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Estimation of Topological Dimension

We present two extensions of the algorithm by Broomhead et al [2] which is based on the idea that singular values that scale linearly with the radius of the data ball can be exploited to develop algorithms for computing topological dimension and for detecting whether data models based on manifolds are appropriate. We present a geometric scaling property and dimensionality criterion that permit the automated application of the algorithm as well as a significant reduction in computational expense. For irregularly distributed data this approach can provide a detailed analysis of the structure of the data including an estimated dimension distribution function. We present our approach on several data sets.