CN104992166A - Robust measurement based handwriting recognition method and system - Google Patents

Abstract

The invention discloses a method and system for handwriting recognition based on robust metrics. Through similarity learning of handwriting training samples, a weighted similarity graph is constructed, and all the components are kept while compacting local intra-class divergence and separating local inter-class divergence. Local properties of the training samples. In order to improve the robustness of handwriting description, the 1-norm metric is proposed to be applied to the semi-supervised feature learning model, and a robust handwriting recognition method and system are designed, which can be used for in-sample and out-of-sample handwriting image feature extraction. Projection matrix P. The induction of the out-of-sample image projects the test sample to the projection matrix P, and then inputs the extracted features into an efficient label propagation classifier for classification, and takes the position of the maximum probability in the soft label of the corresponding category to determine the test sample categories to get the most accurate character recognition results. At the same time, by establishing a ratio model, the model parameters are reduced, and the projection matrix P satisfies the orthogonality characteristic.

Description

A Handwriting Recognition Method and System Based on Robust Metrics

technical field

The invention relates to the technical fields of computer vision and image recognition, in particular to a handwritten body recognition method and system based on robust metrics.

Background technique

Today is an era of information explosion, and there is a large amount of valuable multimedia high-dimensional information in our daily life. Offline handwriting recognition is an example of feature extraction and utilization of some high-dimensional information. It uses a computer to digitize paper images to obtain computer-stored character images, and then uses a series of machine learning methods to extract image features, classify and other operations to finally recognize characters. Once an efficient and accurate method for character recognition is obtained, it can be applied to fields such as office automation and machine translation, which can bring huge social and economic benefits. However, because the process of effectively extracting handwritten image features is difficult, so far, offline handwritten (referred to as handwritten in the present invention) character recognition still has a certain distance from practical requirements. Most of the current research work is focused on the feature extraction of handwritten images, and some results have been achieved. However, handwritten images collected from the real world usually contain noise, heterogeneous data or missing data, and handwritten images have problems such as irregular strokes caused by writing habits and other reasons. Therefore, more robust algorithms are needed for feature extraction.

In recent years, some 1-norm-based robust models have been proposed, such as 1-norm-based principal component analysis algorithm (PCA-L1), 1-norm-based discriminative locality-preserving projection algorithm (DLPP-L1) wait. The idea proposed by these robust algorithms is: the traditional algorithm based on 2-norm distance measure is sensitive to noise or heterogeneous data in the data, while the distance measure based on 1-norm can overcome this shortcoming and improve the robustness of the model. Stickiness. These algorithms do make the results more robust, but since there are currently only unsupervised and fully supervised algorithms, which cannot make full use of labeled data and unlabeled data information, there is still a lot of room for improvement in the accuracy of the results. In addition, some empirical parameters in the algorithm are also very difficult to optimally determine.

Therefore, it is an urgent problem to be solved by those skilled in the art to provide a handwriting recognition method and system based on robust metrics, to realize robust extraction of features of handwritten character images, and to improve the representation ability and recognition accuracy of handwritten character images.

Contents of the invention

In view of this, the present invention provides a handwriting recognition method and system based on robust metrics, which can realize the robust extraction of handwritten character image features, and at the same time improve the handwritten character image representation ability and recognition accuracy, so as to overcome the problems in the prior art. Only using labeled or unlabeled data does not fully consider the characteristics of real-world data information.

In order to solve the above-mentioned technical problems, the present invention provides a handwriting recognition method based on robust metrics, based on the discriminativeness of labeled data and the idea of 1-norm projection locally maintained by all samples, the method includes:

Carry out similarity learning on handwriting training samples, construct a weighted similarity graph, and maintain the local characteristics of all training samples while compacting local intra-class divergence and separating local inter-class divergence; construct a robust semi-supervised model based on 1-norm metrics Handwritten character image feature learning model, the model optimizes and outputs a projection matrix P that can be used for in-sample and out-of-sample image feature extraction; at the same time, by establishing a ratio model, model parameters are reduced, and the optimized output projection matrix P satisfies the orthogonality characteristic ;

Using the projection matrix P to perform feature extraction on the handwriting test sample, the induction of the out-of-sample image is mainly by mapping the test sample to the projection matrix P;

Use the label propagation classifier to complete the test on the feature of the test sample after dimensionality reduction, output the soft label of the category of the test sample, and take the position corresponding to the maximum value of the probability in the soft label of the category to determine the position of the test sample Category, to get the character recognition result;

Wherein, the numerical value in the category soft label represents the probability that the test sample belongs to each category.

