改进稀疏子空间聚类算法：避免k-means初始点依赖

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本文主要探讨了"两个修改后的稀疏子空间聚类"（TwoModiﬁedSparseSubspaceClustering）这一主题，该研究发表在一项研究论文中，由来自中国北方大学的信息与通信工程学院和科学学院的研究者XIAOYAN WANG、CAIXIA ZHANG和YANPING BAI共同完成。他们的研究集中在解决稀疏表示（sparse representation）在子空间聚类中的应用问题。原始的稀疏子空间聚类算法（Sparse Subspace Clustering, SSC）利用稀疏表示的系数构建相似度图，通过最小化L1范数获取稀疏系数，并利用谱聚类算法进行数据分组。谱聚类算法依赖于k-means算法进行数据聚类，然而k-means方法对初始点的选择非常敏感，且需要多次迭代，这可能导致结果不稳定和效率低下。为了克服k-means算法的这些局限性，研究人员提出了两种改进的稀疏子空间聚类算法。首先，他们提出了一种方法，其中避免了对中心点的依赖，通过某种策略减少了对初始条件的敏感性。这种方法可能通过优化聚类过程，减少对随机初始化的影响，从而提高聚类的准确性和稳定性。另一种改进是关注减少迭代次数的需求，可能采用了启发式搜索或者其他非迭代策略来确定最佳的聚类分组。这种改变旨在提高算法的计算效率，尤其是在处理大规模数据集时，减少了对计算资源的占用。这两个修改后的稀疏子空间聚类算法旨在提升稀疏表示在复杂数据集上的聚类性能，通过改进现有技术，提高聚类效果的鲁棒性和效率。研究者们的贡献对于处理实际应用中的高维稀疏数据具有重要的理论价值和实践意义，对于机器学习、计算机视觉等领域中的异常检测、模式识别等问题具有潜在的应用前景。

Two Modiﬁed Sparse Subspace Clustering

XIAOYAN WANG

North University of China

School of Information

and Communication Engineering

Xueyuan Road 3, 030051 Taiyuan

CHINA

xywang00@126.com

CAIXIA ZHANG

North University of China

School of Science

Xueyuan Road 3, 030051 Taiyuan

CHINA

18535152702@163.com

YANPING BAI

North University of China

School of Science

Xueyuan Road 3, 030051 Taiyuan

CHINA

baiyp666@163.com

Abstract: Sparse Subspace Clustering constructs a sparse similarity graph by using the coefﬁcient of sparse rep-

resentation to subspace clustering. Based on sparse representation techniques, the algorithm gets the sparse coef-

ﬁcient by using l

-minimization and gets clusters’ data by spectral clustering algorithm. The spectral clustering

algorithm depends on k-means algorithm for data clustering, while k-means algorithm is sensitive to the choice

of initial starting conditions and it needs iterations. In order to avoid the drawbacks of k-means algorithm, we

propose two modiﬁed Sparse Subspace Clustering algorithm, then the results are not be affected by the centers or

the iterations. In one of the method, we get the clusters by comparing the positions of nonzero elements in the

sparse adjacent matrix of similarity graph and the eigenvector. And in the second method, we use SOM algorithm

instead of k-means algorithm. The experiment results show our proposed algorithm outperforms the initial Sparse

Subspace Clustering.

Key–Words: subspace clustering,spectral clustering,k-means,SOM

1 Introduction

Clustering is one of classic problems in pattern

recognition, image processing, machine learning and

statistics [1, 2], which aims to partition a collection

of patterns into disjoint clusters, such that patterns in

the same cluster are similar, however patterns belong

to two different clusters are dissimilar. In many areas

of machine learning, image processing and computer

vision applications require processing and represen-

tation of high-dimensional data. In fact, these high-

dimensional data often can be represented by a low-

dimensional subspace. For example, face images of

a object under varying illumination conditions can be

well approximated by 9-dimensional linear subspace

[3]. Subspace clustering [4] separates data according

to their underlying subspaces and is applied to image

processing [5] and computer vision [6].

Recently, Elhamifar and Vidal [7, 8] have intro-

duced an approach which constructed a sparse similar-

ity graph by using the coefﬁcient of sparse represen-

tation to subspace clustering, called Sparse Subspace

Clustering(SSC). The algorithm based on sparse rep-

resentation techniques and got the sparse coefﬁcient

by using l

-minimization, and clustered data by spec-

tral clustering. The spectral clustering algorithm em-

ployed k-means algorithm for data clustering, how-

ever the k-means algorithm is sensitive to the choice

of initial starting conditions [9, 10] and the process

of the algorithm need iterations. In the literatures,

some modiﬁed algorithms are available: Scalable S-

parse Subspace Clustering(SSSC) [11] and Reweight-

ed Sparse Subspace Clustering [12]. Kernel version

[13, 14] can also be gotten. Patel et al. [15] introduces

an algorithm Latent Space Sparse Subspace Cluster-

ing based on SSC.

In this paper, two modiﬁed SSC algorithms are

proposed in order to avoid the drawbacks of k-means

which gets uncertain results and needs iterations. We

also improve the efﬁciency of the algorithm. By ob-

serving the structure of the adjacent matrix, we ﬁnd

that the nonzero element of columns of matrix is in

the same position as the corresponding eigenvector,

therefore we can get the clusters by comparing nonze-

ro elements in the columns of adjacent matrix and the

eigenvectors. k-means algorithm also can be instead

of by SOM algorithm which can gets better result-

s. We do experiments on synthetic data sets and face

clustering data sets, the results show that our proposed

algorithms are better than original SSC [7, 8].

The rest of paper is organized as follows. We

brieﬂy describe the sparse subspace clustering in sec-

tion 2. In section 3 we analysis SSC algorithm and

propose our algorithms. Experimental evaluation is p-

resented in section 4. Finally section 5 conclude our

work.

Xiaoyan Wang et al.

International Journal of Mathematical and Computational Methods

http://www.iaras.org/iaras/journals/ijmcm

ISSN: 2367-895X

400

Volume 1, 2016

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