CN111695011A - Tensor expression-based dynamic hypergraph structure learning classification method and system - Google Patents
Tensor expression-based dynamic hypergraph structure learning classification method and system Download PDFInfo
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Abstract
The application discloses a tensor expression-based dynamic hypergraph structure learning classification method and system, wherein the method comprises the following steps: step 1, extracting characteristic vectors of sample data in a database, constructing a hypergraph structure according to the characteristic vectors, and expressing the connection strength between any point set in the hypergraph structure by using a tensor; and 2, introducing potential energy loss functions and empirical loss functions into potential energy of the label vector set, the hypergraph structure represented by the tensor and the point set in the database to generate a dynamic hypergraph structure learning model, performing optimization solution on the dynamic hypergraph structure learning model by using an alternative optimization method, and performing optimal solution of the label vector set after the model solution for data classification. According to the technical scheme, tensor is introduced as a representation form of the dynamic hypergraph structure and a dynamic hypergraph structure learning method, the hypergraph structure and the label vectors of data are optimized alternately, and finally data classification is achieved according to the optimal solution of the label vectors of the data.
Description
Technical Field
The application relates to the technical field of data label processing, in particular to a dynamic hypergraph structure learning classification method based on tensor expression and a dynamic hypergraph structure learning classification system based on tensor expression.
Background
In practical applications, usually a small portion of the data is tagged, and most of the data is untagged. In such a case, the semi-supervised learning method can simultaneously utilize tagged data and untagged data, and exhibits excellent performance.
The hypergraph is a semi-supervised classification method, each vertex of the hypergraph represents one sample data, and the hypergraph represents the association between the sample data.
The learning method based on the hypergraph structure can be regarded as a process of label propagation on the hypergraph structure, points which are connected more closely on the hypergraph should have similar labels, and points which are farther away should have different labels. A good hypergraph structure can accurately model the relevance between data, and therefore better classification performance is obtained.
In the prior art, methods for establishing a hypergraph structure comprise methods for establishing a hypergraph structure based on k-nearest neighbor and methods for establishing a hypergraph structure based on sparse representation, and the methods are used for establishing a static hypergraph structure according to characteristic representation or sparse representation of data, and the hypergraph structure is kept unchanged in the subsequent hypergraph learning process. Obviously, this static hypergraph structure is not guaranteed to be optimal.
In addition, there is also a way to adjust the weights of the hyperedges during hypergraph learning, since different connections may have different importance. However, such adjustments do not completely repair improper or even erroneous connections, and thus the performance of the hypergraph structure is improved only marginally.
Disclosure of Invention
The purpose of this application lies in: and a dynamic hypergraph structure is provided, a tensor is introduced as a representation form of the dynamic hypergraph structure and a dynamic hypergraph structure learning method, the hypergraph structure and the label vector of the data are alternately optimized, a stable and more excellent hypergraph structure and label vector of the data are finally obtained, label-free data are classified according to the label vector, the defect that the traditional static hypergraph structure cannot accurately represent data association is overcome, and the accuracy of data classification is effectively improved.
The technical scheme of the first aspect of the application is as follows: a tensor representation-based dynamic hypergraph structure learning classification method is provided, and comprises the following steps:
step 1, extracting characteristic vectors of sample data in a database, constructing a hypergraph structure according to the characteristic vectors, and expressing the connection strength between any point set in the hypergraph structure by using a tensor, wherein the sample data comprises label data and label-free data;
the calculation formula of the dynamic hypergraph structure learning model is as follows:
in the formula (I), the compound is shown in the specification,for the joint strength of the ω -th set of points,for all joint strengthsWhere row vectors are arranged as a row indexed by omega,as a row vectorInitial value of fωIs the potential energy of the point set, lambda and β are weight coefficients, Y is the label vector set0Is the initial set of values for the tag vector.
In any of the above technical solutions, further, in step 1, tensor representation is performed on the connection strength between any point set in the hypergraph structure by using a tensor, which specifically includes: initial values of the row vectors in the tensor representationCorresponding element with middle index of omegaThe calculation formula of (2) is as follows:
ω∈ΨN
in the formula (I), the compound is shown in the specification,is any point set { viCenter of | i ∈ ω }, viAs the point of the i-th spot,is a power set with the set omega being 1,2, …, N being the number of vertices in the hypergraph structure,represents the ith point viTo the centerThe distance of (a) to (b),is the set of points { viThe average distance between every two points in | i ∈ ω } is the super-edge set of the hypergraph structure.
In any of the above technical solutions, further, in step 2, a calculation formula of potential energy of the point set is:
where α is the balance parameter, (ω) is the number of points in the set of points, yiIs a label vector, x, of the ith sample dataiIs the feature vector of the ith sample data.
