CN113269231A - Local kernel-based optimal neighbor multi-core clustering method and system - Google Patents

Local kernel-based optimal neighbor multi-core clustering method and system Download PDF

Info

Publication number
CN113269231A
CN113269231A CN202110447615.9A CN202110447615A CN113269231A CN 113269231 A CN113269231 A CN 113269231A CN 202110447615 A CN202110447615 A CN 202110447615A CN 113269231 A CN113269231 A CN 113269231A
Authority
CN
China
Prior art keywords
matrix
kernel
representing
core
clustering
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202110447615.9A
Other languages
Chinese (zh)
Inventor
朱信忠
徐慧英
刘吉元
刘新旺
赵建民
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Zhejiang Normal University CJNU
Original Assignee
Zhejiang Normal University CJNU
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Zhejiang Normal University CJNU filed Critical Zhejiang Normal University CJNU
Priority to CN202110447615.9A priority Critical patent/CN113269231A/en
Publication of CN113269231A publication Critical patent/CN113269231A/en
Priority to PCT/CN2022/082643 priority patent/WO2022227956A1/en
Priority to LU503092A priority patent/LU503092B1/en
Priority to ZA2022/07734A priority patent/ZA202207734B/en
Pending legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/23—Clustering techniques
    • G06F18/232—Non-hierarchical techniques
    • G06F18/2321—Non-hierarchical techniques using statistics or function optimisation, e.g. modelling of probability density functions
    • G06F18/23213—Non-hierarchical techniques using statistics or function optimisation, e.g. modelling of probability density functions with fixed number of clusters, e.g. K-means clustering
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/23—Clustering techniques
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/21—Design or setup of recognition systems or techniques; Extraction of features in feature space; Blind source separation
    • G06F18/213—Feature extraction, e.g. by transforming the feature space; Summarisation; Mappings, e.g. subspace methods

Abstract

The invention discloses an optimal neighbor multi-core clustering method and system based on local cores, wherein the related optimal neighbor multi-core clustering method based on local cores comprises the following steps: s11, acquiring clustering tasks and target data samples; s12, calculating a kernel matrix of each view corresponding to the target data sample, and performing centralization and normalization processing on the kernel matrix to obtain a processed kernel matrix; s13, establishing an optimal neighbor multi-core clustering target function based on a local core according to the obtained processed core matrix; s14, solving the established objective function in a circulation mode to obtain a division matrix after view fusion; and S15, carrying out k-means clustering on the obtained partition matrix to obtain a clustering result.

