CN112508117A - Self-adaptive multi-view dimension reduction method and device based on graph embedding - Google Patents

Self-adaptive multi-view dimension reduction method and device based on graph embedding Download PDF

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CN112508117A
CN112508117A CN202011484154.4A CN202011484154A CN112508117A CN 112508117 A CN112508117 A CN 112508117A CN 202011484154 A CN202011484154 A CN 202011484154A CN 112508117 A CN112508117 A CN 112508117A
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尹宝才
张超辉
王博岳
胡永利
孙艳丰
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Abstract

The self-adaptive multi-view dimension reduction method and device based on graph embedding can fully explore the relevance of data among different views, do not ignore the relation between data in a single view and can highlight the importance of partial features. The method comprises the following steps: (1) embedding high-dimensional data into a low-dimensional space by means of graph embedding; (2) calculating the distance between different samples according to the same view, and measuring the similarity of different samples; (3) the same similarity matrix is shared by different visual angles to explore the relation between samples of different visual angles; (4) measuring the similarity, and exploring the relation among different views; (5) and obtaining a projection matrix of each view, and multiplying the projection matrix by the original data to obtain a final dimension reduction result.

Description

Self-adaptive multi-view dimension reduction method and device based on graph embedding
Technical Field
The invention relates to the technical field of data mining, machine learning and pattern recognition, in particular to a graph embedding-based self-adaptive multi-view dimension reduction method and a graph embedding-based self-adaptive multi-view dimension reduction device.
Background
Dimension reduction is a common basic method for processing high-dimensional data, and aims to reduce the characteristic dimension of the data from an original dimension to a specified dimension, so that the data subjected to dimension reduction can still keep a local structure between the data, the similar data are more similar, and the difference between the dissimilar data is larger. Over the past few decades, many classical dimension reduction methods (e.g., PCA dimension reduction, LLE dimension reduction, CCA dimension reduction, etc.) have been proposed and have had great success in data mining, image processing, etc.
In today's society, with the widespread use of technologies such as cameras and sensors, data is often composed of different information sources, modalities or features. For example, the same news article may be reported in different languages; pictures can be characterized by HOG, GIST, LBP, etc.; a person may be photographed by cameras from different angles, which may describe different characteristic information of the data, all referred to as multi-view data.
The current main method for machine learning is to perform dimensionality reduction on data represented by a single view, which is called single-view dimensionality reduction (or traditional dimensionality reduction), because it does not consider relevant information from different views, easily causes a partial problem, and therefore cannot truly reflect the full appearance of the data. For multi-view data, the compatible information and complementary information of each view are utilized to comprehensively reflect the data overview, so that the dimension reduction performance is improved.
With the advent of the big data age, people have increasingly advanced data acquisition and storage capacity, but the huge amount of data can cause the overload of scientific information. The method has the advantages that more and more researchers attract attention aiming at the dimensionality reduction of multi-view data, the multi-view data without any label is reduced to a very low dimensionality, the data can be processed by the existing method, and meanwhile, the occupied space of a memory is saved. Plays an important role in information retrieval, biological data analysis, medical diagnosis and the like.
The multi-view dimensionality reduction aims to consider information of different views, and finally obtain low-dimensional representation of the multi-view high-dimensional data by fusing the information of each view, so that the original structural relationship can be maintained under the condition that the data dimensionality is low. Most of the existing methods for solving the multi-view dimension reduction problem directly use a single-view dimension reduction method to directly reduce the dimension of multi-view data, and the correlation and complementarity between views are not considered. PCA is the most classical dimension reduction method, and the flexible multi-view collaborative dimension reduction proposed by Zhang Changqing and the like is concerned by directly processing multi-view data and enhancing the correlation among the views by using a Hilbert-Schmidt independent criterion. However, the current multi-view dimension reduction method has two defects: 1) the relevance of data between different views is not fully explored. 2) The relevance between different-view data is explored, but the relation between the data and the data in a single view is ignored. 3) Most dimension reduction methods cannot highlight the importance of part of the features.
Disclosure of Invention
In order to overcome the defects of the prior art, the technical problem to be solved by the invention is to provide a graph embedding-based adaptive multi-view dimension reduction method, which can fully explore the relevance of data among different views, does not ignore the relation between data and data in a single view, and can highlight the importance of partial features.
The technical scheme of the invention is as follows: the self-adaptive multi-view dimension reduction method based on graph embedding comprises the following steps:
