WO2022267955A1 - 基于局部最大对齐的后期融合多视图聚类方法及系统 - Google Patents
基于局部最大对齐的后期融合多视图聚类方法及系统 Download PDFInfo
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Definitions
- the present application relates to the technical field of machine learning, and in particular to a late fusion multi-view clustering method and system based on local maximum alignment.
- the collected data can have multiple representations, for example, a video can have image data and sound data from different angles.
- Such data in the field of machine learning, is called multi-view data.
- Clustering algorithms play an important role in the field of unsupervised learning in machine learning, which aims to divide unlabeled data into disjoint parts. Clustering with multiple views can extract sample information from different angles, which is better than the clustering effect of a single view.
- Multi-view clustering can be roughly divided into the following three categories: i) Co-training Multi-view clustering (A.Blum and T.Mitchell, “Combining labeled and unlabeled data with co-training,” in COLT 1998, pp.92–100 ). Such methods, in addition to extracting information from each view, simultaneously seek consistent clustering results across views. ii) Subspace clustering (X.Cao, C.Zhang, H.Fu, S.Liu, and H.Zhang, “Diversity-induced multi-view subspace clustering,” in CVPR 2015, pp.586–594.) . This approach aims to construct a consistent subspace through the representations of different views to achieve the purpose of view fusion.
- Multi-kernel clustering M. and AA Margolin, “Localized data fusion for kernel kmeans clustering with application to cancer biology,” in NeurIPS 2014, pp.1305–1313.).
- the principle of the algorithm is to find the optimal combination coefficient of the base kernel by means of optimization, so as to achieve the purpose of improving the clustering effect.
- the multi-kernel clustering algorithm in the above method has attracted much attention because of its strong interpretability and good effect.
- it has the following two disadvantages: First, the calculation and storage complexity is relatively high. Because several kernel matrices need to be stored and calculated, the space complexity of this type of algorithm is O(n ⁇ 2); the eigendecomposition of the kernel matrix is also required, resulting in a time complexity of O(n ⁇ 3). The second is the more complicated optimization process, which increases the risk of falling into a poor local optimum.
- Late fusion multi-view clustering no longer uses the kernel matrix for fusion, but fuses more lightweight basic divisions.
- Late fusion multi-view clustering based on maximum alignment (S.Wang, X.Liu, E.Zhu, et al., “Multi-view clustering via late fusion alignment maximization,” in IJCAI 2019, pp.3778–3784.) , not only reduces the computational complexity from O(n ⁇ 3) to O(n), but also further improves the clustering effect.
- the purpose of this application is to address the defects of the prior art and provide a late-fusion multi-view clustering method and system based on local maximum alignment.
- a late fusion multi-view clustering method based on local maximum alignment including steps:
- kernel k-means clustering in the step S2 is expressed as:
- the calculation of the basic division of each view in the step S3 is specifically: constructing different kernel matrices for different views And run the kernel k-means clustering separately to get the basic division of each view
- step S3 the maximum alignment-based late fusion multi-view clustering objective function is established, expressed as:
- F represents the optimal partition obtained by optimization
- ⁇ represents the vector composed of the combination coefficients of each view
- ⁇ p represents the coefficient of the pth view
- M represents the average partition obtained by performing kernel k-means clustering on the average kernel
- F T represents the permutation of F
- W T represents the permutation of W
- H p represents each view obtained by kernel k-means clustering
- the basic division of ; m represents the number of views.
- step S4 a late fusion multi-view clustering objective function based on local maximum alignment is established, expressed as:
- step S5 the established local maximum alignment-based post-fusion multi-view clustering objective function is solved in a cyclic manner, specifically:
- step S5 the established local maximum alignment-based post-fusion multi-view clustering objective function is solved in a cyclic manner, wherein the termination condition of the loop is expressed as:
- obj (t-1) and obj (t) represent the value of the objective function of the t-th and t-1 round iterations respectively; ⁇ represents the set precision.
- a late fusion multi-view clustering system based on local maximum alignment including:
- Obtaining module used for obtaining clustering tasks and target data samples
- the initialization module is used to initialize the permutation matrix of each view, the combination coefficient of each view, the average division of kernel k-means clustering to the average kernel, and the neighbor matrix of each view;
- the first building module is used to calculate the basic division of each view, and establish a late fusion multi-view clustering objective function based on maximum alignment;
- the second building module is used to obtain the basic division with local information, and combine the neighbor matrix of each view and the objective function in the first building module to establish a late fusion multi-view clustering objective function based on local maximum alignment;
- the solution module is used to solve the established local maximum alignment-based post-fusion multi-view clustering objective function in a cyclic manner, and obtain the optimal division after the fusion of each basic division;
- the clustering module is used to perform k-means clustering on the optimal partition to obtain a clustering result.
