【15-22期VALSE Webinar活动】 报告嘉宾1： 刘光灿 (南京信息工程大学)
主持人： 张开华 (南京信息工程大学)
报告题目：Robust Subspace Clustering in High Dimension: A Deterministic Result [Slides]
报告时间：2015年7月22日晚20:00（北京时间）
文章信息：
[1] Guangcan Liu, Huan Xu, Jinhui Tang, Qingshan Liu, and Shuicheng Yan, A Deterministic Analysis for LRR, EEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI), 2015.
[2] Guangcan Liu, Zhouchen Lin, Shuicheng Yan, Ju Sun, Yong Yu, and Yi Ma. Robust Recovery of Subspace Structures by Low-Rank Representation. IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI), vol. 35, no. 1, pp.171-184, 2013.
[3] Guangcan Liu, Zhouchen Lin, and Yong Yu, Robust Subspace Segmentation by Low-Rank Representation. International Conference on Machine Learning (ICML), pp. 663-670, Haifa, Isreal, June 2010.
[4] Bing Chen, Guangcan Liu, and Shuicheng Yan. Multi-task Low-rank Affinity Pursuit for Image Segmentation. International Conference on Computer Vision (ICCV), pp. 2439-2447, Barcelona, Spain, 2011.
[5] Congyan Lang, Guangcan Liu, and Shuicheng Yan. Saliency Detection by Multi-Task Sparsity Pursuit. IEEE Transactions on Image Processing (TIP), vol.21, no.3, pp. 1327-133, 2011.
报告摘要： It is of great interest to explore the problem of Robust Subspace Clustering: Given a collection of data points approximately drawn from a union of multiple subspaces, the goal is to segment the points into their respective subspaces and remove possible errors as well. In general, without any presumptions about the data, it is virtually hard to resolve this problem for sure. Fortunately, today's data is often high-dimensional and massive, and thus very often the sum of those multiple subspace together has a rank of fairly low, i.e., the union of multiple subspaces could be regarded as a single low-dimensional subspace. This fact drives us to propose a simple yet effectual method for subspace clustering. Similar to prevalent clustering methods, our method also adopts a two-stage framework: It firstly learns an affinity matrix from the given data points and then uses spectral clustering techniques to produce the final clustering results. The inference process of the affinity matrix is formulated as a nuclear norm minimization problem, termed Low-Rank Representation (LRR), which seeks the lowest rank representation among all the candidates that can represent each data point as a linear combination of the other points. It is shown that the convex program associated with LRR solves the subspace clustering problem in the following sense: Under certain conditions, it is proved that LRR can exactly recover the authentic row projector from a given set of data points possibly contaminated by corruptions. Since the subspace membership of the data points is provably determined by the authentic row projector, this further implies that LRR can well solve the robust subspace clustering problem under certain conditions.
报告人简介： Dr. Guangcan Liu received the bachelor's degree in mathematics and the Ph.D. degree in computer science and engineering from Shanghai Jiao Tong University, Shanghai, China, in 2004 and 2010, respectively. He was a Post-Doctoral Researcher with the National University of Singapore, Singapore, from 2011 to 2012, the University of Illinois at Urbana-Champaign, Champaign, IL, USA, from 2012 to 2013, Cornell University, Ithaca, NY, USA, from 2013 to 2014, and Rutgers University, Piscataway, NJ, USA, in 2014. Since 2014, he has been a Professor with the School of Information and Control, Nanjing University of Information Science and Technology, Nanjing, China. His research interests mainly include machine learning, computer vision, and image processing. |
