Adaptive graph construction for Isomap manifold learning

Loc Tran; Zezhong Zheng; Guoqing Zhou; Jiang Li

doi:10.1117/12.2082646

16 March 2015 Adaptive graph construction for Isomap manifold learning

Loc Tran, Zezhong Zheng, Guoqing Zhou, Jiang Li

Proceedings Volume 9399, Image Processing: Algorithms and Systems XIII; 939904 (2015) https://doi.org/10.1117/12.2082646
Event: SPIE/IS&T Electronic Imaging, 2015, San Francisco, California, United States

Abstract

Isomap is a classical manifold learning approach that preserves geodesic distance of nonlinear data sets. One of the main drawbacks of this method is that it is susceptible to leaking, where a shortcut appears between normally separated portions of a manifold. We propose an adaptive graph construction approach that is based upon the sparsity property of the ℓ₁ norm. The ℓ₁ enhanced graph construction method replaces k-nearest neighbors in the classical approach. The proposed algorithm is first tested on the data sets from the UCI data base repository which showed that the proposed approach performs better than the classical approach. Next, the proposed approach is applied to two image data sets and achieved improved performances over standard Isomap.

Citation Download Citation

Loc Tran, Zezhong Zheng, Guoqing Zhou, and Jiang Li "Adaptive graph construction for Isomap manifold learning", Proc. SPIE 9399, Image Processing: Algorithms and Systems XIII, 939904 (16 March 2015); https://doi.org/10.1117/12.2082646

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