Description

Local kernel-based optimal neighbor multi-core clustering method and system
Technical Field
The invention relates to the technical field of data analysis, in particular to an optimal neighbor multi-core clustering method and system based on local cores.
Background
Kernel clustering has been widely explored in current machine learning and data mining literature. It implicitly maps the original non-separable data to a high-dimensional hilbert space, with the corresponding vertices having explicit decision boundaries. Then, various clustering methods are applied, including k-means [ K.Krishna And N.M.Murty, "Genetic k-means algorithm," IEEE Transactions On Systems Man And Cybernetics-Part B: Cybernetics, vol.29, No.3, pp.433-439,1999 ], fuzzy c-means [ J.C.Bezdek, R.Ehrlich, And W.full, "Fcm: The fuzzy c-means clustering," Computers & Geosciences, vol.10, No.2-3, pp.191-203,1984 ], spectral clustering [ A.Y.Ng, M.I.Jordan, And Y.Weiss, "On spectral clustering: Analysis," in Advance in, And G.I.J.P.12, And Y.Weiss, "On spectral clustering" And "Analysis: Analysis," in addition, And "classification into high-density data (PR.12, P.31, P.V.S.V.V.S. transformation, P.V.V.V.V.V.V.S. 849, P.V.S.V.V.V.S. transformation). Although core clustering algorithms have met with great success in a large number of applications, they can only process data using a single core. Meanwhile, the kernel functions have different types, such as polynomial, gaussian, linear, etc., and need to be parameterized manually. How to select the correct kernel function and optimize the predefined parameters for a particular clustering task remains an open question. Nevertheless, in most practical environments sample features are collected from different sources. For example, news is reported by a plurality of news agencies; a person can be described by a fingerprint, palm vein, palm print, DNA, etc. The most common approach is to concatenate all features into one vector. But it ignores the fact that these functions may not be directly comparable.
The multi-core clustering (MKC) algorithm solves the above problems using complementary information of pre-specified cores, has been widely studied in the literature, and can be roughly classified into three categories. The method in the first class is to construct a cluster consensus kernel by integrating low rank optimization [ A.Trivedi, P.rai, H.Daume III, and S.L.DuVall, "Multi' clustering with completed views," in NIPS Workshop, vol.224,2010 ]. For example, Zhou et al first recover a shared low rank matrix from the transition probability matrices of the multi-core and then cluster it as input to the standard markov chain method [ p.zhou, l.du, l.shi, h.wang, and y. -d.shen "," Recovery of corrected multiple kernels for clustering ", in two-Fourth International Joint Conference on intelligent Intelligence 2015 ]. The second category of techniques uses a partitioning matrix generated from each core to compute their clustering results. Liu et al first performs a kernel k-means on each incomplete view, and then explores complementary information among all incomplete clustering results to obtain a final solution [ X.Liu, X.Zhu, M.Li, L.Wang, C.Tang, J.Yin, D.Shen, H.Wang, and W.Gao, "Late fusion in complete multi-view clustering," IEEE transactions on pattern analysis and machine interaction, 2018 ]. In contrast, the third class of algorithms establishes a consistent kernel during the clustering process. The basic assumption of most algorithms is that the optimal kernel can be represented as a weighted combination of pre-specified kernels. In addition to this, various regularization methods have been proposed to constrain the kernel weights and affinity matrices. For example, Du et al use the L21 norm in the original feature space to minimize reconstruction errors [ l.du, p.zhou, l.shi, h.wang, m.fan, w.wang, and y. -d.shen, "Robust multiple kernel k-means using 21-norm," in two ways source International Joint Conference on intellectual Intelligence,2015 ]. Liu et al processed the incomplete kernel and proposed a cross-kernel complete term to calculate the missing term in the kernel and also learned the weight of the kernel [ X.Liu, X.Zhu, M.Li, L.Wang, E.Zhu, T.Liu, M.Kloft, D.Shen, J.yin, and W.Gao, "Multiple kernel k-means with complete kernel," IEEE transactions on pattern analysis and machine interaction, 2019 ]. Some studies do not assume that samples are equal in a kernel, but perform clustering by assigning different weights to samples, such as [ p.zhang, y.yang, b.peng, and m.he ], "Multi-view clustering algorithm based on variable weight and mkl," in International Joint Conference on Rough sets, springer,2017, pp.599-610 ].
The kernel alignment is an effective regularization method in the multi-kernel k-means algorithm [ G.F.Tzortzis and A.C.Likas, "Multiple view clustering using a weighted combination of empirical-based textures," IEEE Transactions on neural networks, vol.21, No.12, pp.1925-1938,2010 ]. However, Li et al claim that collation forces all pairs of samples to align equally with the same ideal similarity, which is in conflict with the accepted concept that aligning two more distant samples with low similarity in high dimensional space is less reliable [ m.li, x.liu, w.lei, d.yong, j.yin, and e.zhu, 'Multiple kernel clustering with local kernel alignment knowledge,' in International Joint Conference on intellectual alignment, 2016 ]. Observing local kernel techniques in m.gonen and a.a.margolin, "Localized data fusion for kernel k-means clustering with application to cancer biology," in advance in Neural Information Processing Systems,2014, pp.1305-1313 ] can better capture sample-specific features in the data, they construct local kernels using the neighborhood of each sample and maximize their sum of alignments with the ideal similarity matrix. Furthermore, it was demonstrated that Local kernels can help clustering algorithms to better exploit the information provided by closer sample pairs [ q.wang, y.dou, x.liu, f.xia, q.lv, and k.yang, "Local kernel alignment based multi-view clustering using extreme learning machine," neuro clustering, vol.275, pp.1099-1111,2018 ].
The above-mentioned MKC algorithm has two problems: the local density around a single data sample and the expressive power of the over-constrained learning optimal kernel are not fully considered. Specifically, the local kernel in [ m.li, x.liu, w.lei, d.yong, j.yin, and e.zhu, "Multiple kernel clustering with local kernel alignment mapping," in International Joint conference on intelligent intellectual alignment, 2016] globally sets the neighborhood number of each sample to a constant, which does not guarantee that all pairs of samples in the local kernel are relatively close. It is well known that it is less reliable to compare to distant pairs of samples. Thus, such local kernels cannot minimize unreliability due to neglecting the local density around a single data sample. Meanwhile, most multi-core clustering algorithms assume that the optimal core is a weighted combination of pre-specified cores, and ignore some more robust cores in the complementary set of core combinations.
Disclosure of Invention
The invention aims to provide an optimal neighbor multi-core clustering method and system based on local cores, aiming at the defects of the prior art.
In order to achieve the purpose, the invention adopts the following technical scheme:
an optimal neighbor multi-core clustering method based on local cores comprises the following steps:
s1, acquiring a clustering task and a target data sample;
s2, calculating a kernel matrix of each view corresponding to the target data sample, and performing centralization and normalization processing on the kernel matrix to obtain a processed kernel matrix;
s3, establishing an optimal neighbor multi-core clustering target function based on a local core according to the obtained processed core matrix;
s4, solving the established objective function in a circulation mode to obtain a partition matrix after view fusion;
