[go: up one dir, main page]

Auddy et al., 2024 - Google Patents

Tensor methods in high dimensional data analysis: Opportunities and challenges

Auddy et al., 2024

View PDF
Document ID
5860764552508876687
Author
Auddy A
Xia D
Yuan M
Publication year
Publication venue
arXiv preprint arXiv:2405.18412

External Links

Snippet

Large amount of multidimensional data represented by multiway arrays or tensors are prevalent in modern applications across various fields such as chemometrics, genomics, physics, psychology, and signal processing. The structural complexity of such data provides …
Continue reading at arxiv.org (PDF) (other versions)

Classifications

    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06KRECOGNITION OF DATA; PRESENTATION OF DATA; RECORD CARRIERS; HANDLING RECORD CARRIERS
    • G06K9/00Methods or arrangements for reading or recognising printed or written characters or for recognising patterns, e.g. fingerprints
    • G06K9/62Methods or arrangements for recognition using electronic means
    • G06K9/6217Design or setup of recognition systems and techniques; Extraction of features in feature space; Clustering techniques; Blind source separation
    • G06K9/6232Extracting features by transforming the feature space, e.g. multidimensional scaling; Mappings, e.g. subspace methods
    • G06K9/6247Extracting features by transforming the feature space, e.g. multidimensional scaling; Mappings, e.g. subspace methods based on an approximation criterion, e.g. principal component analysis
    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06KRECOGNITION OF DATA; PRESENTATION OF DATA; RECORD CARRIERS; HANDLING RECORD CARRIERS
    • G06K9/00Methods or arrangements for reading or recognising printed or written characters or for recognising patterns, e.g. fingerprints
    • G06K9/62Methods or arrangements for recognition using electronic means
    • G06K9/6217Design or setup of recognition systems and techniques; Extraction of features in feature space; Clustering techniques; Blind source separation
    • G06K9/6218Clustering techniques
    • G06K9/622Non-hierarchical partitioning techniques
    • G06K9/6226Non-hierarchical partitioning techniques based on the modelling of probability density functions
    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06KRECOGNITION OF DATA; PRESENTATION OF DATA; RECORD CARRIERS; HANDLING RECORD CARRIERS
    • G06K9/00Methods or arrangements for reading or recognising printed or written characters or for recognising patterns, e.g. fingerprints
    • G06K9/62Methods or arrangements for recognition using electronic means
    • G06K9/6217Design or setup of recognition systems and techniques; Extraction of features in feature space; Clustering techniques; Blind source separation
    • G06K9/6232Extracting features by transforming the feature space, e.g. multidimensional scaling; Mappings, e.g. subspace methods
    • G06K9/6251Extracting features by transforming the feature space, e.g. multidimensional scaling; Mappings, e.g. subspace methods based on a criterion of topology preservation, e.g. multidimensional scaling, self-organising maps
    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06KRECOGNITION OF DATA; PRESENTATION OF DATA; RECORD CARRIERS; HANDLING RECORD CARRIERS
    • G06K9/00Methods or arrangements for reading or recognising printed or written characters or for recognising patterns, e.g. fingerprints
    • G06K9/62Methods or arrangements for recognition using electronic means
    • G06K9/6217Design or setup of recognition systems and techniques; Extraction of features in feature space; Clustering techniques; Blind source separation
    • G06K9/6261Design or setup of recognition systems and techniques; Extraction of features in feature space; Clustering techniques; Blind source separation partitioning the feature space
    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06KRECOGNITION OF DATA; PRESENTATION OF DATA; RECORD CARRIERS; HANDLING RECORD CARRIERS
    • G06K9/00Methods or arrangements for reading or recognising printed or written characters or for recognising patterns, e.g. fingerprints
    • G06K9/62Methods or arrangements for recognition using electronic means
    • G06K9/6267Classification techniques
    • G06K9/6279Classification techniques relating to the number of classes
    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06KRECOGNITION OF DATA; PRESENTATION OF DATA; RECORD CARRIERS; HANDLING RECORD CARRIERS
    • G06K9/00Methods or arrangements for reading or recognising printed or written characters or for recognising patterns, e.g. fingerprints
    • G06K9/62Methods or arrangements for recognition using electronic means
    • G06K9/6267Classification techniques
    • G06K9/6268Classification techniques relating to the classification paradigm, e.g. parametric or non-parametric approaches
    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06KRECOGNITION OF DATA; PRESENTATION OF DATA; RECORD CARRIERS; HANDLING RECORD CARRIERS
    • G06K9/00Methods or arrangements for reading or recognising printed or written characters or for recognising patterns, e.g. fingerprints
    • G06K9/62Methods or arrangements for recognition using electronic means
    • G06K9/6217Design or setup of recognition systems and techniques; Extraction of features in feature space; Clustering techniques; Blind source separation
    • G06K9/6256Obtaining sets of training patterns; Bootstrap methods, e.g. bagging, boosting
    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06KRECOGNITION OF DATA; PRESENTATION OF DATA; RECORD CARRIERS; HANDLING RECORD CARRIERS
    • G06K9/00Methods or arrangements for reading or recognising printed or written characters or for recognising patterns, e.g. fingerprints
    • G06K9/62Methods or arrangements for recognition using electronic means
    • G06K9/6296Graphical models, e.g. Bayesian networks
    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06FELECTRICAL DIGITAL DATA PROCESSING
    • G06F17/00Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10Complex mathematical operations
    • G06F17/16Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06FELECTRICAL DIGITAL DATA PROCESSING
    • G06F17/00Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/30Information retrieval; Database structures therefor; File system structures therefor
    • G06F17/3061Information retrieval; Database structures therefor; File system structures therefor of unstructured textual data
    • G06F17/30705Clustering or classification
    • G06F17/3071Clustering or classification including class or cluster creation or modification
    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06FELECTRICAL DIGITAL DATA PROCESSING
    • G06F17/00Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/30Information retrieval; Database structures therefor; File system structures therefor
    • G06F17/30286Information retrieval; Database structures therefor; File system structures therefor in structured data stores
    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06FELECTRICAL DIGITAL DATA PROCESSING
    • G06F17/00Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10Complex mathematical operations
    • G06F17/11Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06NCOMPUTER SYSTEMS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N99/00Subject matter not provided for in other groups of this subclass
    • G06N99/005Learning machines, i.e. computer in which a programme is changed according to experience gained by the machine itself during a complete run