In the above method, optionally, the construction of a robust semi-supervised handwritten character image feature learning model based on 1-norm measurement, the model optimizes and outputs a projection matrix P that can be used for in-sample and out-of-sample image feature extraction, include:

Given a noisy original training sample set Among them, n is the dimension of the training sample set, N is the number of training sample sets, and the training sample set contains sample sets with category labels (a total of c categories, c>2) and a sample set without any labels And satisfy the sample size l+u=N; set is the label of l labeled samples, and the label of sample x _i is y _i (i≤l);

A projection matrix with discriminative features and local preservation features is calculated according to the original training sample set Including the output of the projection matrix P that can extract the features of the handwritten character image outside the sample by solving the following optimization equation:

$\begin{array}{c}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\underset{\mathrm{<span\; class="notranslate">\; P</span>}}{\mathrm{<span\; class="notranslate">\; max</span>}}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\underset{\mathrm{<span\; class="notranslate">\; P</span>}}{\mathrm{<span\; class="notranslate">\; max</span>}}\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; P</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; P</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}\\ \mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; .</span>{\mathrm{<span\; class="notranslate">\; P</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}\end{array}$

Among them, ||·|| ₁ is the 1-norm, defined as ||S|| ₁ = ∑ _i,j |S _i,j |, S _i,j represents the (i,j)th element of the S matrix , and W is the weight coefficient matrix.

In the above method, optionally, using the projection matrix P to perform feature extraction on the handwriting test sample image, and the induction of the out-of-sample image is mainly by mapping the test sample image to the projection matrix P, including:

Using the projection matrix P to project the training sample and the test sample to complete the handwritten character image feature extraction.

The present invention also provides a handwriting recognition system based on robust metrics, comprising:

The training module is used for similarity learning of handwriting training samples, constructs a weighted similarity graph, and maintains the local characteristics of all training samples while compacting local intra-class divergence and separating local inter-class divergence; the construction is based on 1-norm A metric robust semi-supervised handwritten character image feature learning model, the model optimizes the output of a projection matrix P that can be used for in-sample and out-of-sample image feature extraction; at the same time, by establishing a ratio model, the model parameters are reduced, and the output projection is optimized The matrix P satisfies the orthogonality property;

The test preprocessing module is used to use the projection matrix P to perform feature extraction on the handwriting test sample, and the induction of the out-of-sample image is mainly by mapping the test sample to the projection matrix P;

The test module is used to use the label propagation classifier to complete the test on the characteristics of the test sample after dimensionality reduction, output the soft label of the category of the test sample, and take the position corresponding to the maximum value of the probability in the soft label of the category for judging The category of the test sample is obtained to obtain the character recognition result;

Wherein, the numerical value in the category soft label represents the probability that the test sample belongs to each category.

It can be seen from the above technical solutions that, compared with the prior art, the present invention discloses a handwriting recognition method and system based on robust metrics. By performing similarity learning on handwriting training samples, a weighted similarity graph is constructed. Intra-class divergence and separation of local inter-class divergence while maintaining the local characteristics of all training samples; in order to improve the robustness of handwriting description, a robust semi-supervised handwritten character image feature learning model based on 1-norm measurement was constructed. The above model optimizes and outputs a projection matrix P that can be used for feature extraction of in-sample and out-of-sample images; the induction of out-of-sample images projects the test samples to the projection matrix P, and then inputs the extracted features into an efficient label propagation classifier for induction. Class, take the position of the maximum value of the probability in the soft label corresponding to the category, and use it to determine the category of the test sample to obtain the most accurate character recognition results. At the same time, by establishing a ratio model, the model parameters are reduced, and the projection matrix P satisfies the orthogonality characteristic.