and S5, carrying out k-means clustering on the obtained partition matrix to obtain a clustering result.
Further, the step S2 is to calculate a kernel matrix of each view corresponding to the target data sample, specifically: for target data sample
Figure BDA0003037454030000041
The p view in (1) is subjected to kernel function mapping to obtain a kernel matrix of the p view, which is expressed as:
Figure BDA0003037454030000042
wherein the content of the first and second substances,
Figure BDA0003037454030000043
and
Figure BDA0003037454030000044
represents the ith, j sample, and sigma represents the average of the distances between all the target data samples; e represents a natural constant; kp(i, j) represents the value of the ith row and j column in the kernel matrix of the pth view; m represents the number of views.
Further, in the step S3, an optimal neighbor multi-core clustering objective function based on the local core is established, and is represented as:
Figure BDA0003037454030000045
wherein H represents a partition matrix; β represents a combination coefficient; j represents an optimal neighbor core; n represents the number of all samples; μ represents an adaptive kernel similarity threshold; m represents a kernel relation matrix; h(i)Representing a partition matrix corresponding to the ith sample; h(i)TRepresents H(i)Transposing; beta is aTRepresenting a combined coefficient vector; m(i)A relation matrix representing an optimal neighbor kernel matrix of the ith sample; rho represents a hyper-parameter and needs to be set in advance; kβRepresenting the matrix obtained by combining the kernel matrices according to the beta coefficient,
Figure BDA0003037454030000046
HT denotes the transpose of the partition matrix; i iskRepresenting a k-order identity matrix; beta is apA value representing the beta vector position p;
Figure BDA0003037454030000047
indicates that for all p; j. the design is a square(i)＝S(i)TJS(i)，
Figure BDA0003037454030000048
Represents μ of the ith sample(i)Nearest neighbor, S(i)TDenotes S(i)Transposing;
Figure BDA0003037454030000049
represents μ(i)The identity matrix of (2).
Further, the step S4 is specifically:
s41, fixing J and beta, and optimizing H;
the objective function is converted into:
Figure BDA0003037454030000051
wherein A is(i)＝S(i)S(i)T；A(i)Denotes an intermediate variable, A(i)＝S(i)S(i)T；InRepresenting an n-order identity matrix;
by pairs
Figure BDA0003037454030000052
Decomposing the characteristic value to obtain a solution of the problem;
s42, fixing H and beta, and optimizing J;
the objective function is converted into:
Figure BDA0003037454030000053
wherein B represents an intermediate variable;
Figure BDA0003037454030000054
the matrix J obtains a solution to the problem by removing the negative characteristic values in the matrix B;
s43, fixing H and J, and optimizing beta;
the objective function is converted into:
Figure BDA0003037454030000055
wherein alpha isTRepresents a transposition of α;
Figure BDA0003037454030000056
representing the relationship between the local kernel matrices p and q for the sample of the ith;
Figure BDA0003037454030000057
a local kernel representing an ith sample in the pth kernel matrix;
Figure BDA0003037454030000058
a local kernel representing an ith sample in the qth kernel matrix; mpqTo representThe relationship between the kernel matrices p and q; kp、KqAnd alpha each represents an intermediate variable; alpha is alphapRepresenting the value of position p in the alpha vector.
Further, the termination conditions in the steps S41, S42, S43 are expressed as:
(objt+1-objt)/objt≤σ
wherein objt+1And objtValues representing the objective function of the t +1 th and the t-th iterations, respectively; σ denotes the setting accuracy.
Correspondingly, an optimal neighbor multi-core clustering system based on local cores is also provided, which comprises:
the acquisition module is used for acquiring clustering tasks and target data samples;
the calculation module is used for calculating a kernel matrix of each view corresponding to the target data sample, and performing centralization and normalization processing on the kernel matrix to obtain a processed kernel matrix;
the establishing module is used for establishing an optimal neighbor multi-core clustering target function based on a local core according to the obtained processed core matrix;
the solving module is used for solving the established objective function in a circulating mode to obtain a division matrix after view fusion;
and the clustering module is used for carrying out k-means clustering on the obtained partition matrix to obtain a clustering result.
Further, the calculating, by the calculating module, the kernel matrix of each view corresponding to the target data sample specifically includes: for target data sample
Figure BDA0003037454030000061
The p view in (1) is subjected to kernel function mapping to obtain a kernel matrix of the p view, which is expressed as:
Figure BDA0003037454030000062
wherein the content of the first and second substances,
Figure BDA0003037454030000063
and
Figure BDA0003037454030000064
represents the ith, j sample, and sigma represents the average of the distances between all the target data samples; e represents a natural constant; kp(i, j) represents the value of the ith row and j column in the kernel matrix of the pth view; m represents the number of views.
Further, the establishing module establishes an optimal neighbor multi-core clustering objective function based on a local core, which is expressed as:
Figure BDA0003037454030000065
wherein H represents a partition matrix; β represents a combination coefficient; j represents an optimal neighbor core; n represents the number of all samples; μ represents an adaptive kernel similarity threshold; m represents a kernel relation matrix; h(i)Representing a partition matrix corresponding to the ith sample; h(i)TRepresents H(i)Transposing; beta is aTRepresenting a combined coefficient vector; m(i)A relation matrix representing an optimal neighbor kernel matrix of the ith sample; rho represents a hyper-parameter and needs to be set in advance; kβRepresenting the matrix obtained by combining the kernel matrices according to the beta coefficient,
Figure BDA0003037454030000066
HTrepresenting a transpose of a partition matrix; i iskRepresenting a k-order identity matrix; beta is apA value representing the beta vector position p;
Figure BDA0003037454030000067
indicates that for all p; j. the design is a square(i)＝S(i)TJS(i)，
Figure BDA0003037454030000068
Represents μ of the ith sample(i)Nearest neighbor, S(i)TDenotes S(i)Transposing;
Figure BDA0003037454030000071
represents μ(i)The identity matrix of (2).
Further, the solving module specifically includes:
the first fixing module is used for fixing J and beta and optimizing H;
the objective function is converted into:
Figure BDA0003037454030000072
wherein A is(i)＝S(i)S(i)T；A(i)Denotes an intermediate variable, A(i)＝S(i)S(i)T；InRepresenting an n-order identity matrix;
by pairs
Figure BDA0003037454030000073
Decomposing the characteristic value to obtain a solution of the problem;
the second fixing module is used for fixing H and beta and optimizing J;
the objective function is converted into:
Figure BDA0003037454030000074
wherein B represents an intermediate variable;
Figure BDA0003037454030000075
the matrix J obtains a solution to the problem by removing the negative characteristic values in the matrix B;
the third fixing module is used for fixing H and J and optimizing beta;
the objective function is converted into:
Figure BDA0003037454030000076
wherein alpha isTRepresents a transposition of α;
Figure BDA0003037454030000077
representing the relationship between the local kernel matrices p and q for the sample of the ith;
Figure BDA0003037454030000078
a local kernel representing an ith sample in the pth kernel matrix;
Figure BDA0003037454030000079
a local kernel representing an ith sample in the qth kernel matrix; mpqRepresenting the relationship between the kernel matrices p and q; kp、KqAnd alpha each represents an intermediate variable; alpha is alphapRepresenting the value of position p in the alpha vector.
