Abstract

Clustering high-dimensional data has been a challenging problem in data mining and machining learning. Spectral clustering via sparse representation has been proposed for clustering high-dimensional data. A critical step in spectral clustering is to effectively construct a weight matrix by assessing the proximity between each pair of objects. While sparse representation proves its effectiveness for compressing high-dimensional signals, existing spectral clustering algorithms based on sparse representation use those sparse coefficients directly. We believe that the similarity measure exploiting more global information from the coefficient vectors will provide more truthful similarity among data objects. The intuition is that the sparse coefficient vectors corresponding to two similar objects are similar and those of two dissimilar objects are also dissimilar. In particular, we propose two approaches of weight matrix construction according to the similarity of the sparse coefficient vectors. Experimental results on several real-world high-dimensional data sets demonstrate that spectral clustering based on the proposed similarity matrices outperforms existing spectral clustering algorithms via sparse representation.

Highlights

  • As an important task in data mining cluster analysis aims at partitioning data objects into several meaningful subsets, called clusters, such that data objects are similar to those in the same cluster and dissimilar to those in different clusters

  • Spectral clustering is based on the spectral graph model, which searches for clusters in the full feature space and is equivalent to graph min-cut problem based on a graph structure constructed from the original objects in vector space [12]

  • We present a study of spectral clustering based on sparse representation, using two novel weight matrix construction approaches to assess the consistency of two sparse vectors

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Summary

Introduction

As an important task in data mining cluster analysis aims at partitioning data objects into several meaningful subsets, called clusters, such that data objects are similar to those in the same cluster and dissimilar to those in different clusters. We focus on effective weight construction for spectral clustering, based on sparse representation theory. Traditional spectral clustering methods based on sparse representation [16] use these sparse coefficients directly to build the weight matrix, only local information is utilized. Exploiting more global information of the whole coefficient vectors promises better performance, followed by an assumption that the sparse representation vectors corresponding to two similar objects should be similar, since they can be reconstructed in a similar fashion using other data objects. We present a spectral clustering approach of high-dimensional data exploiting global information from sparse representation solution. Using sparse representation, we firstly convert each high-dimensional data object into a vector of sparse coefficients.

Techniques for high-dimensional data
Brief review of sparse representation
Sparse representation for clustering
Graph construction with sparse representation
Sparse representation for spectral clustering
Proximity based on a consistent sign set
Proximity based on cosine similarity of coefficient vector
The relationship between consistent sign set (CSS) and cosine similarity of coefficient vector (COS)
DAi Á DAj
Algorithm description
Experimental results
Conclusion
Full Text
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