Description of drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only It is an embodiment of the present invention, and those skilled in the art can also obtain other drawings according to the provided drawings without creative work.

Fig. 1 is a flow chart of a handwriting recognition method based on robust metrics provided by an embodiment of the present invention;

Fig. 2 is a schematic structural block diagram of a handwriting recognition system based on robust metrics provided by an embodiment of the present invention;

FIG. 3 is a schematic diagram of a handwriting recognition method based on robust metrics provided by an embodiment of the present invention.

Detailed ways

The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some, not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

The core of the present invention is to provide a handwriting recognition method and system based on robust metrics, realize the robust extraction of handwritten character image features, and improve the handwriting character image representation ability and recognition accuracy at the same time, to overcome the existing technology that only uses Labeled or unlabeled data, without fully considering the characteristics of real-world data information.

The invention discloses a handwriting recognition method and system based on a robust metric. By performing similarity learning on handwriting training samples, a weighted similarity graph is constructed to maintain compact local intra-class divergence and separate local inter-class divergence. Local characteristics of all training samples; in order to improve the robustness of handwriting description, construct a robust semi-supervised handwriting character image feature learning model based on 1-norm metric, the model optimizes the output of an image feature that can be used for in-sample and out-of-sample The extracted projection matrix P; the induction of the out-of-sample image projects the test sample to the projection matrix P, and then inputs the extracted features into an efficient label propagation classifier for classification, and takes the position of the maximum probability in the soft label of the corresponding category , which is used to determine the category of the test sample and obtain the most accurate character recognition result. At the same time, by establishing a ratio model, the model parameters are reduced, and the projection matrix P satisfies the orthogonality characteristic.

In order to enable those skilled in the art to better understand the solution of the present invention, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

The invention was tested on three handwritten character image databases: CAS, USPS and ORHD. CAS is the handwritten database of the Institute of Automation, Chinese Academy of Sciences, including 3755 Chinese characters and 171 letters, numbers or symbols; USPS is the handwritten number database of the US postal system, including 9298 handwritten numbers 0-9; ORHD is the University of California, Irvine (UCI) A machine learning database containing 5620 digital samples, each containing an integer in the range 0-16. These databases are collected from multiple sources so that the test results are generally descriptive.

Given a set of handwritten samples, it is divided into a training set and a test set, which contain the original training samples and test samples respectively.

Referring to FIG. 1 , it shows a flowchart of a handwriting recognition method based on a robust metric provided by an embodiment of the present invention. The method is based on the discriminability of labeled data and the idea of 1-norm projection locally maintained by all samples, Specifically, the following steps may be included:

Step S100 , performing similarity learning on handwritten training samples, constructing a weighted similarity graph, and maintaining local characteristics of all training samples while compacting local intra-class divergence and separating local inter-class divergence. In order to improve the robustness of the system, step S100 will also construct a robust semi-supervised handwritten character image feature learning model based on the 1-norm metric, and the model optimizes the output of a projection matrix that can be used for in-sample and out-of-sample image feature extraction P; At the same time, by establishing a ratio model, the model parameters are reduced, and the optimized output projection matrix P satisfies the orthogonality characteristic;

Step S101, using the projection matrix P obtained in the step S100 to perform feature extraction on the handwriting test sample, and the induction of the out-of-sample image is mainly by mapping the test sample to the projection matrix P;

Step S102, use the label propagation classifier to complete the test on the features of the test sample after dimensionality reduction, output the soft label of the category of the test sample, and take the position corresponding to the maximum value of the probability in the soft label of the category to determine the The category of the test sample to obtain the character recognition result; wherein, the numerical value in the category soft label represents the probability that the test sample belongs to each category.

