Abstract
Isometric feature mapping (ISOMAP) has two computational bottlenecks. The first is calculating the N×N graph distance matrix D N . 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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Lei, YK., Xu, Y., Zhang, SW., Wang, SL., Ding, ZG. (2010). Fast ISOMAP Based on Minimum Set Coverage. In: Huang, DS., Zhang, X., Reyes García, C.A., Zhang, L. (eds) Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence. ICIC 2010. Lecture Notes in Computer Science(), vol 6216. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14932-0_22
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DOI: https://doi.org/10.1007/978-3-642-14932-0_22
Publisher Name: Springer, Berlin, Heidelberg
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