Three-Way Spectral Clustering
Hong Shi
1
, Qiang Liu
1
, and Pingxin Wang
1,2(
B
)
1
School of Computer Science, Jiangsu University of Science and Technology,
Zhenjiang 212003, China
wangpingxin@just.edu.cn
2
College of Mathematics and Information Science, Hebei Normal University,
Shijiazhuang 050024, China
Abstract. In recent years, three-way clustering has shown promising
performance in many different fields. In this paper, we present a new
three-way spectral clustering by combining three-way decision and spec-
tral clustering. In the proposed algorithm, we revise the process of spec-
tral clustering and obtain an upper bound of each cluster. Perturbation
analysis is applied to separate the core region from upper bound and
the differences between upper bound and core region are regarded as the
fringe region of specific cluster. The results on UCI data sets show that
such strategy is effective in reducing the value of DBI and increasing the
values of ACC and AS.
Keywords: Spectral clustering
· Three-way decision
Three-way clustering
· Three-way spectral clustering
1 Introduction
Clustering plays a key role in identifying the internal structure of data. The
purpose of clustering is divide a group of unmarked samples into different clusters
in light of similarity, such that the clusters have high intra-class similarity and
low inter-class similarity. Cluster analysis is an unsupervised learning method,
which has been positively applied in image processing [1],websearch[2], security
assurance [3] and bioinformatics [4].
Roughly speaking, hierarchical clustering and partition clustering are the
two most commonly used clustering approaches [5]. We focus on the latter in
this paper. As we know, the k-means [6] is the most frequently used partition
clustering method. It has converged when the centroids no longer change. But
the original k-means algorithm is easy to converge to a local optimal solution and
sensitive to the initial data. With the purpose of clustering on arbitrary shape
sample space and converge to global optimal solution, the spectral clustering [7,
8] method was proposed. The idea of that is to view objects as vertices and
similarities between objects as weighted edges. It turns a clustering problem into
a graph segmentation problem that makes the weights of the edges connecting
different clusters as low as possible and the weights of the edges within a cluster
as high as possible.
c
Springer Nature Switzerland AG 2018
M. Ceci et al. (Eds.): ISMIS 2018, LNAI 11177, pp. 389–398, 2018.
https://doi.org/10.1007/978-3-030-01851-1
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