In any one of the above technical solutions, further, in step 2, performing optimization solution on the dynamic hypergraph structure learning model by using an alternating optimization method, specifically including:
step 21, fixing the label vector set Y, and iteratively updating tensor expression of the hypergraph structure by using the projection gradient and the first objective functionThe calculation formula of the hypergraph structure iterative updating is as follows:
in the formula (I), the compound is shown in the specification,in order to be a gradient of the magnetic field,is tensor representation of the hypergraph structure after k iterations, h is the step length of each optimization, P is projection of the feasible set, and f is all potential energy fωRow vectors arranged in a row by taking omega as an index;
step 22, fixing the tensor representation of the hypergraph structureCalculating a tag transfer function by using the second objective function;
and 23, repeating the step 21 and the step 22 until the dynamic hypergraph structure learning model converges, and finishing the optimization solution.
In any one of the above technical solutions, further, in step 1, extracting a feature vector of sample data in the database specifically includes: judging the data type of the sample data; determining a feature extraction method according to the data type; and extracting the feature vector of the sample data by using the determined feature extraction method.
In any one of the above technical solutions, further, the label vector set is determined by a class to which the labeled data and the unlabeled data belong.
In any of the above technical solutions, further, the method is suitable for gesture recognition and three-dimensional object recognition.
The technical scheme of the second aspect of the application is as follows: a tensor representation-based dynamic hypergraph structure learning classification system is provided, which comprises: a tensor expression unit and a label classification model generation unit;
the tensor expression unit is used for extracting the characteristic vector of sample data in the database, constructing a hypergraph structure according to the characteristic vector, and expressing the connection strength between any point set in the hypergraph structure by utilizing the tensor, wherein the sample data comprises label data and label-free data;
the label classification model generation unit is used for introducing potential energy loss functions and empirical loss functions into potential energy of a label vector set, a hypergraph structure represented by a tensor and a point set in a database to generate a dynamic hypergraph structure learning model, performing optimization solution on the dynamic hypergraph structure learning model by using an alternative optimization method, recording the model after optimization solution as a label classification model, and performing data classification by using the label classification model to solve the optimal solution of the label vector set,
the calculation formula of the dynamic hypergraph structure learning model is as follows:
in the formula (I), the compound is shown in the specification,for the joint strength of the ω -th set of points,for all joint strengthsWhere row vectors are arranged as a row indexed by omega,as a row vectorInitial value of fωIs the potential energy of the point set, lambda and β are weight coefficients, Y is the label vector set0Is the initial set of values for the tag vector.
In any one of the above technical solutions, further, when the tensor representing unit tensor represents the connection strength between any one point set in the hypergraph structure by using a tensor, the tensor representing unit specifically includes: initial values of the row vectors in the tensor representationCorresponding element with middle index of omegaThe calculation formula of (2) is as follows:
ω∈ΨN
in the formula (I), the compound is shown in the specification,is any point set { viCenter of | i ∈ ω }, viAs the point of the i-th spot,is a power set with the set omega being 1,2, …, N being the number of vertices in the hypergraph structure,represents the ith point viTo the centerThe distance of (a) to (b),is the set of points { viThe average distance between every two points in | i ∈ ω } is the super-edge set of the hypergraph structure.
In any one of the above technical solutions, further, the tag classification model generating unit is further configured to: calculating potential energy of the point set, wherein the potential energy is calculated according to the formula:
wherein α is a balance parameter,(ω) is the number of points in the set of points, yiIs a label vector, x, of the ith sample dataiIs the feature vector of the ith sample data.
In any one of the above technical solutions, further, when the label classification model generation unit performs optimization solution on the dynamic hypergraph structure learning model by using an alternative optimization method, the method specifically includes:
fixing a label vector set Y, and iteratively updating tensor representation of the hypergraph structure by using projection gradient and a first objective functionThe calculation formula of the hypergraph structure iterative updating is as follows:
in the formula (I), the compound is shown in the specification,in order to be a gradient of the magnetic field,is tensor representation of the hypergraph structure after k iterations, h is the step length of each optimization, P is projection of the feasible set, and f is all potential energy fωRow vectors arranged in a row by taking omega as an index;
tensor representation of a fixed hypergraph structureCalculating a tag transfer function by using the second objective function;
refastening the labelstock set Y and tensor representation of the hypergraph structure, respectivelyAnd completing the optimization solution until the dynamic hypergraph structure learning model converges.
In any one of the above technical solutions, further, the extracting, by the tensor expression unit, the eigenvector of the sample data in the database specifically includes: judging the data type of the sample data; determining a feature extraction method according to the data type; and extracting the feature vector of the sample data by using the determined feature extraction method.
In any one of the above technical solutions, further, the label vector set is determined by a class to which the labeled data and the unlabeled data belong.
In any of the above technical solutions, further, the system is suitable for gesture recognition and three-dimensional object recognition.
The beneficial effect of this application is:
according to the technical scheme, the connection strength among the point sets in the hypergraph structure is expressed by adopting the tensor, sample data in the database are correlated on each order, the hypergraph structure is optimized alternately to form a dynamic hypergraph structure, and then label-free data are classified according to label vectors, so that the accuracy of data classification is effectively improved.