In the present invention, according to the above step S100, the handwriting training image is discriminated and the geometric structure is preserved, and a robust semi-supervised feature learning model based on 1-norm measurement is proposed, and a projection matrix that can be used for feature extraction of out-of-sample test images is optimized and output P, the specific process is as follows:

For a given set of original handwriting vectors that may be noisy Referred to as the original training sample set (where n is the dimension of the handwritten sample, N is the number of samples), the training sample set contains a sample set of category labels (a total of c categories, c>2) and a sample set without any labels And the sample size l+u=N is satisfied. set up is the label of l labeled samples, and the label of sample x _i is y _i (i≤l).

Calculate a projection matrix with discriminative features and local preservation features based on the original training set Specifically, the projection matrix P that can extract the image features of out-of-sample handwritten characters is obtained by solving the following optimization equation:

$\begin{array}{c}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\underset{\mathrm{<span\; class="notranslate">\; P</span>}}{\mathrm{<span\; class="notranslate">\; max</span>}}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\underset{\mathrm{<span\; class="notranslate">\; P</span>}}{\mathrm{<span\; class="notranslate">\; max</span>}}\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; P</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; P</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}\\ \mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; .</span>{\mathrm{<span\; class="notranslate">\; P</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}\end{array}$

Where ||·|| ₁ is the 1-norm, defined as follows:

$<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; |</span>$

Where S _{i, j} represents the (i, j)th element of the S matrix, the weight coefficient matrix W is defined as follows:

$\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; =</span>{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span>$

Among them, M is the reconstruction coefficient matrix, and γ∈[0,1] is the trade-off parameter for feature extraction of labeled data and unlabeled data. matrix It is defined as follows:

The reconstruction coefficient matrix M can be obtained by solving the following optimization problem:

$\begin{array}{ccc}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}& \mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>& \mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; .</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}$

Among them, ||·|| is the 2-norm, which is defined as follows:

$<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$

When calculating, this embodiment adopts an iterative method to gradually approximate the local optimal solution, and the case where the dimension is reduced to 1 dimension can be calculated first. Firstly, the following optimization problem is calculated by the existing method to obtain the reconstruction coefficient matrix M:

$\begin{array}{ccc}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}& \mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>& \mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; .</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}$

Then calculate the weight coefficient matrix and

Thus the weight coefficient matrix W in the problem is obtained:

$\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; =</span>{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span>$

The 1-norm optimization solution is performed below. Let sign function

${\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>& {\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>& {\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right.<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; )</span>$

Substituting into the original optimization function to get:

$\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>}{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>}$

Reincrement

$\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>}{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; -</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>}{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}$

Then update p(t+1)=p(t)+βδ(t). Among them, β is a small positive number. If the value of F(p(t+1)) does not increase significantly, output p ^* =p(t+1), otherwise iterate until convergence.

The above description is the case of reducing to 1 dimension, that is, d=1, and the following further explains the situation of reducing to multi-dimensional, that is, d>1:

First set p ₀ =0, (x _i ) ₀ =x _i (i=1,2,...,N); then for each i in i=1,2,...,N, the calculation is as follows formula:

${<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; )</span>$

Substitute ( _xi ) _k into the aforementioned iterative method to calculate p _k .

The specific algorithm is as follows:

Handwriting Feature Extraction Algorithm Based on Robust Metrics

Input: raw data matrix Control parameters γ, β, d.

Output: projection matrix P ^* .

Initialization: d ₀ ＝0, p ₀ ＝0, ( _xi ) ₀ ＝ _xi , k＝0, γ＝0.2, β＝0.01, ε＝10 ^-6

step1: Solve and calculate $\begin{array}{ccc}mi\mathrm{no}& \mathrm{\&epsiv;}\left(m\right)=\underset{i}{\&Sigma;}\left|\right|x_i-\underset{j}{\&Sigma;}{m}_{i,j}{x}_j|{|}^2,& \mathrm{the\; s}.t.\underset{j}{\&Sigma;}{m}_{i,j}=1\end{array}$

step2: Calculate:

