Conference Paper

Fast ISOMAP Based on Minimum Set Coverage

DOI: 10.1007/978-3-642-14932-0_22 Conference: Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence, 6th International Conference on Intelligent Computing, ICIC 2010, Changsha, China, August 18-21, 2010. Proceedings
Source: DBLP


Isometric feature mapping (ISOMAP) has two computational bottlenecks. The first is calculating the N×N graph distance matrix D
. Using Floyd’s algorithm, this is O(N
3); this can be improved to O(kN
2 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(N
3). 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.

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