- a late fusion multi-view clustering objective function based on maximum alignment is established, expressed as:
- F represents the optimal partition obtained by optimization
- ⁇ represents the vector composed of the combination coefficients of each view
- ⁇ p represents the coefficient of the pth view
- M represents the average partition obtained by performing kernel k-means clustering on the average kernel
- F T represents the permutation of F
- W T represents the permutation of W
- H p represents each view obtained by kernel k-means clustering
- the basic division of ; m represents the number of views.
- a late fusion multi-view clustering objective function based on local maximum alignment is established, expressed as:
- this application proposes a novel post-fusion multi-view clustering machine learning method based on local maximum alignment, which includes obtaining the neighbor matrix and basic division of each view, and constructing objective function. Then through optimization, an optimal partition matrix with local structure is learned, so as to achieve the purpose of improving the clustering effect. At the same time, this application can also solve the clustering problem on large-scale data. Experimental results on 8 multi-core datasets (including 6 benchmark datasets and 2 large-scale datasets) demonstrate that our application outperforms existing methods.
- FIG. 1 is a flow chart of a late fusion multi-view clustering method based on local maximum alignment provided in Embodiment 1;
- Fig. 2 is a schematic diagram of the variation of the objective function value as the number of iterations increases provided by embodiment two;
- Fig. 3 is a schematic diagram of parameter sensitivity provided in Example 2.
- the purpose of this application is to address the defects of the prior art and provide a late-fusion multi-view clustering method and system based on local maximum alignment.
- This embodiment provides a post-fusion multi-view clustering method based on local maximum alignment, as shown in Figure 1, including steps:
- the late fusion multi-view clustering objective function based on the local maximum alignment is adopted to solve the establishment in a cyclic manner, and the optimal division after the fusion of each basic division is obtained;
- the post-fusion multi-view clustering method based on local maximum alignment in this embodiment allows the basic partition matrix to have local cluster structure information, so that the learned optimal partition has a better cluster structure.
- step S2 the permutation matrix of each view, the combination coefficient of each view, the average division of kernel k-means clustering for the average kernel, and the neighbor matrix of each view are initialized.
- the permutation matrix of each matrix be The combination coefficient of each view is ⁇ , the average division of kernel k-means clustering on the average kernel is M, and the neighbor matrix of each view Then initialize the above data.
- the basic division is firstly obtained through kernel k-means clustering.
- the sample set is in is the sample space.
- the objective formula of kernel k-means clustering is as follows:
- the above formula can be solved by performing eigendecomposition on K, and the solution is the eigenvector corresponding to the k largest eigenvalues before K.
- step S3 the basic division of each view is calculated, and a maximum alignment-based late fusion multi-view clustering objective function is established.
- kernel matrices can be constructed for different views Run the kernel k-means clustering separately to get the basic division of each view
- the objective function of late fusion multi-view clustering based on maximum alignment is:
- F represents the optimal partition obtained by optimization
- ⁇ represents the vector composed of the combination coefficients of each view
- ⁇ p represents the coefficient of the pth view
- M represents the average partition obtained by performing kernel k-means clustering on the average kernel
- F T represents the permutation of F
- W T represents the permutation of W
- H p represents each view obtained by kernel k-means clustering
- the basic division of ; m represents the number of views.
- the optimization of F can be obtained by performing economical singular value decomposition on X+ ⁇ M, and taking the product of its left and right singular value vectors; the optimization of ⁇ can be obtained by using the condition that the equal sign of Cauchy’s inequality holds true; the optimization of W p , Singular value decomposition can be performed on F T H p , and obtained by taking the product of its left and right singular value vectors.
- step S4 the basic division with local information is obtained, and combined with the neighbor matrix of each view and step S3, a late fusion multi-view clustering objective function based on local maximum alignment is established.
- step S3 only has the global clustering structure of the respective view, but ignores its local clustering structure.
- the matrix An indicator matrix representing whether the p-th view is a ⁇ -neighbor in sample i. Accordingly, the basic partition matrix with the local information of the i-th sample in the p-th view can be defined And the average partition matrix with the local information of the i-th sample where M is the mean partition obtained by performing kernel k-means clustering on the mean kernel.
- the objective function of late fusion multi-view clustering based on local maximum alignment is:
- step S5 the established local maximum alignment-based post-fusion multi-view clustering objective function is solved in a cyclic manner to obtain the optimal division after fusing each basic division.
- a three-step alternate optimization method is used to solve the objective function in step S4, specifically:
- obj (t-1) and obj (t) represent the value of the objective function of the t-th and t-1 round iterations respectively; ⁇ represents the set precision.
- step S6 k-means clustering is performed on the optimal partition to obtain a clustering result.
- the obtained optimal division is the variable F in the objective function in step S4, each row of F is regarded as a sample, and k-means clustering is performed on it to obtain the final clustering result.
