| Summary: | A new method for analyzing the intrinsic dimensionality (ID) of low dimensional manifolds in high dimensional feature spaces is presented. The basic idea is to first extract a low-dimensional representation that captures the intrinsic topological structure of the input data and then to analyze this representation, i.e. estimate the intrinsic dimensionality. More specifically, the representation we extract is an optimally topology preserving feature map (OTPM) which is an undirected parametrized graph with a pointer in the input space associated with each node. Estimation of the intrinsic dimensionality is based on local PCA of the pointers of the nodes in the OTPM and their direct neighbors. The method has a number of important advantages compared with previous approaches: First, it can be shown to have only linear time complexity w.r.t. the dimensionality of the input space, in contrast to conventional PCA based approaches which have cubic complexity and hence become computational imp.
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