$\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; =</span>{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span>$

step3: When d ₀ <d, k←k+1, for each i in i=1,2,...,N, calculate

${<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; )</span>$

Otherwise output P ^* =P

step4: command (m _i represents the mean value of the i-th sample), and normalized $p_{d_0}\left(0\right)=p_{d_0}\left(0\right)/\left|\right|p_{d_0}\left(0\right)\left|\right|$

step5: do when the while has not yet converged

calculate $q_{i,j}\left(t\right)=\left\{\begin{array}{cc}1,& p_{d_0}^T\left(t\right)\left({\left(x_i\right)}_{d_0}-{\left(x_j\right)}_{d_0}\right)\&Greater\; Equal;0\\ -1,& p_{d_0}^T\left(t\right)\left({\left(x_i\right)}_{d_0}-{\left(x_j\right)}_{d_0}\right)<0\end{array}\right.,\left(i,j=1,2,...,N\right)$

Calculate increment

$\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}_{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>}_{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span>}{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}_{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>}_{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; -</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}_{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>}_{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span>}{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}_{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>}_{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}$

renew $p_{d_0}^T(t+1)=p_{d_0}^T\left(t\right)+\mathrm{\&beta;}\mathrm{\&delta;}\left(t\right)$

Check for convergence:

like Then stop, set P(:,d ₀ )=p(t+1);

Otherwise t=t+1

end while

step6: set d ₀ ←d ₀ +1, and continue to execute step3.

The selection of the initial value of iteration in this example: γ = 0.2; β = 0.01 is the initial value, which decreases continuously during the iteration.

Thus, we get the handwritten character image feature extraction matrix P.

In the present invention, for step S101, using the projection matrix P to perform feature extraction on the handwriting test sample, the induction of the out-of-sample image is mainly by mapping the test sample to the projection matrix P, specifically including:

Use the projection matrix P obtained above to extract the features of the handwriting test image sample and generate a new test set, specifically: based on the training set, the projection matrix can be used to Then embed the training samples and test samples to obtain the projection space, complete the feature extraction of handwritten character images, and generate the training set and test set after feature extraction.

Among them, the feature extraction results of the training sample x _train and the test sample x _test are expressed as follows: in are the feature extraction results of the original training samples and test samples, respectively.

In the present invention, for step S102, use the label propagation classifier to complete the test on the characteristics of the test sample after dimensionality reduction, output the soft label of the category of the test sample, and take the position corresponding to the maximum value of the probability in the soft label of the category, Used to determine the category of the test sample to obtain character recognition results, specifically including:

After obtaining the original training set and test set character image features through step S101 calculation, it is easy to construct a handwritten sample test set after feature extraction and the training set in Corresponding to the features of each original sample _xi . Then use the label propagation classifier to classify the test set samples, and obtain the classification results of the test set samples.

Compared with the prior art, the present invention discloses a method and system for handwriting recognition based on robust metrics. Through similarity learning of handwriting training samples, a weighted similarity graph is constructed to diverge and separate local While maintaining the local characteristics of all training samples between classes; in order to improve the robustness of handwriting description, a robust semi-supervised handwriting character image feature learning model based on 1-norm measurement is constructed, and the model optimization output can be used for The projection matrix P for in-sample and out-of-sample image feature extraction; the induction of the out-of-sample image is by projecting the test sample to the projection matrix P, and then inputting the extracted features into an efficient label propagation classifier for classification, and taking the soft label of the corresponding category The position of the maximum value of the medium probability is used to determine the category of the test sample and obtain the most accurate character recognition result. At the same time, by establishing a ratio model, the model parameters are reduced, and the projection matrix P satisfies the orthogonality property.