In the application, in the optimization updating process of the dynamic hypergraph structure, the prior information (labeled data) of the existing labels and characteristics is fully combined, the smoothness of the hypergraph structure in each characteristic space of a label space is kept, the hypergraph structure in the label classification process is greatly optimized, and the complex high-order association of data can be expressed more intuitively.
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The advantages of the above and/or additional aspects of the present application will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a schematic flow diagram of a tensor representation-based dynamic hypergraph structure learning classification method according to one embodiment of the present application;
FIG. 2 is a schematic diagram of a label classification model according to an embodiment of the present application.
Detailed Description
In order that the above objects, features and advantages of the present application can be more clearly understood, the present application will be described in further detail with reference to the accompanying drawings and detailed description. It should be noted that the embodiments and features of the embodiments of the present application may be combined with each other without conflict.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present application, however, the present application may be practiced in other ways than those described herein, and therefore the scope of the present application is not limited by the specific embodiments disclosed below.
The first embodiment is as follows:
the traditional static hypergraph structure is directly constructed by prior information, and the structure of the hypergraph structure is fixed and invariable in the hypergraph learning process and is usually represented by a adjacency matrix. In the embodiment, a dynamic hypergraph structure different from a traditional static hypergraph structure is provided, dynamic updating is performed in the hypergraph learning process, particularly, in the classification of label-free data, tensors are introduced to express the connection strength between point sets in the hypergraph structure, label vectors of the hypergraph structure and the data are optimized alternately, and the data classification is achieved.
As shown in fig. 1, the embodiment provides a dynamic hypergraph structure learning and classification method based on tensor expression, which is applicable to gesture recognition and three-dimensional object recognition. The method comprises the following steps:
step 1, extracting characteristic vectors of sample data in a database, constructing a hypergraph structure according to the characteristic vectors, and expressing the connection strength between any point set in the initial hypergraph structure by using a tensor, wherein the sample data comprises label data and label-free data;
specifically, in the present embodiment, the three-dimensional object feature description data is classified as an example, and the database uses a three-dimensional model data set (NTU) including 67 classes of 2020 objects, such as bombs, bottles, cars, chairs, cups, doors, maps, airplanes, swords, watches, tanks, trucks, etc., wherein 400 three-dimensional objects have tag information and 1620 three-dimensional objects have no tag information. Two parameters: the weight coefficient beta of the empirical loss term of the hypergraph structure is set to be 10, because if beta is larger, the difference between the finally optimized tag classification model and the hypergraph structure is smaller, and beta is too large, the hypergraph structure is difficult to optimize, and if beta is smaller, the difference between the finally optimized tag classification model and the hypergraph structure is larger, and beta is too small, overfitting is caused, so that an intermediate value is selected; the weighting factor λ of the data tag experience loss term is set to 1, because λ is too small, the contribution of information with tag data is smaller, and therefore λ ≧ 0 is generally set.
Further, in step 1, extracting a feature vector of sample data in the database specifically includes: judging the data type of the sample data; determining a feature extraction method according to the data type; and extracting the feature vector of the sample data by using the determined feature extraction method.
It should be noted that one data corresponds to one feature vector, and the feature vector represents information of the data in the feature space. The feature extraction method is determined by the data type and characteristics of the sample data, and therefore, the data type of the sample data needs to be judged. When the sample data is judged to be three-dimensional object feature description data, extracting feature vectors of the sample data through a multi-view convolution neural network; when the sample data is judged to be text feature description data, feature vectors of the sample data are extracted through a Bag-of-Words model.
Therefore, in this embodiment, the multi-view convolutional neural network is used to extract the feature vector of the sample data, and after the sample data is input into the multi-view convolutional neural network, a 4096-dimensional MVCNN feature vector can be output.
The hypergraph structure constructed in this embodiment is Is the set of all points in the hypergraph, each point representing a datum, is the set of all hyper-edges in the hypergraph, each hyper-edge representing a high order association between those points connected by the hyper-edge. The method for constructing the hypergraph structure is a k-nearest neighbor method.
First, let k be 2, for each three-dimensional object, calculate the euclidean distance between its feature vector and the feature vectors of other three-dimensional objects, find the 2 three-dimensional objects closest to it, and establish a super edge between these three objects. In the embodiment, there are 2020 three-dimensional objects in total, so 2020 super edges are established, each super edge connects 3 objects, which we call express 3-degree association between the objects. Then let k be 4, for each three-dimensional object, find the 4 three-dimensional objects closest to it, and establish a super edge between these 5 objects. Thus we have further added 2020 super edges, each connecting 5 objects, which we call express 5 th order associations between objects. We further let k be 8 and 16, and establish the super-edge in the same way. Finally we obtained a hypergraph structure with 8080 hyperedges.