- This embodiment includes obtaining the neighbor matrix and basic division of each view, using the local information of each view to construct an objective function; and then learning an optimal division matrix with a local structure through optimization, so as to achieve the purpose of improving the clustering effect.
- the post-fusion multi-view clustering method based on local maximum alignment provided in this embodiment is different from Embodiment 1 in that:
- image datasets include face image datasets, plant image datasets, handwritten Arabic numerals image datasets, medical image datasets, object behavior and gestures, business order data, massive order group waves, order wave combinations, order data Mining and analysis, inventory allocation, shelf adjustment, supply chain optimization, intelligent replenishment, etc.
- the clustering performance of our method is tested on 6 multi-core standard datasets (5 benchmark datasets and 1 large-scale dataset).
- the 6 multi-core standard datasets include AR10P, YALE, Plant, Caltech102-30 (abbreviated as Cal102-30), Flower17 and Mnist.
- AR10P is a face image database, and each person has photos in different situations such as different expressions, lighting or camouflage.
- YALE Faces contains 165 photos from 15 people, each with different facial expressions, poses, or lighting conditions.
- Plant and Flower17 are image datasets of plants.
- Caltech102 is a data set consisting of 102 types of photos of different items. We select 30 samples from each category as a training set, which is denoted as Caltech102-30.
- Mnist is a large-scale data set, which contains 60,000 handwritten Arabic numeral images, to verify the performance of the algorithm on large-scale data sets.
- Kernel matrices for all datasets can be downloaded from the Internet.
- AKKM average kernel k-means clustering algorithm
- SB-KKM optimal single-view kernel k-means clustering algorithm
- MKKM multi-kernel k-means clustering
- CRSC collaborative regularized spectral clustering
- RKKM Lu Rod multikernel clustering
- RMSC robust multi-view spectral clustering
- LKKM local multikernel k-means clustering
- MKKM-MR matrix-induced regularization
- LKAM Multikernel Clustering with Local Kernel Maximal Alignment
- the comparison algorithms used in this experiment all set parameters according to the corresponding literature.
- the parameter ⁇ of this method is determined by grid searching the range [2 -5 ,2 -4 ,...,2 5 ], and the parameter ⁇ is determined by grid searching the range [0.1,0.2,...,1].
- This experiment uses common clustering accuracy (ACC) and normalized mutual information (NMI) to show the clustering performance of each method. All methods are randomly initialized and repeated 50 times and show the best results to reduce the randomness caused by k-means.
- ACC common clustering accuracy
- NMI normalized mutual information
- Table 2 shows the clustering effect of this method (Proposed) and the comparison algorithm on the five benchmark data sets, and the mark "-" means memory overflow, and the algorithm cannot run. According to the table, it can be observed that: 1. This method is superior to all comparison algorithms under the two evaluation criteria. 2. The performance of this method on the six data sets ACC is 12.31%, 2.58%, 4.58%, 3.86%, 3.53% higher than that of the suboptimal comparison algorithm. Table 3 shows the performance of this method on large-scale datasets. It can be seen from Table 3 that when many comparison algorithms cannot run due to memory overflow, this method can not only run smoothly, but also achieve the best results. This demonstrates the effectiveness of our method on large-scale datasets.
- This example also gives the change of the objective function at each iteration, as shown in Figure 2. It can be seen that the value of the objective function increases monotonically and usually converges within 40 iterations.
- Figure 3 demonstrates parameter sensitivity. It can be seen from the figure: 1) In a wide range, the change of parameters can achieve better performance; 2) The clustering performance on some data sets is more sensitive to parameters, and when the value of ⁇ is 0.1, the overall effect better. This is instructive for the choice of hyperparameters.
- This embodiment can solve the clustering problem on large-scale data.
- Experimental results on 7 multi-kernel image datasets demonstrate that our method outperforms existing methods.
- This embodiment provides a late fusion multi-view clustering system based on local maximum alignment, including:
- Obtaining module used for obtaining clustering tasks and target data samples
- the initialization module is used to initialize the permutation matrix of each view, the combination coefficient of each view, the average division of kernel k-means clustering to the average kernel, and the neighbor matrix of each view;
- the first building module is used to calculate the basic division of each view, and establish a late fusion multi-view clustering objective function based on maximum alignment;
- the second building module is used to obtain the basic division with local information, and combine the neighbor matrix of each view and the objective function in the first building module to establish a late fusion multi-view clustering objective function based on local maximum alignment;
- the solution module is used to solve the established local maximum alignment-based post-fusion multi-view clustering objective function in a cyclic manner, and obtain the optimal division after the fusion of each basic division;
- the clustering module is used to perform k-means clustering on the optimal partition to obtain a clustering result.
- a late fusion multi-view clustering objective function based on maximum alignment is established, expressed as:
- F represents the optimal partition obtained by optimization
- ⁇ represents the vector composed of the combination coefficients of each view
- ⁇ p represents the coefficient of the pth view
- M represents the average partition obtained by performing kernel k-means clustering on the average kernel
- F T represents the permutation of F
- W T represents the permutation of W
- H p represents each view obtained by kernel k-means clustering
- the basic division of ; m represents the number of views.