Further, the termination conditions in the first, second and third fixed modules are expressed as:
(objt+1-objt)/objt≤σ
wherein objt+1And objtValues representing the objective function of the t +1 th and the t-th iterations, respectively; σ denotes the setting accuracy.
Compared with the prior art, the invention provides a novel local kernel-based optimal neighbor multi-kernel clustering method and system, which comprises three parts of constructing a self-adaptive local kernel matrix, searching and constructing an optimal neighbor kernel matrix and fusing the construction of the self-adaptive local kernel matrix, searching and clustering the optimal neighbor kernel matrix, and fusing the three parts in the same target formula for solving. The method greatly improves the performance of the multi-core clustering algorithm, and the experimental results on four public data sets prove that the performance of the method is superior to that of the existing algorithm.
Drawings
FIG. 1 is a flowchart of a local-core-based optimal neighbor multi-core clustering method according to an embodiment;
fig. 2 is a comparison diagram of the local kernel provided in the first embodiment and the second embodiment.
Detailed Description
The embodiments of the present invention are described below with reference to specific embodiments, and other advantages and effects of the present invention will be easily understood by those skilled in the art from the disclosure of the present specification. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention. It is to be noted that the features in the following embodiments and examples may be combined with each other without conflict.
Aiming at the existing defects, the invention provides an optimal neighbor multi-core clustering method and system based on local cores.
Example one
The optimal neighbor multi-core clustering method based on local cores provided by this embodiment, as shown in fig. 1, includes:
s11, acquiring clustering tasks and target data samples;
s12, calculating a kernel matrix of each view corresponding to the target data sample, and performing centralization and normalization processing on the kernel matrix to obtain a processed kernel matrix;
s13, establishing an optimal neighbor multi-core clustering target function based on a local core according to the obtained processed core matrix;
s14, solving the established objective function in a circulation mode to obtain a division matrix after view fusion;
and S15, carrying out k-means clustering on the obtained partition matrix to obtain a clustering result.
Compared with the existing method, the new method for optimal neighbor multi-core clustering based on the local core comprises three parts of constructing an adaptive local core matrix, searching and constructing an optimal neighbor core matrix and fusing the construction of the adaptive local core matrix, searching and clustering the optimal neighbor core matrix, and fusing the three parts in the same target formula for solving, so that the clustering performance is greatly improved.
In step S12, a kernel matrix of each view corresponding to the target data sample is calculated, and the kernel matrix is subjected to centering and normalization processing to obtain a processed kernel matrix.
For target data sample
Figure BDA0003037454030000091
In the present embodiment, the gaussian kernel function is taken as an example, and finally, a kernel matrix of the vth view is obtained, where the kernel matrix is expressed as:
Figure BDA0003037454030000092
wherein the content of the first and second substances,
Figure BDA0003037454030000093
and
Figure BDA0003037454030000094
represents the ith, j sample, and sigma represents the average of the distances between all the target data samples; e represents a natural constant; kp(i, j) represents the value of the ith row and j column in the kernel matrix of the pth view; m represents the number of views.
Thus, a kernel matrix of v views can be obtained
Figure BDA0003037454030000095
Next, each kernel matrix is centered and normalized, i.e., the mean is 0 and the variance is 1.
In step S13, an optimal neighbor multi-core clustering objective function based on the local core is established according to the obtained processed core matrix.
In this embodiment, an adaptive local kernel matrix based on adaptation is employed. The adaptive local kernel matrix is constructed as follows: for the kernel matrix J, the local kernel matrix corresponding to the ith sample consists of samples with the similarity greater than zeta, and can be formally expressed as J(i)＝S(i)TJS(i)，
Figure BDA0003037454030000096
Represents μ of the ith sample(i)Nearest neighbor, S(i)TDenotes S(i)The transposing of (1). Drawing (A)2 is its visualization. Fig. 2(a) is a kernel matrix J, and the greater the inter-sample similarity, the higher the grayscale value, labeled 1, 0.75, 0.5, and 0.25 in order. When ζ is set to 0.75, subfigures 2(b.1) and 2(c.2) can be obtained. Fig. 2(b.1) shows an adaptive local kernel corresponding to the 1 st sample, and fig. 2(c.2) shows an adaptive local kernel corresponding to the 3 rd sample.
In this embodiment, an optimal neighbor multi-core clustering objective function based on a local core is established, and is expressed as:
Figure BDA0003037454030000097
Figure BDA0003037454030000101
wherein H represents a partition matrix; β represents a combination coefficient; j represents an optimal neighbor core; n represents the number of all samples; μ represents an adaptive kernel similarity threshold; m represents a kernel relation matrix; h(i)Representing a partition matrix corresponding to the ith sample; h(i)TRepresents H(i)Transposing; beta is aTRepresenting a combined coefficient vector; m(i)A relation matrix representing an optimal neighbor kernel matrix of the ith sample; rho represents a hyper-parameter and needs to be set in advance; kβRepresenting the matrix obtained by combining the kernel matrices according to the beta coefficient,
Figure BDA0003037454030000102
HTrepresenting a transpose of a partition matrix; i iskRepresenting a k-order identity matrix; beta is apA value representing the beta vector position p;
Figure BDA0003037454030000103
indicates that for all p; j. the design is a square(i)＝S(i)TJS(i)，
Figure BDA0003037454030000104
Represents μ of the ith sample(i)Nearest neighbor, S(i)TDenotes S(i)Transposing;
Figure BDA0003037454030000105
represents μ(i)The identity matrix of (2).
In step S14, the established objective function is solved in a cyclic manner to obtain a partition matrix after view fusion. The method specifically comprises the following steps:
s141, fixing J and beta, and optimizing H;
the objective function is converted into:
Figure BDA0003037454030000106
wherein A is(i)＝S(i)S(i)T；A(i)Denotes an intermediate variable, A(i)＝S(i)S(i)T；InRepresenting an n-order identity matrix;
by pairs
Figure BDA0003037454030000107
Decomposing the characteristic value to obtain a solution of the problem;
s142, fixing H and beta, and optimizing J;
the objective function is converted into:
Figure BDA0003037454030000108
wherein B represents an intermediate variable;
Figure BDA0003037454030000109
the matrix J obtains a solution to the problem by removing the negative characteristic values in the matrix B;
s143, fixing H and J, and optimizing beta;
the objective function is converted into:
Figure BDA0003037454030000111
wherein alpha isTRepresents a transposition of α;
Figure BDA0003037454030000112
representing the relationship between the local kernel matrices p and q for the sample of the ith;
Figure BDA0003037454030000113
a local kernel representing an ith sample in the pth kernel matrix;
Figure BDA0003037454030000114
a local kernel representing an ith sample in the qth kernel matrix; mpqRepresenting the relationship between the kernel matrices p and q; kp、KqAnd alpha each represents an intermediate variable; alpha is alphapRepresenting the value of position p in the alpha vector.