Corresponding to the robust metric-based handwriting recognition method disclosed in the above-mentioned embodiments of the present invention, the embodiment of the present invention also provides a robust metric-based handwriting recognition system. Referring to FIG. 2 , the system 200 may include the following content :

The training module 201 is used to perform similarity learning on handwriting training samples, construct a weighted similarity graph, and maintain local characteristics of all training samples while compacting local intra-class divergence and separating local inter-class divergence. In addition, a robust semi-supervised handwritten character image feature learning model based on the 1-norm metric will be constructed, which optimizes the output of a projection matrix P that can be used for in-sample and out-of-sample image feature extraction; at the same time, by establishing a ratio model , reduce the model parameters, and the optimized output projection matrix P satisfies the orthogonality property;

The test preprocessing module 202 is used to perform feature extraction on the handwriting test sample by using the projection matrix P, and the induction of the out-of-sample image is mainly by mapping the test sample to the projection matrix P;

The testing module 203 is used to use the label propagation classifier to complete the test on the test sample features after dimensionality reduction, output the soft label of the category of the test sample, and take the position corresponding to the maximum value of the probability in the soft label of the category, for Determine the category of the test sample to obtain a character recognition result;

Wherein, the numerical value in the category soft label represents the probability that the test sample belongs to each category.

Please refer to Table 1, for the method of the present invention and semi-supervised maximum distance criterion algorithm (SSMMC), semi-supervised linear discriminant analysis algorithm (SSLDA), discriminative local preserving projection algorithm (DLPP-L1) method based on 1-norm The comparison table of recognition results shows the average recognition rate and the highest recognition rate of each method experiment. In this example, the SSMMC, SSLDA, and DLPP-L1 methods involved in the comparison use the projection matrix P calculated by each for the feature extraction of the test samples, and the classification uses the label propagation classifier.

Table 1. Comparison of recognition results between the present invention and SSMMC, SSLDA, DLPP-L1 methods

Through three real data sets, namely (a) CAS Offline Chinese Handwriting Digits, (b) USPS and (c) Optical Recognition of Handwritten Digits, the example experiment results show that the method of the present invention can be effectively used for automatic feature extraction of handwritten characters.

Please refer to FIG. 3 , which shows a schematic diagram of a handwriting recognition method based on robust metrics provided by an embodiment of the present invention.

From the experimental results, we can see that the handwritten character image feature extraction and recognition effect of the present invention is significantly better than the related SSMMC, SSLDA and DLPP-L1 methods, and it shows strong stability and has certain advantages.

To sum up: the present invention discloses a method and system for handwriting recognition based on robust metrics. Through the similarity learning of handwriting training samples, a weighted similarity graph is constructed, and the divergence between compact local classes and the separation between local classes Divergence while maintaining the local characteristics of all training samples; in order to improve the robustness of handwriting description, a robust semi-supervised handwriting character image feature learning model based on 1-norm metric is constructed, and the model optimizes an output that can be used in samples and the projection matrix P of the out-of-sample image feature extraction; the induction of the out-of-sample image is by projecting the test sample to the projection matrix P, and then inputting the extracted features into an efficient label propagation classifier for classification, and taking the probability of the soft label of the corresponding category The position of the maximum value of is used to determine the category of the test sample and obtain the most accurate character recognition result. At the same time, by establishing a ratio model, the model parameters are reduced, and the projection matrix P satisfies the orthogonality characteristic.

It should be noted that each embodiment in this specification is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. For the same and similar parts in each embodiment, refer to each other, that is, Can. As for the system embodiment, because it is basically similar to the method embodiment, the description is relatively simple, and for the related parts, please refer to the part of the description of the method embodiment.

The robust metric-based handwriting recognition method and system provided by the present invention are described above in detail. In this paper, specific examples are used to illustrate the principle and implementation of the present invention, and the descriptions of the above embodiments are only used to help understand the method and core idea of the present invention. It should be pointed out that for those skilled in the art, without departing from the principle of the present invention, some improvements and modifications can be made to the present invention, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

Claims (4)

1. based on a Manuscripted Characters Identification Method for robust tolerance, it is characterized in that, based on the thought of the 1-norm projection having the identification of label data and all samples local to keep, the method comprises:

