Fast ISOMAP based on minimum set coverage

Authors:
Ying-Ke Lei;Yangming Xu;Shan-Wen Zhang;Shu-Lin Wang;Zhi-Guo Ding
Affiliations:
State Key Lab. of Pulsed Power Laser Techn., Electronic Eng. Inst., Hefei, Anhui, China and Int. Computing Lab., Inst. of Int. Machines, Chinese Academy of Sciences, Hefei, Anhui, China and Dept. ...;State Key Laboratory of Pulsed Power Laser Technology, Electronic Engineering Institute, Hefei, Anhui, China;Intelligent Computing Laboratory, Institute of Intelligent Machines, Chinese Academy of Sciences, Hefei, Anhui, China;Intelligent Computing Laboratory, Institute of Intelligent Machines, Chinese Academy of Sciences, Hefei, Anhui, China and School of Computer and Communication, Hunan University, Changsha, Hunan, C ...;State Key Laboratory of Pulsed Power Laser Technology, Electronic Engineering Institute, Hefei, Anhui, China
Venue:
ICIC'10 Proceedings of the Advanced intelligent computing theories and applications, and 6th international conference on Intelligent computing
Year:
2010

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Abstract

Isometric feature mapping (ISOMAP) has two computational bottlenecks. The first is calculating the N×N graph distance matrix DN. Using Floyd's algorithm, this is O(N3); this can be improved to O(kN2 log N) by implementing Dijkstra's algorithm. The second bottleneck is the MDS eigenvalue calculation, which involves a full N×N matrix and has complexity O(N3). In this paper, we address both of these inefficiencies by a greedy approximation algorithm of minimum set coverage (MSC). The algorithm learns a minimum subset of overlapping neighborhoods for high dimensional data that lies on or near a low dimensional manifold. The new framework leads to order-of-magnitude reductions in computation time and makes it possible to study much larger problems in manifold learning.