Kernel Isomap
نویسندگان
چکیده
Isomap [4] is a manifold learning algorithm, which extends classical multidimensional scaling (MDS) by considering approximate geodesic distance instead of Euclidean distance. The approximate geodesic distance matrix can be interpreted as a kernel matrix, which implies that Isomap can be solved by a kernel eigenvalue problem. However, the geodesic distance kernel matrix is not guaranteed to be positive semidefinite. In this letter we employ a constant-adding method, which leads to the Mercer kernel-based Isomap algorithm. Numerical experimental results with noisy ”Swiss roll” data, confirm the validity and high performance of our kernel Isomap algorithm. Indexing terms: Embedding, Kernel PCA, Manifold learning, MDS, Nonlinear dimensionality reduction. Appeared in Electronics Letters vol. 40, no. 25, pp. 1612-1613, December 2004. Please address correspondence to Prof. Seungjin Choi, Department of Computer Science, POSTECH, San 31 Hyoja-dong, Nam-gu, Pohang 790-784, Korea, Tel: +82-54-279-2259, Fax: +82-54-279-2299, Email: [email protected]
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