Similar Documents

Publication Publication Date Title
Vannieuwenhoven et al. A new truncation strategy for the higher-order singular value decomposition
Auddy et al. Tensor methods in high dimensional data analysis: Opportunities and challenges
Sharan et al. Orthogonalized ALS: A theoretically principled tensor decomposition algorithm for practical use
Zhou et al. Fast nonnegative matrix/tensor factorization based on low-rank approximation
Bazerque et al. Rank regularization and Bayesian inference for tensor completion and extrapolation
Laclau et al. Co-clustering through optimal transport
Anandkumar et al. Learning overcomplete latent variable models through tensor methods
Han et al. Multi-stage multi-task learning with reduced rank
Jain et al. Learning mixtures of discrete product distributions using spectral decompositions
Bhojanapalli et al. A new sampling technique for tensors
Cai et al. Kopa: Automated kronecker product approximation
Anandkumar et al. Tensor decompositions for learning latent variable models (A survey for ALT)
Aravkin et al. Orthogonal matching pursuit for sparse quantile regression
Dasarathy et al. Sketching sparse matrices
Koo et al. Popularity adjusted block models are generalized random dot product graphs
Shi et al. Efficient semi-supervised spectral co-clustering with constraints
Auddy et al. Tensors in high-dimensional data analysis: Methodological opportunities and theoretical challenges
Li et al. Online tensor learning: Computational and statistical trade-offs, adaptivity and optimal regret
Balasubramanian et al. Tensor methods for additive index models under discordance and heterogeneity
Su et al. Global convergence of federated learning for mixed regression
Zhao et al. Spatial sign based principal component analysis for high dimensional data
Chatterji et al. Alternating minimization for dictionary learning: Local convergence guarantees
Sarkar et al. When random initializations help: a study of variational inference for community detection
Xu et al. Statistical inference for low-rank tensor models
Bazerque et al. Inference of Poisson count processes using low-rank tensor data