When a data set resides on a d-dimensional manifold that is not a subspace, linear methods cannot effectively reduce the data dimension. Nonlinear methods need to be applied in this case. In this chapter, we introduce Isomap method, which unfolds a manifold by keeping the geodesic metric on the original data set. The description of the method is given in Section 8.1, and the Isomap algorithm is presented in Section 8.2. In Section 8.3, we introduce Dijkstra’s algorithm that effectively computes graph distances. The experiments and applications of Isomaps are included in Section 8.4. We present the justification of Isomaps in Section 8.5.
KeywordsDimensionality Reduction Geodesic Distance Neighborhood Size Graph Distance Path Distance
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