This is a standard QP problem that can be solved by existing algorithmic packages.
In the prior art, the algorithm can be solved by a Lagrange multiplier method, and the algorithm is directly called in Matlab for solving.
In the present embodiment, steps S141, S142, and S143 need to be performed alternately by an alternating method until convergence, where the termination condition (i.e., convergence condition) is expressed as:
(objt+1-objt)/objt≤σ
wherein objt+1And objtValues representing the objective function of the t +1 th and the t-th iterations, respectively; σ denotes the setting accuracy.
In step S15, k-means clustering is performed on the obtained partition matrix to obtain a clustering result.
And performing k-means clustering on the obtained partition matrix to obtain a clustering result, namely performing standard k-means clustering on the matrix H to obtain a final clustering result.
Compared with the whole kernel matrix ONKC, the clustering performance obtained by the method is different by adopting the self-adaptive local kernel matrix of the embodiment. This example results in better performance (expressed using cluster accuracy ACC) as shown in table 1 below:
ONKC method for producing a composite material
41.56 45.44
91.00 96.30
35.91 38.04
39.19 40.63
TABLE 1
The traditional multi-kernel clustering algorithm does not fully consider the local density among samples, and severely limits the value range of the optimal kernel for final clustering, so that the obtained performance is not high. The embodiment aims to provide an optimal neighbor multi-core clustering method based on local cores. The method comprises the steps of constructing a self-adaptive local kernel matrix, searching an optimal neighbor kernel around a linear combination of a plurality of predefined kernels, and clustering by using the neighbor kernel. Meanwhile, the three processes are put in the same target formula for alternate optimization, and when the change of loss tends to be stable, the final clustering result is obtained.
Correspondingly, the present embodiment further provides an optimal neighbor multi-core clustering system based on local cores, including:
the acquisition module is used for acquiring clustering tasks and target data samples;
the calculation module is used for calculating a kernel matrix of each view corresponding to the target data sample, and performing centralization and normalization processing on the kernel matrix to obtain a processed kernel matrix;
the establishing module is used for establishing an optimal neighbor multi-core clustering target function based on a local core according to the obtained processed core matrix;
the solving module is used for solving the established objective function in a circulating mode to obtain a division matrix after view fusion;
and the clustering module is used for carrying out k-means clustering on the obtained partition matrix to obtain a clustering result.
Further, the calculating, by the calculating module, the kernel matrix of each view corresponding to the target data sample specifically includes: for target data sample
Figure BDA0003037454030000121
The p view in (1) is subjected to kernel function mapping to obtain a kernel matrix of the p view, which is expressed as:
Figure BDA0003037454030000122
wherein the content of the first and second substances,
Figure BDA0003037454030000123
and
Figure BDA0003037454030000124
represents the ith, j sample, and sigma represents the average of the distances between all the target data samples; e represents a natural constant; kp(i, j) represents the value of the ith row and j column in the kernel matrix of the pth view; m represents the number of views.
Further, the establishing module establishes an optimal neighbor multi-core clustering objective function based on a local core, which is expressed as:
Figure BDA0003037454030000125
wherein H representsDividing a matrix; β represents a combination coefficient; j represents an optimal neighbor core; n represents the number of all samples; μ represents an adaptive kernel similarity threshold; m represents a kernel relation matrix; h(i)Representing a partition matrix corresponding to the ith sample; h(i)TRepresents H(i)Transposing; beta is aTRepresenting a combined coefficient vector; m(i)A relation matrix representing an optimal neighbor kernel matrix of the ith sample; rho represents a hyper-parameter and needs to be set in advance; kβRepresenting the matrix obtained by combining the kernel matrices according to the beta coefficient,
Figure BDA0003037454030000126
HTrepresenting a transpose of a partition matrix; i iskRepresenting a k-order identity matrix; beta is apA value representing the beta vector position p;
Figure BDA0003037454030000131
indicates that for all p; j. the design is a square(i)＝S(i)TJS(i)，
Figure BDA0003037454030000132
Represents μ of the ith sample(i)Nearest neighbor, S(i)TDenotes S(i)Transposing;
Figure BDA0003037454030000133
represents μ(i)The identity matrix of (2).
Further, the solving module specifically includes:
the first fixing module is used for fixing J and beta and optimizing H;
the objective function is converted into:
Figure BDA0003037454030000134
wherein A is(i)＝S(i)S(i)T；A(i)Denotes an intermediate variable, A(i)＝S(i)S(i)T；InRepresenting an n-order identity matrix;
by pairs
Figure BDA0003037454030000135
Decomposing the characteristic value to obtain a solution of the problem;
the second fixing module is used for fixing H and beta and optimizing J;
the objective function is converted into:
Figure BDA0003037454030000136
wherein B represents an intermediate variable;
Figure BDA0003037454030000137
the matrix J obtains a solution to the problem by removing the negative characteristic values in the matrix B;
the third fixing module is used for fixing H and J and optimizing beta;
the objective function is converted into:
Figure BDA0003037454030000138
wherein alpha isTRepresents a transposition of α;
Figure BDA0003037454030000139
representing the relationship between the local kernel matrices p and q for the sample of the ith;
Figure BDA00030374540300001310
a local kernel representing an ith sample in the pth kernel matrix;
Figure BDA00030374540300001311
a local kernel representing an ith sample in the qth kernel matrix; mpqRepresenting the relationship between the kernel matrices p and q; kp、KqAnd alpha each represents an intermediate variable; alpha is alphapRepresenting the value of position p in the alpha vector.
Further, the termination conditions in the first, second and third fixed modules are expressed as:
(objt+1-objt)/objt≤σ
wherein objt+1And objtValues representing the objective function of the t +1 th and the t-th iterations, respectively; σ denotes the setting accuracy.
Compared with the prior art, the invention provides a novel local kernel-based optimal neighbor multi-core clustering system which comprises three parts of building a self-adaptive local kernel matrix, searching and building an optimal neighbor kernel matrix and fusing the building of the self-adaptive local kernel matrix, searching and clustering the optimal neighbor kernel matrix, and fusing the three parts in the same objective formula for solving. The method greatly improves the performance of the multi-core clustering algorithm.
Example two
The difference between the optimal neighbor multi-core clustering method based on the local core provided by the embodiment and the embodiment one is that:
the main content of the embodiment includes that aiming at two problems that the local density of a single data sample and the representation capability of an optimal kernel learned by over-limitation are not fully considered in the current multi-kernel clustering algorithm, a self-adaptive local kernel is designed, and the optimal kernel is positioned from a pre-specified linear combination neighborhood of kernels; utilizing both techniques into a single multi-kernel cluster framework; the popularization range of the optimal neighborhood multi-core clustering algorithm based on the self-adaptive local core is researched.
