图 书 馆
大噪声矩阵中结构信息的极小极大局部化Minimax Localization of Structural Information in Large Noisy Matrices |
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| 课程网址: | http://videolectures.net/nips2011_balakrishnan_matrices/ |
| 主讲教师: | Sivaraman Balakrishnan |
| 开课单位: | 卡内基梅隆大学 |
| 开课时间: | 信息不详。欢迎您在右侧留言补充。 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | We consider the problem of identifying a sparse set of relevant columns and rows in a large data matrix with highly corrupted entries. This problem of identifying groups from a collection of bipartite variables such as proteins and drugs, biological species and gene sequences, malware and signatures, etc is commonly referred to as biclustering or co-clustering. Despite its great practical relevance, and although several ad-hoc methods are available for biclustering, theoretical analysis of the problem is largely non-existent. The problem we consider is also closely related to structured multiple hypothesis testing, an area of statistics that has recently witnessed a flurry of activity. We make the following contributions: i) We prove lower bounds on the minimum signal strength needed for successful recovery of a bicluster as a function of the noise variance, size of the matrix and bicluster of interest. ii) We show that a combinatorial procedure based on the scan statistic achieves this optimal limit. iii) We characterize the SNR required by several computationally tractable procedures for biclustering including element-wise thresholding, column/row average thresholding and a convex relaxation approach to sparse singular vector decomposition. |
| 关 键 词: | 聚类; 计算机科学; 机器学习; 特征选择; 数据矩阵 |
| 课程来源: | 视频讲座网 |
| 最后编审: | 2019-11-22：cwx |
| 阅读次数: | 17 |