Further, the label vector set in step 1 is determined by the class to which the labeled data and the unlabeled data belong;
specifically, for a hypergraph structure comprising N verticesThe dimension of its tensor is 2N-1. Order toRepresents a power set of {1,2, …, N } and is used in combinationTo index each element in its tensor. For arbitraryIs defined as viThe strength of the connection between the set of points i ∈ ω if there is a super edge connection and only viAll vertices in i ∈ ω }, thenOtherwiseFor all the connection strengths(where ω ∈ ΨN) In a row vector arranged in a row with omega as an indexSince the vector is a special case of tensor, the row vectorIs a tensor, and its corresponding formula is:
using tensorsThe connection strength of all possible higher-order associations between N points, i.e. the tensor representation between the sets of points in the hypergraph structure, can be expressed as a tensorTensor if hypergraph structure changes, i.e. the strength of the connections of some hyperedges changesThe corresponding elements in (a) may also change.
Further, based on the above setting, it can be found that in step 1, the connection strength between any one point set in the initial hypergraph structure is expressed by a tensor, where the initial value of a line vector is expressed by the tensorCorresponding elements of the middle index ωThe calculation formula of (2) is as follows:
ω∈ΨN
in the formula (I), the compound is shown in the specification,is any point set { viCenter of | i ∈ ω }, viAs the point of the i-th spot,is a power set of the set Ω {1,2, …, N }, N being the number of vertices in the hypergraph structure,represents the ith point viTo the centerMay be a euclidean distance,is the set of points { viThe average distance between every two points in | i ∈ ω }, exp () is an exponential function with a natural constant e as the base, and is a super-edge set of the hypergraph structure.
And 2, introducing a potential energy loss function and an empirical loss function into a label vector set in the database, expressing the potential energy of the hypergraph structure and the point set by a tensor, generating a dynamic hypergraph structure learning model, performing optimization solution on the dynamic hypergraph structure learning model by using an alternative optimization method, and recording the model after the optimization solution as a label classification model.
Specifically, the purpose of this embodiment is to obtain a label of unlabeled data in sample data, and set xiA feature vector representing the ith sample data, and a set of feature vectors X ═ X for all sample data1,x2,…,xN},yiA label vector representing the ith sample data, the set of label vectors for all sample data Y ═ Y1,y2,…,yNWhere for the label vector yiThe initial values of (a) are defined as follows:
for tagged data, if it belongs to class j, we have yijIf the data is unlabeled, all elements are set to 0.5, and the set of initial values of the label vectors of all sample data is marked as Y0。
Therefore, if (ω) is set to represent the number of points in the point set, the potential energy of the point set is calculated as:
where α is the balance parameter, (ω) is the number of points in the set of points, yiIs a label vector, x, of the ith sample dataiIs the feature vector of the ith sample data.
If the characteristics and labels of the point in the point set are similar, its potential energy is small, otherwise the potential energy is large.
And (3) expressing a label vector set, potential energy of the point set and tensor of the hypergraph structure in the database, introducing a potential energy loss function and an empirical loss function, and obtaining a calculation formula of a dynamic hypergraph structure learning model, wherein the calculation formula is as follows:
in the formula (I), the compound is shown in the specification,for the joint strength of the ω -th set of points,for all joint strengthsWhere row vectors, i.e. tensor representations of the hypergraph structure,vector of execution (hypergraph structure)Initial value of fωIs the potential energy of the point set, lambda and β are weight coefficients, Y is the label vector set0Is the initial set of values for the tag vector.
First term in the above formulaIs a potential energy loss term defined as: the joint strength of the point set is multiplied by the sum of the potential energy, and the term indicates that for the point set with larger potential energy, the super edge is not needed to connect the group of points, and if the super edge is connected, the joint strength is as small as possible; for a point set with a relatively large potential energy, it is preferable to have a super edge connecting the points and to have the highest possible connecting strength.
Second term in the above formulaFor the empirical loss term of the hypergraph structure, the term can be learned by setting the weight coefficient β to 10 to reduce the difference between the optimized dynamic hypergraph structure and the initially constructed hypergraph structureConvergence is accelerated in the learning process.
The third term λ R in the above formulaempAnd (Y) setting the weight coefficient lambda of the experience loss term of the label to be 1, so that the label obtained by learning the dynamic hypergraph structure learning model has small difference with the initial label vector of the sample data.