- a late fusion multi-view clustering objective function based on local maximum alignment is established, expressed as:
- This embodiment includes obtaining the neighbor matrix and basic division of each view, and using the local information of each view to construct an objective function. Then through optimization, an optimal partition matrix with local structure is learned, so as to achieve the purpose of improving the clustering effect.
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Abstract
一种基于局部最大对齐的后期融合多视图聚类方法及系统。其中涉及的基于局部最大对齐的后期融合多视图聚类方法,包括步骤:S1.获取聚类任务和目标数据样本;S2.初始化各个视图的置换矩阵、各个视图的组合系数、对平均核进行核k均值聚类的平均划分、各个视图的邻居矩阵;S3.计算各个视图的基础划分,建立基于最大对齐的后期融合多视图聚类目标函数;S4.获取带局部信息的基础划分,并结合各个视图的邻居矩阵和步骤S3,建立基于局部最大对齐的后期融合多视图聚类目标函数;S5.采用循环方式求解建立的基于局部最大对齐的后期融合多视图聚类目标函数,得到融合各个基础划分后的最优划分;S6.对最优划分进行k均值聚类,得到聚类结果。
Description
本申请涉及机器学习技术领域,尤其涉及基于局部最大对齐的后期融合多视图聚类方法及系统。
随着多源信息采集技术的发展,所收集的数据可以有多种表示,例如,一段视频可以有不同角度的影像数据和声音数据。此类数据,在机器学习领域,被称之为多视图数据。对这类数据的充分合理的应用,一直是理论研究和科学实践中的重要课题。聚类算法在机器学习中的无监督学习领域有重要地位,它旨在将无标签的数据进行不相交的划分。利用多视图进行聚类,可以从不同角度提取样本信息,从而要比单个视图的聚类效果更好。
多视图聚类可以大致分为以下三类:i)协同训练多视图聚类(A.Blum and T.Mitchell,“Combining labeled and unlabeled data with co-training,”in COLT 1998,pp.92–100)。此类方法除了从各个视图提取信息之外,同时寻求各个视图的一致的聚类结果。ii)子空间聚类(X.Cao,C.Zhang,H.Fu,S.Liu,and H.Zhang,“Diversity-induced multi-view subspace clustering,”in CVPR 2015,pp.586–594.)。这种方法旨在通过不同视图的表示,构建一个一致的子空间,达到视图融合的目的。iii)多核聚类(M.
and A.A.Margolin,“Localized data fusion for kernel kmeans clustering with application to cancer biology,”in NeurIPS 2014,pp.1305–1313.)。该算法的原理是,通过优化的方式寻找基核的最优组合系数,以达到提升聚类效果的目的。
上述方法中的多核聚类算法因为可解释性强和效果好,而备受关注。然而在实际应用过程中,其存在以下两个缺点:一是计算和存储复杂度较高。因为要对若干个核矩阵进行存储核计算,所以导致该类算法空间复杂度为O(n^2);还要对核矩阵进行特征分解,导致时间复杂度为O(n^3)。二是较为复杂的优化过程,增加了其陷入较差的局部最优的风险。
为了克服以上缺点,达到降低复杂度和简化优化过程的目的。后期融合的多视图聚类不再利用核矩阵进行融合,而是对更为轻量级的基础划分进行融合。基于最大对齐的后期融合多视图聚类(S.Wang,X.Liu,E.Zhu,et al.,“Multi-view clustering via late fusion alignment maximization,”in IJCAI 2019,pp.3778–3784.),不但将计算复杂度从O(n^3)下降至O(n),还进一步提高了聚类效果。高效且有效的带正则化项的缺失多视图聚类算法(Liu X,Li M,Tang C,et al.,“Efficient and Effective Regularized Incomplete Multi-view Clustering”,in TPAMI,2020,preprint)利用后期融合的方法处理缺失多视图聚类问题,不但聚类效果超过同类型算法,且达到了较低计算复杂度。但是,这种方法并没有考虑到数据的局部结构。目前,尚没有方法能够综合后期融合较快的运算速度和数据局部结构等两个优点。