Similarity-based learning is carried out to handwritten form training sample, structure weighting similar diagram, divergence and keep the local characteristics of all training samples while being separated locally between class scatter in the class of compact local; Build the robust semi-supervised handwritten character characteristics of image learning model based on 1-norm measure, described model optimization exports one and can be used in sample and the projection matrix P of image characteristics extraction outside sample; Meanwhile, by setting up ratio model, reduce model parameter, and the projection matrix P optimizing output meets orthogonal property;

Utilize described projection matrix P originally to carry out feature extraction to hand-written body examination sample, the conclusion of the outer image of sample is mainly through mapping described test sample book to projection matrix P;

Utilize label Category of Communication device, test is completed to the test sample book feature after dimensionality reduction, exports the soft label of classification of described test sample book, get the position of the maximal value of probability in the soft label of corresponding described classification, for judging the classification of described test sample book, obtain character identification result;

Wherein, the numerical value in the soft label of described classification represents the probability that described test sample book belongs to each classification.

2. the method for claim 1, it is characterized in that, described structure is based on the robust semi-supervised handwritten character characteristics of image learning model of 1-norm measure, and described model optimization exports one and can be used in sample and the projection matrix P of image characteristics extraction outside sample, comprising:

A given original training sample collection that there is noise wherein, n is the dimension of training sample set, and N is the quantity of training sample set, and training sample concentrates the sample set including class label (c classification altogether, c>2) with the sample set without any label and meet sample size l+u=N; If for l has the label of exemplar, and sample x _ilabel be y _i(i≤l);

Calculate one according to described original training sample collection and there is identification feature and the projection matrix locally keeping feature comprise and export by solving following optimization method the projection matrix P obtaining extracting the outer handwritten form character picture feature of sample:

$\begin{array}{c}{P}_{opt}=\arg \underset{P}{\max }F\left(P\right)\\ =\arg \underset{P}{\max }\frac{\underset{i,j=1}{\overset{N}{\mathrm{\&Sigma;}}}{\tilde{W}}_{i,j}^{\left(b\right)}\left|\right|P^T\left(x_i-x_j\right)|{|}_1}{\underset{i,j=1}{\overset{N}{\mathrm{\&Sigma;}}}{W}_{i,j}\left|\right|P^T\left(x_i-x_j\right)|{|}_1}\\ s.t.P^{T}P=I_d\end{array}$

Wherein, || || ₁for 1-norm, be defined as || S|| ₁=Σ _i,j| S _i,j|, S _i,jrepresent (i, j) number element of s-matrix, be weight coefficient matrix with W.

3. method as claimed in claim 2, is characterized in that, describedly utilizes described projection matrix P to carry out feature extraction to hand-written body examination examination sample image, and the conclusion of the outer image of sample, mainly through described test sample image being mapped to projection matrix P, comprising:

Use described projection matrix P to project to training sample and test sample book, complete handwritten character image characteristics extraction.

4., based on a handwriting recongnition system for robust tolerance, it is characterized in that, comprising:

Training module, for carrying out similarity-based learning to handwritten form training sample, structure obtains weighting similar diagram, divergence and keep the local characteristics of all training samples while being separated locally between class scatter in the class of compact local; Build the robust semi-supervised handwritten character characteristics of image learning model based on 1-norm measure, described model optimization exports one and can be used in sample and the projection matrix P of image characteristics extraction outside sample; Meanwhile, by setting up ratio model, reduce model parameter, and the projection matrix P optimizing output meets orthogonal property;

Test pretreatment module, for utilizing described projection matrix P originally to carry out feature extraction to hand-written body examination sample, the conclusion of the outer image of sample is mainly through mapping described test sample book to projection matrix P;

Test module, for utilizing label Category of Communication device, completes test to the test sample book feature after dimensionality reduction, export the soft label of classification of described test sample book, getting the position of the maximal value of probability in the soft label of corresponding described classification, for judging the classification of described test sample book, obtaining character identification result;

Wherein, the numerical value in the soft label of described classification represents the probability that described test sample book belongs to each classification.