Further, in step 2, the optimization solution is performed on the dynamic hypergraph structure learning model by using an alternating optimization method, which specifically includes:
step 21, fixing the label vector set Y, and iteratively updating tensor expression of the hypergraph structure by using the projection gradient and the first objective functionThe calculation formula of the hypergraph structure iterative updating is as follows:
in the formula (I), the compound is shown in the specification,in order to be a gradient of the magnetic field,is tensor representation of the hypergraph structure after k iterations, h is the step size of each optimization, and P is the value of the feasible setProjection, f is all potential energy fω(where ω ∈ ΨN) A row vector which is arranged into a row by taking omega as an index, namely representing the potential energy of all point sets in a vector form;
specifically, the tensor representation of the hypergraph structure is updated iteratively while the label vector set Y is fixedThe first objective function is:
the constraint optimization of the function can be solved by utilizing projection gradient and set tensor expression of the hypergraph structureThe gradient of (a) is calculated as:
wherein f is all of fω(where ω ∈ ΨN) The potential energy of all point sets is represented in a vector form by a row vector arranged in a row with omega as an index. The tensor representation of the hypergraph structure is then updated by iterationNamely:
in the formula (I), the compound is shown in the specification,in order to be a gradient of the magnetic field,for the hypergraph structure after k iterations, h is the step length of each optimization, and P is the feasible setProjection of (2);
step 22, fixing the tensor representation of the hypergraph structureCalculating a tag transfer function by using the second objective function;
specifically, the second objective function is set as follows:
in the formula, ΨijFor all contained points viAnd vjα is a balance parameter, SijIs an element of the ith row and jth column of the matrix S, DSIs a diagonal matrix whose diagonal elements are the sum of S per row.
Thus, the optimal solution for the tag transfer function is:
and 23, repeating the step 21 and the step 22 until the dynamic hypergraph structure learning model converges, and finishing the optimization solution.
Specifically, after solving, the optimal label vector set Y and the optimal tensor representation of the hypergraph structure are obtainedThen the tag vector of the ith sample data is yiFind yiSubscript of the element having the highest value in (a) if yijIs yiThe ith sample data is classified into the jth class. In this way, 1620 unlabeled data without labeled information in the sample data can be classified.
Example two:
the embodiment also provides a dynamic hypergraph structure learning classification system based on tensor expression, and the system can be applied to gesture recognition and three-dimensional object recognition. The system comprises: a tensor expression unit and a label classification model generation unit; the tensor expression unit is used for extracting the eigenvector of sample data in a database, constructing a hypergraph structure according to the eigenvector, and expressing the connection strength between any point set in the hypergraph structure by utilizing tensor, wherein the sample data comprises labeled data and unlabeled data, and a label vector set is determined by the class to which the labeled data and the unlabeled data belong.
Specifically, in the present embodiment, the three-dimensional object feature description data is classified as an example, and the database uses a three-dimensional model data set (NTU) including 67 classes of 2020 objects, such as bombs, bottles, cars, chairs, cups, doors, maps, airplanes, swords, watches, tanks, trucks, etc., wherein 400 three-dimensional objects have tag information and 1620 three-dimensional objects have no tag information. Two parameters: the weight coefficient beta of the empirical loss term of the hypergraph structure is set to be 10, because if beta is larger, the difference between the finally optimized tag classification model and the hypergraph structure is smaller, and beta is too large, the hypergraph structure is difficult to optimize, and if beta is smaller, the difference between the finally optimized tag classification model and the hypergraph structure is larger, and beta is too small, overfitting is caused, so that an intermediate value is selected; the weighting factor λ of the data tag experience loss term is set to 1, because λ is too small, the contribution of information with tag data is smaller, and therefore λ ≧ 0 is generally set.
Further, the tensor expression unit extracts the eigenvector of the sample data in the database, and specifically includes: judging the data type of the sample data; determining a feature extraction method according to the data type; and extracting the feature vector of the sample data by using the determined feature extraction method.
It should be noted that one data corresponds to one feature vector, and the feature vector represents information of the data in the feature space. The feature extraction method is determined by the data type and characteristics of the sample data, and therefore, the data type of the sample data needs to be judged. When the sample data is judged to be three-dimensional object feature description data, extracting feature vectors of the sample data through a multi-view convolution neural network; when the sample data is judged to be text feature description data, feature vectors of the sample data are extracted through a Bag-of-Words model.
Therefore, in this embodiment, the multi-view convolutional neural network is used to extract the feature vector of the sample data, and after the sample data is input into the multi-view convolutional neural network, a 4096-dimensional MVCNN feature vector can be output.
The hypergraph structure constructed in this embodiment is Is the set of all points in the hypergraph, each point representing a datum, is the set of all hyper-edges in the hypergraph, each hyper-edge representing a high order association between those points connected by the hyper-edge. The method for constructing the hypergraph structure is a k-nearest neighbor method.
First, let k be 2, for each three-dimensional object, calculate the euclidean distance between its feature vector and the feature vectors of other three-dimensional objects, find the 2 three-dimensional objects closest to it, and establish a super edge between these three objects. In the embodiment, there are 2020 three-dimensional objects in total, so 2020 super edges are established, each super edge connects 3 objects, which we call express 3-degree association between the objects. Then let k be 4, for each three-dimensional object, find the 4 three-dimensional objects closest to it, and establish a super edge between these 5 objects. Thus we have further added 2020 super edges, each connecting 5 objects, which we call express 5 th order associations between objects. We further let k be 8 and 16, and establish the super-edge in the same way. Finally we obtained a hypergraph structure with 8080 hyperedges.