The adaptive local kernel is a sub-matrix of the kernel function, and the main function is to reflect the relationship between the sample and its neighborhood. First, a threshold ζ is defined, and the corresponding index set Ω of the ith sample(i)Can be written as omega(i){ j | K (i, j) ≧ ζ } then the corresponding index matrix
Figure BDA0003037454030000141
Figure BDA0003037454030000142
Is defined as:
Figure BDA0003037454030000143
the ith adaptive local kernel of matrix K can be represented as:
Figure BDA0003037454030000144
in other words, the above equation selects μ with a kernel value greater than ζ corresponding to the ith sample(i)Adjacent samples and the other samples are discarded. Using the constructed local kernels in the multi-kernel k-means and setting the weight of matrix-induced regularization in to 1, we can rewrite the following form
Figure BDA0003037454030000145
Wherein
Figure BDA0003037454030000151
H(i)＝S(i)TH，
Figure BDA0003037454030000152
Is in the size of mu(i)And mu(i)The identity matrix of (a) varies with the density around the sample.
The adaptive local kernel proposed in this example is extended from the local kernel in [ m.li, x.liu, w.lei, d.yong, j.yin, and e.zhu, "Multiple kernel clustering with local kernel alignment mapping," in International Joint conference on intelligent kernel, 2016], directly to make the size of the local kernel constant. However, this does not guarantee that all pairs of samples are in a local kernel of high similarity. In contrast, the present embodiment constructs the ith adaptive local kernel by selecting samples whose similarity to sample i is higher than the threshold ζ. Fig. 2 compares these two types of local kernels globally. It can be seen that the local kernels generated in [ m.li, x.liu, w.lei, d.yong, j.yin, and e.zhu, "Multiple kernel clustering with local kernel alignment mapping," in International Joint conference on scientific intellgence, 2016] have the same size, while the proposed adaptive local kernel is determined by the similarity of the sample pairs. Comparing b.1, b.2 and c.1, c.2 in fig. 2, it can be noted that the proposed adaptive local kernel is generally smaller than the local kernel in [ m.li, x.liu, w.lei, d.yong, j.yin, and e.zhu, "Multiple kernel clustering with local kernel alignment knowledge," in International Joint conference on scientific integration, 2016] ], thus ensuring relatively high similarity of all neighbors and reducing the unreliability of further comparison sample pairs.
Local kernel comparison as shown in fig. 2: the darkness of the boxes indicates the degree of similarity between the sample pairs. The darker the box, the more similar the corresponding sample pair. a is the original kernel matrix, b.1 and b.2 are the local kernels corresponding to the 1/3 samples generated in [ M.Li, X.Liu, W.Lei, D.Yong, J.Yin, and E.Zhu, "Multiple kernel clustering with local kernel alignment mapping," in International Joint conference on Intelligent Intelligence,2016 ]. The size mu is fixed to 3; c.1 and c.2 are adaptive local kernels corresponding to the 1/3 samples. The similarity to its neighbors is higher than ζ.
The optimal core (referred to as J) is assumed to reside in the neighborhood of the core combination, denoted as:
Figure BDA0003037454030000153
this assumption yields the target equation in the equation as follows:
Figure BDA0003037454030000161
the objectives in the objective equation above are difficult to optimize due to constraints on J. It was observed that KβProvides prior knowledge for clustering, J is more likely to be at KβThe optimum value is reached in the case where the difference between them is small. This example does notThe maximum gap theta is set explicitly, and the actual gap is learned in the clustering process, so that the final target formula is formed
Figure BDA0003037454030000162
Wherein the content of the first and second substances,
Figure BDA0003037454030000163
K(i)＝S(i)TKS(i)，J(i)＝S(i)TJS(i)，
Figure BDA0003037454030000164
represents μ of the ith sample(i)A nearest neighbor, where n is the number of all samples,
Figure BDA0003037454030000165
is in the size of mu(i)The identity matrix of (2). The optimal kernel J serves as a linkage clustering process and a knowledge acquisition process. In this case, it uses complementary information in the pre-specified cores to assist in the clustering process, and information from the clusters to assist in the weight assignment of the pre-specified cores as feedback.
EXAMPLE III
The difference between the optimal neighbor multi-core clustering method based on the local core provided by the embodiment and the embodiment one is that:
this example compares the present invention across multiple data sets to verify the effectiveness of the invention.
Data set:
flower 102: the data set contains 8189 samples, evenly distributed in 102 classes, with 4 kernel matrices.
Digital: the data set consists of 2000 samples, evenly distributed in 10 classes, with 3 kernel matrices.
Caltech 101: the data set contains 1530 samples, evenly distributed in 102 classes, with 25 kernel matrices.
Protein Fold: the data set comprised 694 samples, evenly distributed in 27 classes, with 12 kernel matrices.
The statistical information of the above data sets is shown in table 2.
Figure BDA0003037454030000171
TABLE 2
Data preparation and parameter setting:
in the initialization phase, the core matrix is centered according to the method described in [ C.Cortes, M.Mohri, and A.Rosemizadeh, "Algorithms for Learning kernels based on centered alignment," Journal of Machine Learning Research, vol.13, No.2, pp.795-828,2012 ]. It is then normalized to better specify a range of similarity values between pairs of samples between-1 and 1.
The method has two superparameters, namely rho and xi. And p represents the relative importance degree of the construction of the self-adaptive local kernel matrix and the optimal neighbor kernel matrix. ξ represents the similarity threshold between the neighbor samples. A grid search technique is employed for selecting these two parameters, where p is at 2-15To 215And ξ varies from-0.5 to 0.5.
Evaluation indexes are as follows:
and evaluating by adopting a clustering algorithm general Accuracy (ACC) evaluation index.
This example compares the results of RMKC [ P.ZHOU, L.Du, L.Shi, H.Wang, and Y. -D.Shen, "Recovery of corrected Multiple keys for use in the clustering," in twin-Fourth International journal Conference architecture, 2015.], RMKKM [ L.Du, P.ZHOU, L.Shi, H.Wang, M.Fan, W.Wang, and Y. -D.Shen, "Robust Multiple keys k-means using 21-norm," in twin-Fourth International journal architecture, and III ] comparing the results with the results of the three multi-view clustering methods in the literature, as shown in the results of RMKC [ P.ZHOU, L.Du, L.Shi, W.Wang, and Y. -D.Shen, "Mr. K-media linkage architecture k-means using 21-norm," in twin-Fourth journal architecture, III.J., and M.J., while "III-III".
Figure BDA0003037454030000181
TABLE 3
The experimental results of the embodiment on four common data sets prove that the performance of the method is superior to that of the existing algorithm.
It is to be noted that the foregoing is only illustrative of the preferred embodiments of the present invention and the technical principles employed. It will be understood by those skilled in the art that the present invention is not limited to the particular embodiments described herein, but is capable of various obvious changes, rearrangements and substitutions as will now become apparent to those skilled in the art without departing from the scope of the invention. Therefore, although the present invention has been described in greater detail by the above embodiments, the present invention is not limited to the above embodiments, and may include other equivalent embodiments without departing from the spirit of the present invention, and the scope of the present invention is determined by the scope of the appended claims.

