Linear-Time Subspace Clustering Via Sparse Representations

Amir Adler, Ph.D. Thesis Seminar
Thursday, 26.6.2014, 11:30
Taub 401
Prof. Michael Elad and Prof. Yacov Hel-Or

Subspace clustering is the unsupervised learning problem of clustering a collection of data samples drawn from a union of subspaces, according to their spanning subspaces. State-of-the-art algorithms employ a self-expressive data model in order to construct a graph of relations between data samples, and partition the graph using spectral clustering. These algorithms provide excellent performance for small to medium data collections, however, their polynomial complexity (in the number of data samples) prevents them from scaling up to large data collections with possibly millions of data samples. In this talk I will present linear complexity approaches to solve this problem that are based on sparse representations. The core idea of the proposed approaches is to model the relations between data samples to dictionary atoms (basis elements). The number of the atoms is fixed regardless of the number of data samples, thus, enabling to reduce significantly the overall complexity. Subspace clustering is obtained by two methods: the first employs a probability mixture model followed by a maximum-likelihood decision rule; and the second utilizes a bipartite graph modeling followed by bipartite graph clustering.

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