发明内容
本申请的目的是针对现有技术的缺陷,提供了基于局部最大对齐的后期融合多视图聚类方法及系统。
为了实现以上目的,本申请采用以下技术方案:
基于局部最大对齐的后期融合多视图聚类方法,包括步骤:
S1.获取聚类任务和目标数据样本;
S2.初始化各个视图的置换矩阵、各个视图的组合系数、对平均核进行核k均值聚类的平均划分、各个视图的邻居矩阵;
S3.计算各个视图的基础划分,建立基于最大对齐的后期融合多视图聚类目标函数;
S4.获取带局部信息的基础划分,并结合各个视图的邻居矩阵和步骤S3,建立基于局部最大对齐的后期融合多视图聚类目标函数;
S5.采用循环方式求解建立的基于局部最大对齐的后期融合多视图聚类目标函数,得到融合各个基础划分后的最优划分;
S6.对最优划分进行k均值聚类,得到聚类结果。
进一步的,所述步骤S2中核k均值聚类表示为:
其中,H∈R
n×k表示根据核矩阵K所求的划分矩阵;I
m表示维度为m(∈N
+)的单位矩阵;H
T表示H的置换;I
k表示k维单位矩阵。
进一步的,所述步骤S3中建立基于最大对齐的后期融合多视图聚类目标函数,表示为:
其中,F表示优化所得的最优划分;β表示各个视图的组合系数组成的向量,β
p表示第p个视图的系数,
表示各个视图的置换矩阵;M表示对平均核进行核k均值聚类获得的平均划分;F
T表示F的置换;W
T表示W的置换;H
p表示由核k均值聚类得到的各个视图的基础划分;m表示视图数量。
进一步的,所述步骤S4中建立基于局部最大对齐的后期融合多视图聚类目标函数,表示为:
其中,
表示第p个视图中样本i中的τ近邻的指示矩阵,即各个视图的邻居矩阵;n表示样本数;
表示第p个视图中带第i样本局部信息的基础划分矩阵;
表示各个视图的置换矩阵;λ表示正则化参数;
表示带第i个样本局部信息的平均划分矩阵;
表示
的置换。
进一步的,所述步骤S5中采用循环方式求解建立的基于局部最大对齐的后期融合多视图聚类目标函数,具体为:
进一步的,所述步骤S5中采用循环方式求解建立的基于局部最大对齐的后期融合多视图聚类目标函数,其中循环的终止条件表示为:
(obj
(t-1)-obj
(t))/obj
(t)≤ε
其中,obj
(t-1)、obj
(t)分别表示第t和t-1伦迭代的目标函数的值;ε表示设定精度。
相应的,还提供基于局部最大对齐的后期融合多视图聚类系统,包括:
获取模块,用于获取聚类任务和目标数据样本;
初始化模块,用于初始化各个视图的置换矩阵、各个视图的组合系数、对平均核进行核k均值聚类的平均划分、各个视图的邻居矩阵;
第一建立模块,用于计算各个视图的基础划分,建立基于最大对齐的后期融合多视图聚类目标函数;
第二建立模块,用于获取带局部信息的基础划分,并结合各个视图的邻居矩阵和第一建立模块中的目标函数,建立基于局部最大对齐的后期融合多视图聚类目标函数;
求解模块,用于采用循环方式求解建立的基于局部最大对齐的后期融合多视图聚类目标函数,得到融合各个基础划分后的最优划分;
聚类模块,用于对最优划分进行k均值聚类,得到聚类结果。
进一步的,所述第一建立模块中建立基于最大对齐的后期融合多视图聚类目标函数,表示为:
其中,F表示优化所得的最优划分;β表示各个视图的组合系数组成的向量,β
p表示第p个视图的系数,
表示各个视图的置换矩阵;M表示对平均核进行核k均值聚类获得的平均划分;F
T表示F的置换;W
T表示W的置换;H
p表示由核k均值聚类得到的各个视图的基础划分;m表示视图数量。
进一步的,所述第二建立模块中建立基于局部最大对齐的后期融合多视图聚类目标函数,表示为:
F
TF=I
k,W
TW=I
k,‖β‖
2=1,β
p≥0
其中,
表示第p个视图中样本i中的τ近邻的指示矩阵,即各个视图的邻居矩阵;n表示样本数;
表示第p个视图中带第i样本局部信息的基础划分矩阵;
表示各个视图的置换矩阵;λ表示正则化参数;
表示带第i个样本局部信息的平均划分矩阵;
表示
的置换。