Claims (10)

1. An optimal neighbor multi-core clustering method based on local cores is characterized by comprising the following steps:
s1, acquiring a clustering task and a target data sample;
s2, calculating a kernel matrix of each view corresponding to the target data sample, and performing centralization and normalization processing on the kernel matrix to obtain a processed kernel matrix;
s3, establishing an optimal neighbor multi-core clustering target function based on a local core according to the obtained processed core matrix;
s4, solving the established objective function in a circulation mode to obtain a partition matrix after view fusion;
and S5, carrying out k-means clustering on the obtained partition matrix to obtain a clustering result.
2. The local-core-based optimal neighbor multi-core aggregation according to claim 1The class method is characterized in that the step S2 of calculating the kernel matrix of each view corresponding to the target data sample is specifically: for target data sample
Figure FDA0003037454020000011
The p view in (1) is subjected to kernel function mapping to obtain a kernel matrix of the p view, which is expressed as:
Figure FDA0003037454020000012
wherein the content of the first and second substances,
Figure FDA0003037454020000013
and
Figure FDA0003037454020000014
represents the ith, j sample, and sigma represents the average of the distances between all the target data samples; e represents a natural constant; kp(i, j) represents the value of the ith row and j column in the kernel matrix of the pth view; m represents the number of views.
3. The method according to claim 2, wherein the step S3 is implemented by establishing an optimal neighbor multi-core clustering objective function based on the local core, which is expressed as:
Figure FDA0003037454020000015
Figure FDA0003037454020000016
wherein H represents a partition matrix; β represents a combination coefficient; j represents an optimal neighbor core; n represents the number of all samples; μ represents an adaptive kernel similarity threshold; m represents a kernel relation matrix; h(i)Represents the ith sampleThe corresponding division matrix;
Figure FDA0003037454020000019
represents H(i)Transposing;
Figure FDA00030374540200000110
representing a combined coefficient vector; m(i)A relation matrix representing an optimal neighbor kernel matrix of the ith sample; rho represents a hyper-parameter and needs to be set in advance; kβRepresenting the matrix obtained by combining the kernel matrices according to the beta coefficient,
Figure FDA0003037454020000017
Figure FDA00030374540200000111
representing a transpose of a partition matrix; i iskRepresenting a k-order identity matrix; beta is apA value representing the beta vector position p;
Figure FDA0003037454020000018
indicates that for all p;
Figure FDA00030374540200000213
Figure FDA0003037454020000021
represents μ of the ith sample(i)The nearest neighbourhood of the nearest neighbourhood,
Figure FDA00030374540200000214
denotes S(i)Transposing;
Figure FDA0003037454020000022
represents μ(i)The identity matrix of (2).
4. The optimal neighbor multi-core clustering method based on local cores according to claim 3, wherein the step S4 specifically comprises:
s41, fixing J and beta, and optimizing H;
the objective function is converted into:
Figure FDA0003037454020000023
Figure FDA00030374540200000215
wherein the content of the first and second substances,
Figure FDA00030374540200000216
A(i)the intermediate variable is represented by a number of variables,
Figure FDA00030374540200000217
Inrepresenting an n-order identity matrix;
by pairs
Figure FDA0003037454020000024
Decomposing the characteristic value to obtain a solution of the problem;
s42, fixing H and beta, and optimizing J;
the objective function is converted into:
Figure FDA0003037454020000025
Figure FDA0003037454020000026
wherein B represents an intermediate variable;
Figure FDA0003037454020000027
the matrix J obtains a solution to the problem by removing the negative characteristic values in the matrix B;
s43, fixing H and J, and optimizing beta;
the objective function is converted into:
Figure FDA0003037454020000028
Figure FDA0003037454020000029
α＝[α1，…，αm]，αp＝-ρTr(JKp)
wherein the content of the first and second substances,
Figure FDA00030374540200000218
represents a transposition of α;
Figure FDA00030374540200000210
representing the relationship between the local kernel matrices p and q for the sample of the ith;
Figure FDA00030374540200000211
a local kernel representing an ith sample in the pth kernel matrix;
Figure FDA00030374540200000212
a local kernel representing an ith sample in the qth kernel matrix; mpqRepresenting the relationship between the kernel matrices p and q; kp、KqAnd alpha each represents an intermediate variable; alpha is alphapRepresenting the value of position p in the alpha vector.
5. The local-kernel-based optimal neighbor multi-kernel clustering method according to claim 4, wherein the termination conditions in the steps S41, S42 and S43 are expressed as:
(objt+1-objt)/objt≤σ
wherein objt+1And objtIndividual watchShowing the values of the objective function of the t +1 th iteration and the t th iteration; σ denotes the setting accuracy.
6. An optimal neighbor multi-core clustering system based on local cores, comprising:
the acquisition module is used for acquiring clustering tasks and target data samples;
the calculation module is used for calculating a kernel matrix of each view corresponding to the target data sample, and performing centralization and normalization processing on the kernel matrix to obtain a processed kernel matrix;
the establishing module is used for establishing an optimal neighbor multi-core clustering target function based on a local core according to the obtained processed core matrix;
the solving module is used for solving the established objective function in a circulating mode to obtain a division matrix after view fusion;
and the clustering module is used for carrying out k-means clustering on the obtained partition matrix to obtain a clustering result.
7. The optimal neighbor multi-core clustering system based on local cores according to claim 6, wherein the calculating module calculates the core matrix of each view corresponding to the target data sample specifically as follows: for target data sample
Figure FDA0003037454020000031
The p view in (1) is subjected to kernel function mapping to obtain a kernel matrix of the p view, which is expressed as:
Figure FDA0003037454020000032
wherein the content of the first and second substances,
Figure FDA0003037454020000033
and
Figure FDA0003037454020000034
represents the ith, j sample, and sigma represents the average of the distances between all the target data samples; e represents a natural constant; kp(i, j) represents the value of the ith row and j column in the kernel matrix of the pth view; m represents the number of views.
8. The system according to claim 7, wherein the establishing module establishes the optimal neighbor multi-core clustering objective function based on the local core, which is expressed as:
Figure FDA0003037454020000035
Figure FDA0003037454020000036
wherein H represents a partition matrix; β represents a combination coefficient; j represents an optimal neighbor core; n represents the number of all samples; μ represents an adaptive kernel similarity threshold; m represents a kernel relation matrix; h(i)Representing a partition matrix corresponding to the ith sample;
Figure FDA00030374540200000413
represents H(i)Transposing;
Figure FDA00030374540200000414
representing a combined coefficient vector; m(i)A relation matrix representing an optimal neighbor kernel matrix of the ith sample; rho represents a hyper-parameter and needs to be set in advance; kβRepresenting the matrix obtained by combining the kernel matrices according to the beta coefficient,
Figure FDA0003037454020000041
Figure FDA00030374540200000415
representing a transpose of a partition matrix; i iskRepresenting units of order kA matrix; beta is apA value representing the beta vector position p;
Figure FDA0003037454020000042
indicates that for all p;
Figure FDA00030374540200000416
Figure FDA0003037454020000043
represents μ of the ith sample(i)The nearest neighbourhood of the nearest neighbourhood,
Figure FDA00030374540200000417
denotes S(i)Transposing;
Figure FDA0003037454020000044
represents μ(i)The identity matrix of (2).
9. The local-kernel-based optimal neighbor multi-kernel clustering system according to claim 8, wherein the solving module is specifically:
the first fixing module is used for fixing J and beta and optimizing H;
the objective function is converted into:
Figure FDA0003037454020000045
Figure FDA00030374540200000418
wherein the content of the first and second substances,
Figure FDA00030374540200000419
A(i)the intermediate variable is represented by a number of variables,
Figure FDA00030374540200000420
Inrepresenting an n-order identity matrix;
by pairs
Figure FDA0003037454020000046
Decomposing the characteristic value to obtain a solution of the problem;
the second fixing module is used for fixing H and beta and optimizing J;
the objective function is converted into:
Figure FDA0003037454020000047
Figure FDA0003037454020000048
wherein B represents an intermediate variable;
Figure FDA0003037454020000049
the matrix J obtains a solution to the problem by removing the negative characteristic values in the matrix B;
the third fixing module is used for fixing H and J and optimizing beta;
the objective function is converted into:
Figure FDA00030374540200000410
Figure FDA00030374540200000411
α＝[α1，…，αm]，αp＝-ρTr(JKp)
wherein the content of the first and second substances,
Figure FDA00030374540200000421
represents a transposition of α;
Figure FDA00030374540200000412
representing the relationship between the local kernel matrices p and q for the sample of the ith;
Figure FDA0003037454020000051
a local kernel representing an ith sample in the pth kernel matrix;
Figure FDA0003037454020000052
a local kernel representing an ith sample in the qth kernel matrix; mpqRepresenting the relationship between the kernel matrices p and q; kp、KqAnd alpha each represents an intermediate variable; alpha is alphapRepresenting the value of position p in the alpha vector.
10. The local-core-based optimal neighbor multi-core clustering system according to claim 9, wherein the termination conditions in the first fixed module, the second fixed module and the third fixed module are expressed as:
(objt+1-objt)/objt≤σ
wherein objt+1And objtValues representing the objective function of the t +1 th and the t-th iterations, respectively; σ denotes the setting accuracy.
CN202110447615.9A 2021-04-25 2021-04-25 Local kernel-based optimal neighbor multi-core clustering method and system Pending CN113269231A (en)

