Landmark-Based Spectral Clustering with Local Similarity Representation

Abstract

Clustering analysis is one of the most important tasks in statistics, machine learning, and image processing. Compared to those clustering methods based on Euclidean geometry, spectral clustering has no limitations on the shape of data and can detect linearly non-separable pattern. Due to the high computation complexity of spectral clustering, it is difficult to handle large-scale data sets. Recently, several methods have been proposed to accelerate spectral clustering. Among these methods, landmark-based spectral clustering is one of the most direct methods without losing much information embedded in the data sets. Unfortunately, the existing landmark-based spectral clustering methods do not utilize the prior knowledge embedded in a given similarity function. To address the aforementioned challenges, a landmark-based spectral clustering method with local similarity representation is proposed. The proposed method firstly encodes the original data points with their most ‘similar’ landmarks by using a given similarity function. Then the proposed method performs singular value decomposition on the encoded data points to get the spectral embedded data points. Finally run k-means on the embedded data points to get the clustering results. Extensive experiments show the effectiveness and efficiency of the proposed method.