与现有技术相比,本申请提出了一种新颖的基于局部最大对齐的后期融合多视图聚类机器学习方法,该方法包括获取各个视图的邻居矩阵和基础划分,利用各视图的局部信息构建目标函数。然后通过优化,学习到一个拥有局部结 构的最优划分矩阵,从而达到提升聚类效果的目的。与此同时,本申请亦可以解决大规模数据上的聚类问题。在8个多核数据集(其中6个基准数据集和2个大规模数据集)上的实验结果证明了本申请的性能优于现有的方法。
图1是实施例一提供的基于局部最大对齐的后期融合多视图聚类方法流程图;
图2是实施例二提供的随迭代次数增加,目标函数值的变化示意图;
图3是实施例二提供的参数敏感性示意图。
以下通过特定的具体实例说明本申请的实施方式,本领域技术人员可由本说明书所揭露的内容轻易地了解本申请的其他优点与功效。本申请还可以通过另外不同的具体实施方式加以实施或应用,本说明书中的各项细节也可以基于不同观点与应用,在没有背离本申请的精神下进行各种修饰或改变。需说明的是,在不冲突的情况下,以下实施例及实施例中的特征可以相互组合。
本申请的目的是针对现有技术的缺陷,提供了基于局部最大对齐的后期融合多视图聚类方法及系统。
实施例一
本实施例提供基于局部最大对齐的后期融合多视图聚类方法,如图1所示,包括步骤:
S1.获取聚类任务和目标数据样本;
S2.初始化各个视图的置换矩阵、各个视图的组合系数、对平均核进行核k均值聚类的平均划分、各个视图的邻居矩阵;
S3.计算各个视图的基础划分,建立基于最大对齐的后期融合多视图聚类目标函数;
S4.获取带局部信息的基础划分,并结合各个视图的邻居矩阵和步骤S3,建立基于局部最大对齐的后期融合多视图聚类目标函数;
S5.采用循环方式求解建立的基于局部最大对齐的后期融合多视图聚类目 标函数,得到融合各个基础划分后的最优划分;
S6.对最优划分进行k均值聚类,得到聚类结果。
本实施例的基于局部最大对齐的后期融合多视图聚类方法,通过让基础划分矩阵拥有局部聚类结构信息,使得学习得到的最优划分拥有更好的聚类结构。
在步骤S2中,初始化各个视图的置换矩阵、各个视图的组合系数、对平均核进行核k均值聚类的平均划分、各个视图的邻居矩阵。
在本实施例中,首先通过核k均值聚类得到基础划分。假设样本集为
其中
为样本空间。设核函数为κ:
据此,可以得到相应的核矩阵K∈R
n×n,该矩阵中元素K
ij=κ(x
i,x
j)。核k均值聚类的目标式如下:
其中,H∈R
n×k表示根据核矩阵K所求的划分矩阵;I
m表示维度为m(∈N
+)的单位矩阵;H
T表示H的置换;I
k表示k维单位矩阵。上式可以通过对K进行特征分解求解,解为K前k个最大特征值对应的特征向量。
在步骤S3中,计算各个视图的基础划分,建立基于最大对齐的后期融合多视图聚类目标函数。
其中,F表示优化所得的最优划分;β表示各个视图的组合系数组成的向量,β
p表示第p个视图的系数,
表示各个视图的置换矩阵;M表示对 平均核进行核k均值聚类获得的平均划分;F
T表示F的置换;W
T表示W的置换;H
p表示由核k均值聚类得到的各个视图的基础划分;m表示视图数量。
关于F的优化可以通过对X+λM进行经济的奇异值分解,取其左右奇异值向量的乘积获得;关于β的优化,可利用柯西不等式等号成立的条件获得;对W
p的优化,可以对F
TH
p进行奇异值分解,取其左右奇异值向量乘积获得。
在步骤S4中,获取带局部信息的基础划分,并结合各个视图的邻居矩阵和步骤S3,建立基于局部最大对齐的后期融合多视图聚类目标函数。
步骤S3中的方法运用的基础划分只拥有各自视图的全局聚类结构,而忽略了其局部聚类结构。本实施例令矩阵
代表第p个视图中是否为样本i中的τ近邻的指示矩阵。据此,可以定义第p个视图中带第i样本局部信息的基础划分矩阵
以及带第i个样本局部信息的平均划分矩阵
其中M为对平均核进行核k均值聚类获得的平均划分。
基于局部最大对齐的后期融合多视图聚类目标函数为:
其中,
表示第p个视图中样本i中的τ近邻的指示矩阵,即各个视图的邻居矩阵;n表示样本数;
表示第p个视图中带第i样本局部信息的基础划分矩阵;
表示各个视图的置换矩阵;λ表示正则化参数;
表示带第i个样本局部信息的平均划分矩阵;
表示
的置换。
在步骤S5中,采用循环方式求解建立的基于局部最大对齐的后期融合多视图聚类目标函数,得到融合各个基础划分后的最优划分。
本实施例利用三步交替优化法求解步骤S4中的目标函数,具体为:
步骤A1-A3的交替法终止条件表示为:
(obj
(t-1)-obj
(t))/obj
(t)≤ε
其中,obj
(t-1)、obj
(t)分别表示第t和t-1伦迭代的目标函数的值;ε表示设定精度。
在步骤S6中,对最优划分进行k均值聚类,得到聚类结果。得到的最优划分为步骤S4中的目标函数中的变量F,将F的每一行看作样本,对其进行k均值聚类,得到最终的聚类结果。