For a hypergraph structure containing N verticesThe dimension of its tensor is 2N-1. Order toRepresents a power set of {1,2, …, N } and is used in combinationTo index each element in its tensor, for any ω ∈ ΨN,Is defined as viThe strength of the connection between the set of points i ∈ ω if there is a super edge connection and only viAll vertices in i ∈ ω }, thenOtherwiseFor all the connection strengths(where ω ∈ ΨN) In a row vector arranged in a row with omega as an indexSince the vector is a special case of tensor, the row vectorIs a tensor, and its corresponding formula is:
using tensorsThe connection strength of all possible higher-order associations between N points, i.e. the tensor representation between the sets of points in the hypergraph structure, can be expressed as a tensorTensor if hypergraph structure changes, i.e. the strength of the connections of some hyperedges changesThe corresponding elements in (a) may also change.
Further, based on the setting, the tensor expression unit tensor-expresses the connection strength between any one point set in the hypergraph structure by using a tensor, specifically includes: initial values of the row vectors in the tensor representationCorresponding element with middle index of omegaThe calculation formula of (2) is as follows:
ω∈ΨN
in the formula (I), the compound is shown in the specification,is any point set { viCenter of | i ∈ ω }, viAs the point of the i-th spot,is a power set with the set omega being 1,2, …, N being the number of vertices in the hypergraph structure,represents the ith point viTo the centerThe distance of (a) to (b),is the set of points { viThe average distance between every two points in | i ∈ ω } is the super-edge set of the hypergraph structure.
The label classification model generation unit is used for introducing potential energy loss functions and experience loss functions into potential energy of a label vector set, a hypergraph structure represented by a tensor and a point set in a database to generate a dynamic hypergraph structure learning model, optimizing and solving the dynamic hypergraph structure learning model by using an alternative optimization method, recording the optimized and solved model as a label classification model, and the label classification model is used for solving the optimal solution of the label vector set to perform data classification.
Specifically, the purpose of this embodiment is to obtain a label of unlabeled data in sample data, and set xiA feature vector representing the ith sample data, and a set of feature vectors X ═ X for all sample data1,x2,…,xN},yiA label vector representing the ith sample data, the set of label vectors for all sample data Y ═ Y1,y2,…,yNWhere for the label vector yiThe initial values of (a) are defined as follows:
for tagged data, if it belongs to class j, we have yijIf the data is unlabeled, all elements are set to 0.5, and the set of initial values of the label vectors of all sample data is marked as Y0。
Therefore, it is assumed that (ω) represents the number of points in the point set, and the label classification model generation unit calculates the potential energy of the point set using the following calculation formula:
where α is the balance parameter, (ω) is the number of points in the set of points, yiIs a label vector, x, of the ith sample dataiIs the feature vector of the ith sample data.
If the characteristics and labels of the point in the point set are similar, its potential energy is small, otherwise the potential energy is large.
And (3) expressing a label vector set, potential energy of the point set and tensor of the hypergraph structure in the database, introducing a potential energy loss function and an empirical loss function, and obtaining a calculation formula of a dynamic hypergraph structure learning model, wherein the calculation formula is as follows:
in the formula (I), the compound is shown in the specification,for the joint strength of the ω -th set of points,for all joint strengthsWhere row vectors, i.e. tensor representations of the hypergraph structure,vector of execution (hypergraph structure)Initial value of fωIs the potential energy of the point set, lambda and β are weight coefficients, Y is the label vector set0Is the initial set of values for the tag vector.
First term in the above formulaIs a potential energy loss term defined as: the joint strength of the point set is multiplied by the sum of the potential energy, and the term indicates that for the point set with larger potential energy, the super edge is not needed to connect the group of points, and if the super edge is connected, the joint strength is as small as possible; for a point set with a relatively large potential energy, it is preferable to have a super edge connecting the points and to have the highest possible connecting strength.
Second term in the above formulaThis term accelerates convergence during learning by setting the weighting factor β to 10 to reduce the difference between the optimized hypergraph structure and the initial hypergraph structure for the empirical loss term of the hypergraph structure.
The third term λ R in the above formulaempAnd (Y) setting the weight coefficient lambda of the experience loss term of the label to be 1, so that the label vector obtained by learning of the dynamic hypergraph structure learning model has small difference with the initial label vector of the sample data.
