CLEAR: Clustering based on locality embedding and reconstruction

Abstract

Spectral clustering (SC) is a fundamental technique in the field of data mining and information processing. The similarity matrix of the input data set plays a vital role in SC methods. Since the similarity matrix computation is independent of the clustering procedure, the final results may be suboptimal if the learned similarity is not optimal in SC methods. In this paper, we proposed a novel data Clustering based on Locality Embedding And Reconstruction, CLEAR for short. The proposed CLEAR model combines the graph similarity matrix computation and data clustering procedure together by assigning adaptive weights to the local neighbors of each data point based on locally linear embedding and reconstruction. It is worth noting that CLEAR imposes a rank constraint to the graph Laplacian matrix of the similarity matrix, which leads to a favorable number of graph components in the final clustering. We formulate the proposed CLEAR model in a efficient way which can be solved easily, and show the theoretical relationship to K-means and SC methods. Extensive results on both synthetic data and real-world data show the effectiveness of our method.