本实施例包括获取各个视图的邻居矩阵和基础划分,利用各视图的局部信息构建目标函数;然后通过优化,学习到一个拥有局部结构的最优划分矩阵,从而达到提升聚类效果的目的。
实施例二
本实施例提供的基于局部最大对齐的后期融合多视图聚类方法与实施例一的不同之处在于:
将本实施例的技术方案应用于图像数据集中,具体为:
S1.获取与图像相关的聚类任务和目标数据样本;
S2.初始化各个视图的置换矩阵、各个视图的组合系数、对平均核进行核k均值聚类的平均划分、各个视图的邻居矩阵;
S3.计算各个视图的基础划分,建立基于最大对齐的后期融合多视图聚类目标函数;
S4.获取带局部信息的基础划分,并结合各个视图的邻居矩阵和步骤S3,建立基于局部最大对齐的后期融合多视图聚类目标函数;
S5.采用循环方式求解建立的基于局部最大对齐的后期融合多视图聚类目标函数,得到融合各个基础划分后的最优划分;
S6.对最优划分进行k均值聚类,得到聚类结果。
其中,图像数据集包括人脸图像数据集、植物图像数据集、手写阿拉伯数字图像数据集、医疗图像数据集、物体行为动作姿态、商订单数据、海量订单组波、订单波次组合、订单数据挖掘与分析、库存调拨、货架调整、供应链优化、智能补货等等。
本实施例以人脸为例进行说明:
在6个多核标准数据集(其中5个基准数据集和1个大规模数据集)上测试了本方法的聚类性能。
6个多核标准数据集包括AR10P、YALE、Plant、Caltech102-30(简写为Cal102-30)、Flower17和Mnist。其中AR10P为人脸图像数据库,每个人拥有不同的表情、光照或伪装等不同情况下照片。YALE人脸包含来自15个人的165张照片,每个人的照片来自不同的面部表情、姿势或者光照条件。Plant和Flower17则是植物的图像数据集。Caltech102则是由102个种类的不同物品照片构成的数据集,我们从每个类别中选取30个样本作为训练集,记为Caltech102-30。Mnist为大规模数据集,其包含60000个手写的阿拉伯数字图像,用以验证算法在大规模数据集上的性能。数据集的相关信息参见表1。所有数据集的核矩阵均可从互联网下载。
Dataset | Samples | Kernels | Clusters |
AR10P | 130 | 6 | 10 |
YALE | 165 | 5 | 15 |
Plant | 940 | 69 | 4 |
Cal102-30 | 3060 | 48 | 102 |
Flower17 | 1360 | 7 | 17 |
CCV | 6773 | 3 | 20 |
Mnist | 60000 | 3 | 10 |
表1 7个多核标准数据集
本实验采用平均核k均值聚类算法(AMKKM)、最优单视图核k均值聚类算法(SB-KKM)、多核k均值聚类(MKKM)、协同正则化谱聚类(CRSC)、鲁棒的多核聚类(RMKKM)、鲁棒的多视图谱聚类(RMSC)、局部多核k均值聚类(LMKKM)、带矩阵诱导正则化项的多核k均值聚类(MKKM-MR)、基于局部核最大对齐的多核聚类(LKAM)。在所有实验中,所有基准核首先被中心化和正则化。对于所有数据集,假设类别数量已知且被设置为聚类类别数量。本实验使用的对比算法均根据相应的文献设置参数。本方法的参数λ通过网格搜索[2
-5,2
-4,…,2
5]的范围来确定,参数τ通过网格搜索[0.1,0.2,…,1]的范围确定。
本实验使用了常见的聚类准确度(ACC)和归一化互信息(NMI)来显示每种方法的聚类性能。所有方法随机初始化并重复50次并显示最佳结果以减少k均值造成的随机性。
表2 五个基准数据集上不同算法的聚类效果
表2展示了本方法(Proposed)以及对比算法在五个基准数据集上的聚类 效果,标注为“-”代表内存溢出,该算法无法运行。根据该表可以观察到:1.本方法在两种评价标准下,均优于所有对比算法。2.本方法在六个数据集ACC上的表现要分别高于次优的对比算法达12.31%,2.58%,4.58%,3.86%,3.53%。表3给出了本方法在大规模数据集上的表现。从表3可以看出,在很多对比算法因为内存溢出而无法运行时,本方法不但可以顺利运行,还能取得令人最好的效果。这说明了本方法在大规模数据集上的有效性。
表3 两个大规模数据集上不同算法的聚类效果
本实例也给出了每次迭代时的目标函数变化,如图2所示。可以看出目标函数值单调增加且通常在40次迭代之内即可收敛。
图3展示了参数敏感性。从图中可以看出:1)在大范围内,参数的变化都能取得较好的性能;2)部分数据集上的聚类表现对参数较为敏感,并且τ取值为0.1时,效果整体较好。这对超参数的选择有指导性作用。