Further, when the label classification model generation unit performs optimization solution on the dynamic hypergraph structure learning model by using an alternative optimization method, the label classification model generation unit specifically includes:
firstly, fixing a label vector set Y, and iteratively updating tensor expression of a hypergraph structure by using projection gradient and a first objective functionThe calculation formula of the hypergraph structure iterative updating is as follows:
in the formula (I), the compound is shown in the specification,in order to be a gradient of the magnetic field,is tensor representation of the hypergraph structure after k iterations, h is the step length of each optimization, P is projection of the feasible set, and f is all potential energy fωRow vectors arranged in a row by taking omega as an index;
specifically, the tensor representation of the hypergraph structure is updated iteratively while the label vector set Y is fixedThe first objective function is:
the constraint optimization of the function can be solved by utilizing projection gradient and set tensor expression of the hypergraph structureThe gradient of (a) is calculated as:
wherein f is all of fω(where ω ∈ ΨN) The potential energy of all point sets is represented in a vector form by a row vector arranged in a row with omega as an index. The tensor representation of the hypergraph structure is then updated by iterationNamely:
in the formula (I), the compound is shown in the specification,in order to be a gradient of the magnetic field,for the hypergraph structure after k iterations, h is the step length of each optimization, and P is the feasible setProjection of (2);
second, the tensor representation of the fixed hypergraph structureCalculating a tag transfer function by using the second objective function;
specifically, the second objective function is set as follows:
in the formula, ΨijFor all contained points viAnd vjα is a balance parameter, SijIs an element of the ith row and jth column of the matrix S, DSIs a diagonal matrix whose diagonal elements are the sum of S per row.
Thus, the optimal solution for the tag transfer function is:
finally, repeating the two processes, and respectively fixing the label vector set Y and the tensor expression of the hypergraph structure againAnd completing the optimization solution until the dynamic hypergraph structure learning model converges.
Specifically, after solving, the optimal label vector set Y and the optimal tensor representation of the hypergraph structure are obtainedThen the tag vector of the ith sample data is yiFind yiSubscript of the element having the highest value in (a) if yijIs yiThe ith sample data is classified into the jth class. In this way, 1620 unlabeled data without labeled information in the sample data can be classified.
As shown in fig. 2, a label classification model is built by using the classification method in the present embodiment, and a support vector machine method and a conventional hypergraph learning method are used as comparison methods to classify a three-dimensional model data set (NTU) used in the present embodiment, where the classification accuracy is shown in table 1, the classification accuracy of the method in the present embodiment is 80.36%, the classification accuracy of the support vector machine method to the data set is 71.6%, and the classification accuracy of the conventional hypergraph learning method to the data set is 74.07%, and compared with the two classification methods, the classification accuracy of the method in the present embodiment is significantly improved.
TABLE 1
Comparison method | Accuracy of classification |
Support vector machine method | 71.6% |
Traditional hypergraph learning method | 74.07% |
Dynamic hypergraph structure learning method | 80.36% |
The technical scheme of the present application is described in detail above with reference to the accompanying drawings, and the present application provides a tensor representation-based dynamic hypergraph structure learning classification method and system, wherein the method includes: step 1, extracting characteristic vectors of sample data in a database, constructing a hypergraph structure according to the characteristic vectors, and expressing the connection strength between any point set in the hypergraph structure by using a tensor, wherein the sample data comprises label data and label-free data; and 2, introducing potential energy loss functions and empirical loss functions into potential energy of the label vector set, the hypergraph structure represented by the tensor and the point set in the database to generate a dynamic hypergraph structure learning model, performing optimization solution on the dynamic hypergraph structure learning model by using an alternative optimization method, and performing optimal solution of the label vector set after the model solution for data classification. According to the technical scheme, tensor is introduced as a representation form of the dynamic hypergraph structure and a dynamic hypergraph structure learning method, the hypergraph structure and the label vectors of data are optimized alternately, and finally data classification is achieved according to the optimal solution of the label vectors of the data.
The steps in the present application may be sequentially adjusted, combined, and subtracted according to actual requirements.
The units in the device can be merged, divided and deleted according to actual requirements.
Although the present application has been disclosed in detail with reference to the accompanying drawings, it is to be understood that such description is merely illustrative and not restrictive of the application of the present application. The scope of the present application is defined by the appended claims and may include various modifications, adaptations, and equivalents of the invention without departing from the scope and spirit of the application.
Claims (10)
1. A dynamic hypergraph structure learning classification method based on tensor expression is characterized by comprising the following steps:
step 1, extracting characteristic vectors of sample data in a database, constructing a hypergraph structure according to the characteristic vectors, and expressing the connection strength between any point set in the hypergraph structure by using tensor, wherein the sample data comprises label data and label-free data;
step 2, introducing potential energy loss functions and empirical loss functions into potential energy of the label vector set, the hypergraph structure represented by tensor and the point set in the database to generate a dynamic hypergraph structure learning model, performing optimization solution on the dynamic hypergraph structure learning model by using an alternative optimization method, recording the optimized model as a label classification model, and performing data classification by using the label classification model to solve the optimal solution of the label vector set,
the calculation formula of the dynamic hypergraph structure learning model is as follows:
in the formula (I), the compound is shown in the specification,for the joint strength of the ω -th set of points,for all joint strengthsWhere row vectors are arranged as a row indexed by omega,as a row vectorInitial value of fωIs the potential energy of the point set, lambda and β are weight coefficients, Y is the label vector set0Is the initial set of values for the tag vector.
