Affiliations: [a] School of Information Engineering, Yancheng Institute of Technology, Yancheng, Jiangsu, China | [b] Department of Statistics and Actuarial Science, The University of Iowa, IA, USA | [c] Acoustic Science and Technology Laboratory, Harbin Engineering University, Harbin, Heilongjiang, China | [d] College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin, Heilongjiang, China
Abstract: We study the cluster ensemble problem and propose a
cluster ensemble approach based on subspace similarity (CEASS). From a
subspace similarity perspective, we seek the optimal subspace which is most
similar to the given subspaces corresponding to the cluster solutions to be
combined. We formulate the cluster ensemble problem as an optimization
problem of minimizing the squared sum of Euclidean distances between the
standard orthogonal basis vectors of the target subspace and the given
subspaces. We derived an explicit solution to the preceding problem in terms
of singular value decomposition. Moreover, the solution consists of the low
dimensional embeddings of instances. Finally, K-means algorithm with the
minimum-maximum principle is utilized to cluster instances according to
their coordinates in the embedding space. In particular, we circumvent the
initialization problem of K-means by employing CEASS that combines
different K-means clustering solutions obtained from random initialization
to obtain a stable clustering result. We evaluate and compare CEASS so
constructed with several other state-of-art cluster ensemble algorithms
using nine real world datasets. Experimental results demonstrate that CEASS
generally outperforms other algorithms in terms of normalized mutual
information and F1 measure. In addition, CEASS is extremely efficient
compared to hierarchy clustering algorithms.
