Regularized Non-negative Spectral Embedding for Clustering

--Spectral Clustering is a popular technique to split data points into groups, especially for complex datasets. The algorithms in the Spectral Clustering family typically consist of multiple separate stages (such as similarity matrix construction, low-dimensional embedding, and K-Means clustering as post-processing), which may lead to sub-optimal results because of the possible mismatch between different stages. In this paper, we propose an end-to-end single-stage learning method to clustering called Regularized Nonnegative Spectral Embedding (RNSE) which extends Spectral Clustering with the adaptive learning of similarity matrix and meanwhile utilizes nonnegative constraints to facilitate one-step clustering (directly from data points to clustering labels). Two well-founded methods, successive alternating projection and strategic multiplicative update, are employed to work out the quite challenging optimization problems in RNSE. Extensive experiments on both synthetic and real-world datasets demonstrate RNSE's superior clustering performance to some state-of-the-art competitors. I NTRODUCTION Clustering is an important unsupervised learning task which aims to group a set of data objects into clusters in such a way that objects in the same cluster are more similar to each other than those in different clusters. For complex datasets, Spectral Clustering [1] and its many variants [2]- [4] are particularly popular due to their ability of discovering highly non-convex clusters.