Speaker：Ivica Kopriva
Title: L0-Motivated Low-Rank Sparse Subspace Clustering
Time: 10：00 AM, Jun. 20th
Location: Room 306, Electronics and Information Building, Tiancizhuang Campus
Abstract：
In many applications high-dimensional data points are well represented by a union of low-dimensional linear subspaces. Subspace clustering refers to assignment of data points or patterns to subspaces they are drawn from. As opposed to clustering algorithms that rely on spatial proximity between data points subspace clustering handles clusters of arbitrary shapes. That is achieved by k-means clustering of eigenvectors of Laplacian matrix which itself is obtained from representation matrix. Thus, good representation matrix is necessary for accurate clustering. To identify the subspaces, it is important to capture a global and local structure of the data which is achieved by imposing low-rank and sparseness constraints on the data representation matrix. In low-rank sparse subspace clustering (LRSSC), S1 and L1 norms are used to measure rank and sparsity. However, the use of S1 and L1 norms norms leads to an overpenalized problem and only approximates the original problem. In this paper, we propose two L0 quasi-norm based regularizations. First, this paper presents regularization based on multivariate generalization of minimax-concave penalty (GMC-LRSSC), which contains the global minimizers of an L0 quasi-norm regularized objective. Afterward, we introduce the S0 and L0 regularized objective and approximate the proximal map of the joint solution using a proximal average method (S0/L0-LRSSC). The resulting nonconvex optimization problems are solved using an alternating direction method of multipliers with established convergence conditions of both algorithms. Results obtained on synthetic and four real-world datasets show the effectiveness of GMC-RSSC and S0/_0-LRS S0/L0-LRSSC when compared to state-of-the-art methods.
Speaker Biography:
Ivica Kopriva obtained PhD degree from the Faculty of Electrical Engineering and Computing, University of Zagreb in 1998 with a subject in blind source separation. From 2001 till 2005 he was research and senior research scientist at Department of Electrical and Computer Engineering, The George Washington University, Washington D.C., USA. Since 2006 he is senior scientist at the Ruđer Bošković Institute, Zagreb, Croatia. His research interests are related to development of algorithms for unsupervised learning with applications in biomedical image analysis, chemometrics and bioinformatics. He published close to 50 papers in internationally recognized journals and holds three US patents and one EU patent. He is co-author of the research monograph: Kernel Based Algorithms for Mining Huge Data Sets: Supervised, Semi-supervised and Unsupervised Learning, Springer Series: Studies in Computational Intelligence, 2006. He is senior member of the IEEE and the OSA.