2. The method for learning and classifying a dynamic hypergraph structure based on tensor representation as claimed in claim 1, wherein in step 1, tensor representation is performed on the connection strength between any point set in the hypergraph structure by using tensor, and specifically includes: said initial values of the row vectors in the tensor representationCorresponding element with middle index of omegaThe calculation formula of (2) is as follows:
ω∈ΨN
in the formula (I), the compound is shown in the specification,is any point set { viCenter of | i ∈ ω }, viAs the point of the i-th spot,is a power set of the set Ω {1,2, …, N }, N being the number of vertices in the hypergraph structure,represents the ith point viTo the centerThe distance of (a) to (b),is the set of points { viThe average distance between every two points in | i ∈ ω } is the super-edge set of the hypergraph structure.
3. The tensor representation-based dynamic hypergraph structure learning classification method as recited in claim 1, wherein in the step 2, the potential energy of the point set is calculated by the formula:
wherein α is a balance parameter, and ω is the sameNumber of points in the set of points, yiIs a label vector, x, of the ith sample dataiIs the feature vector of the ith sample data.
4. The tensor representation-based dynamic hypergraph structure learning classification method as claimed in any one of claims 1 to 3, wherein in the step 2, the optimization solution is performed on the dynamic hypergraph structure learning model by using an alternative optimization method, which specifically includes:
step 21, fixing the label vector set Y, and iteratively updating the tensor expression of the hypergraph structure by using the projection gradient and the first objective functionWherein, the calculation formula of the hypergraph structure iterative update is as follows:
in the formula (I), the compound is shown in the specification,in order to be a gradient of the magnetic field,is tensor representation of the hypergraph structure after k iterations, h is the step length of each optimization, P is projection of the feasible set, and f is all potential energy fωRow vectors arranged in a row by taking omega as an index;
step 22, fixing the tensor representation of the hypergraph structureCalculating a tag transfer function by using the second objective function;
and 23, repeating the step 21 and the step 22 until the dynamic hypergraph structure learning model converges, and finishing the optimization solution.
5. The tensor expression-based dynamic hypergraph structure learning classification method as claimed in claim 1, wherein in step 1, extracting the feature vectors of the sample data in the database specifically comprises:
judging the data type of the sample data;
determining a feature extraction method according to the data type;
and extracting the feature vector of the sample data by using the determined feature extraction method.
6. The tensor representation-based dynamic hypergraph structure learning classification method of claim 1, wherein the set of label vectors is determined by a class to which the labeled data and the unlabeled data belong.
7. The tensor representation-based dynamic hypergraph structure learning classification method as claimed in claim 1, wherein the method is suitable for gesture recognition and three-dimensional object recognition.
8. A system for learning and classifying a dynamic hypergraph structure based on tensor representation, the system comprising: a tensor expression unit and a label classification model generation unit;
the tensor expression unit is used for extracting the eigenvector of sample data in a database, constructing a hypergraph structure according to the eigenvector, and expressing the connection strength between any point set in the hypergraph structure by using a tensor, wherein the sample data comprises label data and label-free data;
the label classification model generation unit is used for introducing a potential energy loss function and an empirical loss function into potential energy of a label vector set, the hypergraph structure represented by tensor and the point set in the database to generate a dynamic hypergraph structure learning model, performing optimization solution on the dynamic hypergraph structure learning model by using an alternative optimization method, recording the model after optimization solution as a label classification model, and performing data classification by using the label classification model to solve the optimal solution of the label vector set,
the calculation formula of the dynamic hypergraph structure learning model is as follows:
in the formula (I), the compound is shown in the specification,for the joint strength of the ω -th set of points,for all joint strengthsWhere row vectors are arranged as a row indexed by omega,as a row vectorInitial value of fωIs the potential energy of the point set, lambda and β are weight coefficients, Y is the label vector set0Is the initial set of values for the tag vector.
9. The tensor representation-based dynamic hypergraph structure learning classification system of claim 8, wherein the label classification model generation unit is further configured to: calculating potential energy of the point set, wherein the potential energy is calculated according to the formula:
where α is the balance parameter, (ω) is the number of points in the set of points, yiIs a label vector, x, of the ith sample dataiIs the feature vector of the ith sample data.
10. The system for learning and classifying a dynamic hypergraph structure based on tensor expression as claimed in claim 9, wherein the label classification model generation unit, when performing the optimization solution on the dynamic hypergraph structure learning model by using an alternating optimization method, specifically comprises:
fixing the label vector set Y, and iteratively updating tensor representation of the hypergraph structure by using projection gradient and a first objective functionWherein, the calculation formula of the hypergraph structure iterative update is as follows:
in the formula (I), the compound is shown in the specification,in order to be a gradient of the magnetic field,is tensor representation of the hypergraph structure after k iterations, h is the step length of each optimization, P is projection of the feasible set, and f is all potential energy fωRow vectors arranged in a row by taking omega as an index;
tensor representation of a fixed hypergraph structureCalculating a tag transfer function by using the second objective function;
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