Large Scale Spectral Clustering with Landmark-Based Representation

Spectral clustering is one of the most popular clustering approaches. Despite its good performance, it is limited in its applicability to large-scale problems due to its high computational complexity. Recently, many approaches have been proposed to accelerate the spectral clustering. Unfortunately, these methods usually sacrifice quite a lot information of the original data, thus result in a degradation of performance. In this paper, we propose a novel approach, called Landmark-based Spectral Clustering (LSC), for large scale clustering problems. Specifically, we select $p\ (\ll n)$ representative data points as the landmarks and represent the original data points as the linear combinations of these landmarks. The spectral embedding of the data can then be efficiently computed with the landmark-based representation. The proposed algorithm scales linearly with the problem size. Extensive experiments show the effectiveness and efficiency of our approach comparing to the state-of-the-art methods.