(1) embedding high-dimensional data into a low-dimensional space by means of graph embedding;
(2) calculating the distance between different samples according to the same view, and measuring the similarity of different samples;
(3) the same similarity matrix is shared by different visual angles to explore the relation between samples of different visual angles;
(4) measuring the similarity, and exploring the relation among different views;
(5) and obtaining a projection matrix of each view, and multiplying the projection matrix by the original data to obtain a final dimension reduction result.
Firstly, embedding high-dimensional data into a low-dimensional space in a graph embedding mode; secondly, calculating distances among different samples according to the same view to measure the similarity of the different samples; then, the same similarity matrix is shared through different visual angles to fully explore the relation among samples among different visual angles; finally, measuring the similarity by distance, thereby exploring the relationship among different views; and finally, a projection matrix of each view is obtained, and a final dimensionality reduction result is obtained by multiplying the projection matrix and the original data, so that the relevance of data among different views can be fully explored, the relation between data in a single view and data is not ignored, and the importance of partial features can be highlighted.
Also provided is an adaptive multi-view dimension reduction device based on graph embedding, which comprises:
the embedding module is used for embedding the high-dimensional data into the low-dimensional space in a graph embedding mode;
the distance calculating module is used for measuring the similarity of different samples by calculating the distance between different samples with the same view;
the sharing module is used for exploring the relation between samples among different views by sharing one same similarity matrix among different views;
a measurement module that measures similarity to explore relationships between different views;
and the iteration module is used for obtaining a projection matrix of each view and obtaining a final dimension reduction result by multiplying the projection matrix and the original data.
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FIG. 1 is a flow chart illustrating an adaptive multi-view dimension reduction method based on graph embedding according to the present invention.
Detailed Description
As shown in FIG. 1, the adaptive multi-view dimension reduction method based on graph embedding includes the following steps:
(1) embedding high-dimensional data into a low-dimensional space by means of graph embedding;
(2) calculating the distance between different samples according to the same view, and measuring the similarity of different samples;
(3) the same similarity matrix is shared by different visual angles to explore the relation between samples of different visual angles;
(4) measuring the similarity, and exploring the relation among different views;
(5) and obtaining a projection matrix of each view, and multiplying the projection matrix by the original data to obtain a final dimension reduction result.
Firstly, embedding high-dimensional data into a low-dimensional space in a graph embedding mode; secondly, calculating distances among different samples according to the same view to measure the similarity of the different samples; then, the same similarity matrix is shared through different visual angles to fully explore the relation among samples among different visual angles; finally, measuring the similarity by distance, thereby exploring the relationship among different views; and finally, a projection matrix of each view is obtained, and a final dimensionality reduction result is obtained by multiplying the projection matrix and the original data, so that the relevance of data among different views can be fully explored, the relation between data in a single view and data is not ignored, and the importance of partial features can be highlighted.
Preferably, in the step (1),
suppose a data set is given
Figure BDA0002838503730000041
Where D represents the dimension of each sample data, N represents the number of samples,
Figure BDA0002838503730000042
is a low-dimensional representation matrix of data X, where K represents the data dimension after sample dimensionality reduction and K <, if the original data XiAnd xjSimilarly, then their lower dimension represents ziAnd zjSimilarly, the similarity between the ith and jth samples is expressed as sijThen the solved target formula (1) represents:
Figure BDA0002838503730000043
the graph regularization of equation (1) is expressed as:
Figure BDA0002838503730000044
wherein L represents a groupA normalized graph Laplacian matrix, and
Figure BDA0002838503730000045
d is a diagonal matrix, wherein
Figure BDA0002838503730000046
For multi-view data, equation (2) becomes:
Figure BDA0002838503730000051
where m denotes data of different views, Z(m)Low dimensional data, L, representing the mth view(m)Normalized graph Laplace matrix representing mth view, again because of the low dimensional data Z(m)Is by projecting a matrix P(m)And original data X(m)Obtained, so equation (3) is written as:
Figure BDA0002838503730000052
Figure BDA0002838503730000058
wherein,
Figure BDA00028385037300000511
the purpose of (a) is to avoid trivial solution.
Preferably, in the step (3), the formula (4) becomes:
Figure BDA0002838503730000053
Figure BDA0002838503730000057
equation (6) adds a regularization term, F-norm of the S-matrix, and equation (6) becomes:
Figure BDA0002838503730000054
Figure BDA00028385037300000510
preferably, in the step (4), after adding the constraint on the original data, equation (7) becomes:
Figure BDA0002838503730000055
Figure BDA0002838503730000059
equation (8) does not take into account data reconstruction errors:
Figure BDA0002838503730000056
Figure BDA0002838503730000069
wherein
Figure BDA0002838503730000061
Represents projecting the raw data into a low-dimensional space, and