Priority Applications (4)

Application Number Priority Date Filing Date Title
CN202110447615.9A CN113269231A (en) 2021-04-25 2021-04-25 Local kernel-based optimal neighbor multi-core clustering method and system
PCT/CN2022/082643 WO2022227956A1 (en) 2021-04-25 2022-03-24 Optimal neighbor multi-kernel clustering method and system based on local kernel
LU503092A LU503092B1 (en) 2021-04-25 2022-03-24 A method and system for optimal neighbor multicore clustering based on local kernels
ZA2022/07734A ZA202207734B (en) 2021-04-25 2022-07-12 A method and system for optimal neighbor multicore clustering based on local kernels

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202110447615.9A CN113269231A (en) 2021-04-25 2021-04-25 Local kernel-based optimal neighbor multi-core clustering method and system

Publications (1)

Publication Number Publication Date
CN113269231A true CN113269231A (en) 2021-08-17

Family

ID=77229306

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110447615.9A Pending CN113269231A (en) 2021-04-25 2021-04-25 Local kernel-based optimal neighbor multi-core clustering method and system

Country Status (4)

Country Link
CN (1) CN113269231A (en)
LU (1) LU503092B1 (en)
WO (1) WO2022227956A1 (en)
ZA (1) ZA202207734B (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2022227956A1 (en) * 2021-04-25 2022-11-03 浙江师范大学 Optimal neighbor multi-kernel clustering method and system based on local kernel

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117292162B (en) * 2023-11-27 2024-03-08 烟台大学 Target tracking method, system, equipment and medium for multi-view image clustering

Family Cites Families (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109145976A (en) * 2018-08-14 2019-01-04 聚时科技(上海)有限公司 A kind of multiple view cluster machine learning method based on optimal neighbours' core
CN110188812A (en) * 2019-05-24 2019-08-30 长沙理工大学 A kind of multicore clustering method of quick processing missing isomeric data
CN113269231A (en) * 2021-04-25 2021-08-17 浙江师范大学 Local kernel-based optimal neighbor multi-core clustering method and system

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2022227956A1 (en) * 2021-04-25 2022-11-03 浙江师范大学 Optimal neighbor multi-kernel clustering method and system based on local kernel

Also Published As

Publication number Publication date
ZA202207734B (en) 2022-07-27
LU503092B1 (en) 2023-03-22
WO2022227956A1 (en) 2022-11-03

Similar Documents

Publication Publication Date Title
Zhou et al. Self-paced clustering ensemble
Wang et al. Feature selection and multi-kernel learning for adaptive graph regularized nonnegative matrix factorization
Wang et al. Robust dimension reduction for clustering with local adaptive learning
CN113269231A (en) Local kernel-based optimal neighbor multi-core clustering method and system
Zamiri et al. MVDF-RSC: Multi-view data fusion via robust spectral clustering for geo-tagged image tagging
Mahmoud et al. Pseudoinverse learning autoencoder with DCGAN for plant diseases classification
Liu et al. Structured block diagonal representation for subspace clustering
CN113837218A (en) Text clustering method and system based on one-step post-fusion multi-view
Liu et al. Incomplete multi-view partial multi-label learning
Fang et al. Learning decomposed spatial relations for multi-variate time-series modeling
Zhu et al. Local information fusion network for 3D shape classification and retrieval
CN113435603A (en) Agent graph improvement-based late-stage fusion multi-core clustering machine learning method and system
Zhou et al. Semantic adaptation network for unsupervised domain adaptation
Chen et al. Dual distance adaptive multiview clustering
CN117409456A (en) Non-aligned multi-view multi-mark learning method based on graph matching mechanism
Wu et al. Deep clustering and representation learning that preserves geometric structures
CN116304768A (en) High-dimensional density peak clustering method based on improved equidistant mapping
Kerner et al. Introduction to machine learning
CN115169436A (en) Data dimension reduction method based on fuzzy local discriminant analysis
CN113095270B (en) Unsupervised cross-library micro-expression identification method
CN113627237A (en) Late-stage fusion face image clustering method and system based on local maximum alignment
Zhang et al. Leverage triple relational structures via low-rank feature reduction for multi-output regression
Dornaika et al. Simultaneous label inference and discriminant projection estimation through adaptive self-taught graphs
Shiao et al. Implementation and comparison of SVM-based multi-task learning methods
Jun et al. Two-view correspondence learning via complex information extraction

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination