Unsupervised Dimensionality Reduction Based on Fusing Multiple Clustering Results

Wei Wei, Qin Yue, Kai Feng, Junbiao Cui, Jiye Liang

Abstract: The majority of the classical dimensionality reduction methods can be unified into a graph-embedding-based framework. A fixed graph constructed in a high-dimensional space has been extensively employed in the graph-embedding-based dimensionality reduction methods. However, a fixed graph often cannot characterize the structure of high-dimensional data owing to the curse of dimensionality. To solve this problem, we combine graph construction and dimensionality reduction into a coherent framework. Thus, the constructed graph can be updated dynamically in dimensionality reduction. In the existing methods based on the coherent framework, graphs are usually constructed by a type of neighborhood relationship and single clustering result. This study proposes an unsupervised dimensionality reduction method guided by fusing multiple clustering results. In the proposed method, multiple clustering results are first obtained by the k-means algorithm, and then a graph is constructed using a weighted co-association matrix of fusing the clustering results to capture data distribution information. Based on the graph, we present an objective function of combining graph construction and dimensionality reduction to implement mutual guidance between them. Numerical experiments on real data sets illustrate that the proposed method achieves significant improvement over some representative and state-of-the-art unsupervised dimensionality reduction methods.