as described in the first aspect of the embodiment.

Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims (10)

1. A multi-dimensional data modeling and analysis method based on subspace sequences, comprising:

acquiring a data set of an object to be analyzed, wherein the data set comprises a plurality of first dimension data of the object to be analyzed, the object to be analyzed comprises a target city, and the first dimension is used for representing a data type;

Selecting a plurality of pieces of data with specified first dimensions from the data set, and constructing subspaces corresponding to the pieces of data with the specified first dimensions based on the pieces of data with the specified first dimensions;

Constructing a subspace sequence common to all subspaces, wherein the subspace sequence is used for representing the logic sequence of data;

performing dual relation mapping processing on the subspace sequence and each subspace based on the subspace sequence to establish a sequence number for each subspace instance in each subspace, wherein the subspace instance in any subspace is used for representing one piece of data in the any subspace;

Constructing a subspace association network diagram containing all subspaces by using each subspace with established sequence numbers, wherein the subspace association network diagram is expressed as G= { V, E, G }, V is a node set, E is a node edge set, G is a diagram attribute set, each node in the node set is a subspace instance in each subspace, and any node is expressed by using the sequence number of the corresponding subspace instance;

performing data mining processing on the subspace association network map to obtain an updated subspace association network map;

And obtaining an analysis result of the target to be analyzed by using the updated subspace association network diagram, wherein the analysis result comprises a city state prediction result of the target city, and the city state prediction result comprises a traffic flow prediction result, an air quality prediction result and/or a people flow distribution prediction result.

2. The method of claim 1, wherein the data set further comprises data having a plurality of second dimensions, wherein the second dimensions are used to characterize data logical dimensions, and wherein the data logical dimensions comprise a time dimension and/or an event dimension;

wherein, constructing a subspace sequence common to all subspaces comprises:

selecting all the data of the second dimension or a plurality of data of the second dimension from the data set;

And constructing a subspace sequence common to all subspaces based on the selected data of the second dimension, wherein the subspace sequence comprises a time sequence and/or an event occurrence sequence.

3. The method of claim 1, wherein performing data mining on the subspace association network map to obtain an updated subspace association network map, comprises:

The method comprises the steps of obtaining feature description information of each subspace, wherein the feature description information of each subspace has the same representation form, and the feature description information of any subspace comprises one or more of vector representation information, tensor representation information, graph representation information, depth representation information and semantic representation information;

and carrying out data mining processing on the subspace association network map by utilizing a data mining algorithm based on the characteristic description information of each subspace so as to obtain the updated subspace association network map after data mining.

4. A method according to claim 3, wherein obtaining the feature description information for each subspace comprises:

and extracting feature description information corresponding to each subspace by utilizing a feature representation algorithm, wherein the feature representation algorithm comprises one or more of a vector representation algorithm, a tensor representation algorithm, a graph representation algorithm, a depth representation algorithm and a semantic representation algorithm.

5. The method of claim 4, wherein the data mining algorithm comprises a graph rolling network algorithm, a network embedding algorithm, a network dynamic modeling algorithm, a multi-granularity semantic learning algorithm, a reinforcement learning algorithm, and/or a wavelet network algorithm.

6. The method of claim 1, wherein using the updated subspace association network map to derive the analysis result of the target to be analyzed comprises:

Performing local state prediction processing on each subspace in the updated subspace association network map by using an incremental learning algorithm or a transfer learning algorithm to obtain a local state prediction result of each subspace;

And obtaining an analysis result of the target to be analyzed by using the local state prediction result of each subspace.

7. The method according to claim 1, wherein after deriving the analysis result of the object to be analyzed, the method further comprises:

And adjusting the subspace correlation network diagram based on the analysis result of the target to be analyzed so as to realize feedback learning of the subspace correlation network diagram.

8. A subspace sequence-based multidimensional data modeling and analysis system, comprising:

the system comprises an acquisition unit, a data analysis unit and a data analysis unit, wherein the acquisition unit is used for acquiring a data set of an object to be analyzed, the data set comprises a plurality of first dimension data of the object to be analyzed, the object to be analyzed comprises an object city, and the first dimension data is used for representing data types;

The subspace construction unit is used for selecting a plurality of pieces of data with specified first dimensions from the data set, and constructing subspaces corresponding to the pieces of data with the specified first dimensions based on the pieces of data with the specified first dimensions;

A subspace sequence unit, configured to construct a subspace sequence common to all subspaces, where the subspace sequence is used to characterize a logical sequence of data;

A mapping unit, configured to perform dual mapping processing on the subspace sequence and each subspace based on the subspace sequence, so as to establish a sequence number for each subspace instance in each subspace, where a subspace instance in any subspace is used to characterize one data in the any subspace;

A subspace association network diagram construction unit, configured to construct a subspace association network diagram including all subspaces by using each subspace with established sequence numbers, where the subspace association network diagram is expressed as g= { V, E, G }, V is a node set, E is a node edge set, G is a diagram attribute set, each node in the node set is a subspace instance in each subspace, and any node uses the sequence number representation of the corresponding subspace instance;

The data mining unit is used for performing data mining processing on the subspace association network map to obtain an updated subspace association network map;

And the analysis unit is used for obtaining an analysis result of the target to be analyzed by utilizing the updated subspace association network diagram, wherein the analysis result comprises a city state prediction result of the target city, and the city state prediction result comprises a traffic flow prediction result, an air quality prediction result and/or a people flow distribution prediction result.

9. An electronic device, comprising: the system comprises a memory, a processor and a transceiver which are connected in sequence in communication, wherein the memory is used for storing a computer program, the transceiver is used for receiving and transmitting messages, and the processor is used for reading the computer program and executing the multidimensional data modeling and analysis method based on the subspace sequence according to any one of claims 1-7.

10. A computer program product comprising instructions which, when run on a computer, cause the computer to perform the multi-dimensional data modeling and analysis method based on subspace sequences as claimed in any one of claims 1 to 7.