Twin Learning for Similarity and Clustering: A Unified Kernel Approach

Many similarity-based clustering methods work in two separate steps including similarity matrix computation and subsequent spectral clustering. However, similarity measurement is challenging because it is usually impacted by many factors, e.g., the choice of similarity metric, neighborhood size, scale of data, noise and outliers. Thus the learned similarity matrix is often not suitable, let alone optimal, for the subsequent clustering. In addition, nonlinear similarity often exists in many real world data which, however, has not been effectively considered by most existing methods. To tackle these two challenges, we propose a model to simultaneously learn cluster indicator matrix and similarity information in kernel spaces in a principled way. We show theoretical relationships to kernel k-means, k-means, and spectral clustering methods. Then, to address the practical issue of how to select the most suitable kernel for a particular clustering task, we further extend our model with a multiple kernel learning ability. With this joint model, we can automatically accomplish three subtasks of finding the best cluster indicator matrix, the most accurate similarity relations and the optimal combination of multiple kernels. By leveraging the interactions between these three subtasks in a joint framework, each subtask can be iteratively boosted by using the results of the others towards an overall optimal solution. Extensive experiments are performed to demonstrate the effectiveness of our method.Comment: Published in AAAI 201

Convex Subspace Clustering by Adaptive Block Diagonal Representation

Subspace clustering is a class of extensively studied clustering methods and the spectral-type approaches are its important subclass whose key first step is to learn a coefficient matrix with block diagonal structure. To realize this step, sparse subspace clustering (SSC), low rank representation (LRR) and block diagonal representation (BDR) were successively proposed and have become the state-of-the-arts (SOTAs). Among them, the former two minimize their convex objectives by imposing sparsity and low rankness on the coefficient matrix respectively, but so-desired block diagonality cannot neccesarily be guaranteed practically while the latter designs a block diagonal matrix induced regularizer but sacrifices convexity. For solving this dilemma, inspired by Convex Biclustering, in this paper, we propose a simple yet efficient spectral-type subspace clustering method named Adaptive Block Diagonal Representation (ABDR) which strives to pursue so-desired block diagonality as BDR by coercively fusing the columns/rows of the coefficient matrix via a specially designed convex regularizer, consequently, ABDR naturally enjoys their merits and can adaptively form more desired block diagonality than the SOTAs without needing to prefix the number of blocks as done in BDR. Finally, experimental results on synthetic and real benchmarks demonstrate the superiority of ABDR.Comment: 13 pages, 11 figures, 8 table

STRUCTURED SPARSITY DRIVEN LEARNING: THEORY AND ALGORITHMS

Ph.DDOCTOR OF PHILOSOPH