本实施例可以解决大规模数据上的聚类问题。在7个多核图像数据集(其中5个基准数据集和1个大规模数据集)上的实验结果证明了本方法的性能优于现有的方法。
实施例三
本实施例提供基于局部最大对齐的后期融合多视图聚类系统,包括:
获取模块,用于获取聚类任务和目标数据样本;
初始化模块,用于初始化各个视图的置换矩阵、各个视图的组合系数、对平均核进行核k均值聚类的平均划分、各个视图的邻居矩阵;
第一建立模块,用于计算各个视图的基础划分,建立基于最大对齐的后期融合多视图聚类目标函数;
第二建立模块,用于获得带局部信息的基础划分,并结合各个视图的邻居矩阵和第一建立模块中的目标函数,建立基于局部最大对齐的后期融合多视图 聚类目标函数;
求解模块,用于采用循环方式求解建立的基于局部最大对齐的后期融合多视图聚类目标函数,得到融合各个基础划分后的最优划分;
聚类模块,用于对最优划分进行k均值聚类,得到聚类结果。
进一步的,所述第一建立模块中建立基于最大对齐的后期融合多视图聚类目标函数,表示为:
其中,F表示优化所得的最优划分;β表示各个视图的组合系数组成的向量,β
p表示第p个视图的系数,
表示各个视图的置换矩阵;M表示对平均核进行核k均值聚类获得的平均划分;F
T表示F的置换;W
T表示W的置换;H
p表示由核k均值聚类得到的各个视图的基础划分;m表示视图数量。
进一步的,所述第二建立模块中建立基于局部最大对齐的后期融合多视图聚类目标函数,表示为:
其中,
表示第p个视图中样本i中的τ近邻的指示矩阵,即各个视图的邻居矩阵;n表示样本数;
表示第p个视图中带第i样本局部信息的基础划分矩阵;
表示各个视图的置换矩阵;λ表示正则化参数;
表示带第i个样本局部信息的平均划分矩阵;
表示
的置换。
需要说明的是,本实施例提供的基于局部最大对齐的后期融合多视图聚类系统与实施例一类似,在此不多做赘述。
本实施例包括获取各个视图的邻居矩阵和基础划分,利用各视图的局部信息构建目标函数。然后通过优化,学习到一个拥有局部结构的最优划分矩阵,从而达到提升聚类效果的目的。
注意,上述仅为本申请的较佳实施例及所运用技术原理。本领域技术人员会理解,本申请不限于这里所述的特定实施例,对本领域技术人员来说能够进行各种明显的变化、重新调整和替代而不会脱离本申请的保护范围。因此,虽然通过以上实施例对本申请进行了较为详细的说明,但是本申请不仅仅限于以上实施例,在不脱离本申请构思的情况下,还可以包括更多其他等效实施例,而本申请的范围由所附的权利要求范围决定。
Claims (10)
- 基于局部最大对齐的后期融合多视图聚类方法,其特征在于,包括步骤:S1.获取聚类任务和目标数据样本;S2.初始化各个视图的置换矩阵、各个视图的组合系数、对平均核进行核k均值聚类的平均划分、各个视图的邻居矩阵;S3.计算各个视图的基础划分,建立基于最大对齐的后期融合多视图聚类目标函数;S4.获取带局部信息的基础划分,并结合各个视图的邻居矩阵和步骤S3,建立基于局部最大对齐的后期融合多视图聚类目标函数;S5.采用循环方式求解建立的基于局部最大对齐的后期融合多视图聚类目标函数,得到融合各个基础划分后的最优划分;S6.对最优划分进行k均值聚类,得到聚类结果。
- 根据权利要求5所述的基于局部最大对齐的后期融合多视图聚类方法,其特征在于,所述步骤S5中采用循环方式求解建立的基于局部最大对齐的后期融合多视图聚类目标函数,具体为:
- 根据权利要求6所述的基于局部最大对齐的后期融合多视图聚类方法,其特征在于,所述步骤S5中采用循环方式求解建立的基于局部最大对齐的后期融合多视图聚类目标函数,其中循环的终止条件表示为:(obj (t-1)-obj (t))/obj (t)≤ε其中,obj (t-1)、obj (t)分别表示第t和t-1伦迭代的目标函数的值;ε表示设定精度。
- 基于局部最大对齐的后期融合多视图聚类系统,其特征在于,包括:获取模块,用于获取聚类任务和目标数据样本;初始化模块,用于初始化各个视图的置换矩阵、各个视图的组合系数、对平均核进行核k均值聚类的平均划分、各个视图的邻居矩阵;第一建立模块,用于计算各个视图的基础划分,建立基于最大对齐的后期融合多视图聚类目标函数;第二建立模块,用于获取带局部信息的基础划分,并结合各个视图的邻居矩阵和第一建立模块中的目标函数,建立基于局部最大对齐的后期融合多视图聚类目标函数;求解模块,用于采用循环方式求解建立的基于局部最大对齐的后期融合多视图聚类目标函数,得到融合各个基础划分后的最优划分;聚类模块,用于对最优划分进行k均值聚类,得到聚类结果。
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