Figure BDA0002838503730000062
the data projected to the low-dimensional space is projected back to the original space, a difference value is calculated with the original data, and formula (8) is combined with formula (9) to obtain:
Figure BDA0002838503730000063
Figure BDA00028385037300000610
preferably, in the step (5), the projection matrix P of each view is finally obtained through iterative update(m)And selecting the dimensions of each dimension to be reduced,
firstly, a similarity matrix S is constructed by the original data, and when the similarity matrix S is fixed and is not changed, the similarity matrix S in the formula (10) is
Figure BDA0002838503730000064
And
Figure BDA0002838503730000065
and (3) fixing, and constructing a Lagrangian function for the residual term to obtain:
Figure BDA0002838503730000068
(11)
solving for P by a method of eigenvalue decomposition(m)And specifies how many dimensions to reduce to;
while fixing the projection matrix P(m)Then, the reconstruction error term does not participate in the update, and equation (10) becomes:
Figure BDA0002838503730000066
Figure BDA00028385037300000611
the distance between the low-dimensional data and the original data in equation (12) is set as dij:
Figure BDA0002838503730000067
Equation (12) is written as:
Figure BDA0002838503730000071
Figure BDA0002838503730000075
solving equation (14) becomes:
Figure BDA0002838503730000072
Figure BDA0002838503730000074
thus, obtain
Figure BDA0002838503730000073
It will be understood by those skilled in the art that all or part of the steps in the method of the above embodiments may be implemented by hardware instructions related to a program, the program may be stored in a computer-readable storage medium, and when executed, the program includes the steps of the method of the above embodiments, and the storage medium may be: ROM/RAM, magnetic disks, optical disks, memory cards, and the like. Therefore, corresponding to the method of the present invention, the present invention also includes an adaptive multi-view dimension reduction device based on graph embedding, which is generally represented in the form of functional modules corresponding to the steps of the method. The device includes:
the embedding module is used for embedding the high-dimensional data into the low-dimensional space in a graph embedding mode;
the distance calculating module is used for measuring the similarity of different samples by calculating the distance between different samples with the same view;
the sharing module is used for exploring the relation between samples among different views by sharing one same similarity matrix among different views;
a measurement module that measures similarity to explore relationships between different views;
and the iteration module is used for obtaining a projection matrix of each view and obtaining a final dimension reduction result by multiplying the projection matrix and the original data.
The technical means of the present invention will be described in more detail below.
The self-adaptive multi-view dimensionality reduction method based on graph embedding mainly comprises the following steps of:
1. dimension reduction based on graph embedding
Suppose a data set is given
Figure BDA0002838503730000081
Where D represents the dimension of each sample data and N represents the number of samples.
Figure BDA0002838503730000082
Is a low-dimensional representation matrix of data X, where K represents the data dimension after sample dimensionality reduction and K < N. If the original data xiAnd xjSimilarly, then their lower dimension represents ziAnd zjShould be similar. The similarity between the ith and jth samples is expressed as sijThen the object we solve can be represented by the following formula:
Figure BDA0002838503730000083
(1) the graph regularization representation of (a) can be written as the following function:
Figure BDA0002838503730000084
wherein L in the formula (2) represents a normalized graph Laplacian matrix, and
Figure BDA0002838503730000085
d is oneA diagonal matrix of which
Figure BDA0002838503730000086
For multi-view data, equation (2) becomes:
Figure BDA0002838503730000087
where m denotes data of different views, Z(m)Low dimensional data, L, representing the mth view(m)A normalized graph laplacian matrix representing the mth view. And because of the low-dimensional data Z(m)Is by projecting a matrix P(m)And original data X(m)The result is that equation (3) can be written again as follows:
Figure BDA0002838503730000088
Figure BDA0002838503730000089
wherein,
Figure BDA00028385037300000810
the purpose of (a) is to avoid trivial solution. (4) The formula does not consider the association relationship between views.
2. Adaptive local structure learning
Since equation (4) does not explore the relationship between views, how the relationship between views is integrated will be described next. The relationship between views can be effectively explored by sharing the similarity matrix through multiple views, because if the similarity matrix between views is the same, the laplacian matrix between views is also the same, and then equation (4) becomes:
Figure BDA0002838503730000091
Figure BDA0002838503730000098
equation (5) is a variation of the following equation:
Figure BDA0002838503730000092
Figure BDA0002838503730000097
however, in the case of equation (6), the similarity of two most similar samples is 1, and the similarity of other samples is 0, and to solve this problem, a regularization term is added to the F norm of the S matrix, and equation (6) becomes:
Figure BDA0002838503730000093
Figure BDA0002838503730000096
3. adaptive multi-view dimensionality reduction based on graph embedding
The similarity in the formula (7) only makes a constraint on the data after dimensionality reduction, and does not constrain the original data before dimensionality reduction, so that the data structure after dimensionality reduction is the same as that before dimensionality reduction. So, after adding the constraints on the original data, equation (7) becomes:
Figure BDA0002838503730000094
Figure BDA0002838503730000095
equation (8) does not take into account data reconstruction errors:
Figure BDA0002838503730000101
Figure BDA0002838503730000108
wherein
Figure BDA0002838503730000102
Represents projecting the raw data into a low-dimensional space, and
Figure BDA0002838503730000103
the data representing the projection to the low dimensional space is projected back to the original space and a difference is calculated from the original data. Combining equation (8) with equation (9) yields the final equation:
Figure BDA0002838503730000104
Figure BDA0002838503730000109
finally, through iterative update, solving P(m)And S.
(1) Fix S, update P(m)
Firstly, a similarity matrix S is constructed through original data, and when the similarity matrix S is fixed and is not changed, the similarity matrix S is represented by the formula (10)
Figure BDA0002838503730000105
And
Figure BDA0002838503730000106
and (3) fixing, and constructing a Lagrangian function for the residual term to obtain:
Figure BDA00028385037300001010
by means of the eigenvalue decomposition method, we can obtain P(m)And may specify how many dimensions to drop to.
(2) Fixed P(m)Update S
While fixing the projection matrix P(m)Then, the reconstruction error term in the formula does not participate in updating, and the formula (10) becomes:
Figure BDA0002838503730000107
Figure BDA0002838503730000115
the distance between the low-dimensional data and the original data in equation (12) is set as dij:
Figure BDA0002838503730000111
Equation (12) can be written as:
Figure BDA0002838503730000112
Figure BDA0002838503730000116
solving equation (14) may become:
Figure BDA0002838503730000113
Figure BDA0002838503730000117
thus, it can obtain
Figure BDA0002838503730000114
In summary, the projection matrix P of each view is finally obtained through continuous iterative updating of the method(m)And the dimensions of each view reduced dimension may be selected.
The data sets used in this experiment were a text data set and an image data set, where the text data set was 3sources and the image data set was IXMAS.
Where 3sources is a multi-view text dataset that collects news from three famous news sites, BBC news, The passerby, and The Guardian (The Guardian). This data set covers 416 different news stories during months 2 to 4 of 2009. The experiment selected 169 news from these three news sites. 3560, 3631 and 3068 dimensional features are respectively extracted from news of three visual angles, and the news categories belong to one of business, entertainment, health, sports, politics and technology. This dataset contains 169 samples, 6 classes. IXMAS is a multi-view image dataset that captures photographs taken at five different angles. The data set included ten people to perform a photo of viewing a watch, crossing arms, grabbing head, sitting, getting up, circling, walking, waving hands, hitting, kicking, picking up the eleven actions, each action repeated three times. This dataset contains 339 samples, 11 classes.
In order to verify the amplified dimensionality reduction performance, a graph embedding-based adaptive multi-view dimensionality reduction Method (MVDR) is compared with a classical PCA method, a multi-view non-negative matrix factorization method (MVNMF) and a flexible multi-view dimensionality reduction method (McDR) capable of directly performing multi-view dimensionality reduction, the dimensionality of data is reduced to 20 dimensions in a unified mode, the data subjected to dimensionality reduction is clustered through a unified clustering method, and clustering performance is compared.
The three indexes of Normalized Mutual Information (NMI), Accuracy (ACC) and Purity (Purity) are used for evaluating the clustering performance of the test, and the higher the value of the index is, the better clustering performance is reflected. Specific results are shown in tables 1 to 2.
Tables 1 and 2 show the clustering performance after dimensionality reduction of the two databases, 3sources and IXMAS, respectively. The single-view representation uses data of one view angle to perform dimensionality reduction and then clustering, and the multi-view representation combines the multi-view data to perform dimensionality reduction and then clustering. Clustering results with best single-view and multi-view performance are marked in bold in the table. From these two tables, it can be seen that the multi-view dimension reduction is superior to the corresponding single-view dimension reduction method in the result, and the MVDR dimension reduction method is superior to other methods no matter whether the single-view or the multi-view is adopted.
Observing these tables, the following conclusions can be drawn:
1) the MVDR is obviously superior to other multi-view dimension reduction methods, and the best performance can be realized on the clustering effect. The method is proved to be capable of well fusing multi-view information to reduce the dimension of the data and extracting more characteristic information to obtain a better clustering result.
2) In the experiment, the clustering result of multi-view dimensionality reduction is basically superior to that of single-view dimensionality reduction, and the effect of multi-view fusion dimensionality reduction is proved to be better than that of single-view dimensionality reduction.
In a word, compared with other dimension reduction methods, the MVDR realizes higher clustering precision and obtains better dimension reduction effect. This indicates that the MVDR method has better prospects in future practical applications.
Figure BDA0002838503730000121
Figure BDA0002838503730000131
TABLE 1
Figure BDA0002838503730000132
TABLE 2
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention in any way, and all simple modifications, equivalent variations and modifications made to the above embodiment according to the technical spirit of the present invention still belong to the protection scope of the technical solution of the present invention.

Claims (6)

1. The self-adaptive multi-view dimension reduction method based on graph embedding is characterized by comprising the following steps: the method comprises the following steps:
(1) embedding high-dimensional data into a low-dimensional space by means of graph embedding;
(2) calculating the distance between different samples according to the same view, and measuring the similarity of different samples;
(3) the same similarity matrix is shared by different visual angles to explore the relation between samples of different visual angles;
(4) measuring the similarity, and exploring the relation among different views;
(5) and obtaining a projection matrix of each view, and multiplying the projection matrix by the original data to obtain a final dimension reduction result.
2. The adaptive multi-view dimension reduction method based on graph embedding according to claim 1, characterized in that: in the step (1), the step (c),
suppose a data set is given
Figure FDA0002838503720000011
Where D represents the dimension of each sample data, N represents the number of samples,
Figure FDA0002838503720000012
is a low-dimensional representation matrix of data X, where K represents the dimension of the data after sample dimensionality reduction and K < N if the original data XiAnd xjSimilarly, then their lower dimension represents ziAnd zjSimilarly, the similarity between the ith and jth samples is expressed as sijThen the solved target formula (1) represents:
Figure FDA0002838503720000013
the graph regularization of equation (1) is expressed as:
Figure FDA0002838503720000014
wherein L represents a normalized graph Laplacian matrix, and
Figure FDA0002838503720000015
d is a diagonal matrix, wherein
Figure FDA0002838503720000016
For multi-view data, equation (2) becomes:
Figure FDA0002838503720000021
where m denotes data of different views, Z(m)Low dimensional data, L, representing the mth view(m)Normalized graph Laplace matrix representing mth view, again because of the low dimensional data Z(m)Is by projecting a matrix P(m)And original data X(m)Obtained, so equation (3) is written as:
Figure FDA0002838503720000022
Figure FDA0002838503720000023
wherein,
Figure FDA0002838503720000024
the purpose of (a) is to avoid trivial solution.
3. The adaptive multi-view dimension reduction method based on graph embedding according to claim 2, characterized in that: in the step (3), the formula (4) becomes:
Figure FDA0002838503720000025
Figure FDA0002838503720000026
equation (6) adds a regularization term, F-norm of the S-matrix, and equation (6) becomes:
Figure FDA0002838503720000027
Figure FDA0002838503720000028
4. the adaptive multi-view dimension reduction method based on graph embedding according to claim 3, characterized in that: in the step (4), after constraint on the original data is added, the formula (7) becomes:
Figure FDA0002838503720000029
Figure FDA00028385037200000210
equation (8) does not take into account data reconstruction errors:
Figure FDA0002838503720000031
Figure FDA0002838503720000032
wherein
Figure FDA0002838503720000033
Represents projecting the raw data into a low-dimensional space, and
Figure FDA0002838503720000034
the data projected to the low-dimensional space is projected back to the original space, a difference value is calculated with the original data, and formula (8) is combined with formula (9) to obtain:
Figure FDA0002838503720000035
Figure FDA0002838503720000036
5. the adaptive multi-view dimension reduction method based on graph embedding according to claim 4, characterized in that: in the step (5), the projection matrix P of each view is finally obtained through iterative update(m)And selecting the dimensions of each dimension to be reduced,
firstly, a similarity matrix S is constructed by the original data, and when the similarity matrix S is fixed and is not changed, the similarity matrix S in the formula (10) is
Figure FDA0002838503720000037
And
Figure FDA0002838503720000038
and (3) fixing, and constructing a Lagrangian function for the residual term to obtain:
Figure FDA0002838503720000039
solving for P by a method of eigenvalue decomposition(m)And specifies how many dimensions to reduce to;
while fixing the projection matrix P(m)Then, the reconstruction error term does not participate in the update, and equation (10) becomes:
Figure FDA00028385037200000310
Figure FDA0002838503720000041
the distance between the low-dimensional data and the original data in equation (12) is set as dij:
Figure FDA0002838503720000042
Equation (12) is written as:
Figure FDA0002838503720000043
Figure FDA0002838503720000044
solving equation (14) becomes:
Figure FDA0002838503720000045
Figure FDA0002838503720000046
thus, obtain
Figure FDA0002838503720000047
6. The self-adaptive multi-view dimension reduction device based on graph embedding is characterized in that: the device includes:
the embedding module is used for embedding the high-dimensional data into the low-dimensional space in a graph embedding mode;
the distance calculating module is used for measuring the similarity of different samples by calculating the distance between different samples with the same view;
the sharing module is used for exploring the relation between samples among different views by sharing one same similarity matrix among different views;
a measurement module that measures similarity to explore relationships between different views;
and the iteration module is used for obtaining a projection matrix of each view and obtaining a final dimension reduction result by multiplying the projection matrix and the original data.
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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113326898A (en) * 2021-06-25 2021-08-31 江苏大学 Distinguishable geometry preserving adaptive graph embedding method, apparatus, device and medium
CN114419382A (en) * 2021-11-30 2022-04-29 西安交通大学 Method and system for embedding picture of unsupervised multi-view image
CN115205941A (en) * 2022-07-13 2022-10-18 山西大学 Generic multi-view graph embedding-based relationship verification method

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20150117764A1 (en) * 2013-10-29 2015-04-30 Nec Laboratories America, Inc. Efficient distance metric learning for fine-grained visual categorization
CN108846046A (en) * 2018-05-30 2018-11-20 大连理工大学 The image search method of insertion is kept based on multi-angle of view Partial Reconstruction
CN110378365A (en) * 2019-06-03 2019-10-25 广东工业大学 A kind of multiple view Subspace clustering method based on joint sub-space learning

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20150117764A1 (en) * 2013-10-29 2015-04-30 Nec Laboratories America, Inc. Efficient distance metric learning for fine-grained visual categorization
CN108846046A (en) * 2018-05-30 2018-11-20 大连理工大学 The image search method of insertion is kept based on multi-angle of view Partial Reconstruction
CN110378365A (en) * 2019-06-03 2019-10-25 广东工业大学 A kind of multiple view Subspace clustering method based on joint sub-space learning

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
何进荣;闭应洲;丁立新;刘斌;: "局部差异正则化的边界判别投影", 计算机学报, no. 04, 5 December 2016 (2016-12-05) *

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113326898A (en) * 2021-06-25 2021-08-31 江苏大学 Distinguishable geometry preserving adaptive graph embedding method, apparatus, device and medium
CN113326898B (en) * 2021-06-25 2022-02-18 江苏大学 Distinguishable geometry preserving adaptive graph embedding method, apparatus, device and medium
CN114419382A (en) * 2021-11-30 2022-04-29 西安交通大学 Method and system for embedding picture of unsupervised multi-view image
CN115205941A (en) * 2022-07-13 2022-10-18 山西大学 Generic multi-view graph embedding-based relationship verification method

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