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Title: A higher order local intrinsic dimension estimator by regression analysis Authors:  Hideitsu Hino - The Institute of Statistical Mathematics (Japan) [presenting]
Abstract: Estimating intrinsic dimension of the observed dataset is an essential step prior to dimensionality reduction, manifold learning, and visualization. We propose a non-parametric method for estimating the intrinsic dimension of the observed data using the notion of local information dimension and generalized linear model with Poisson error structure. When fitting the power of distance from an inspection point, and the number of samples included inside a ball with radius equal to the distance, to a regression model, a goodness of fit is estimated. By using the maximum likelihood method, the intrinsic dimension around the inspection point is estimated. The method is shown to be comparative to conventional methods on both global and local intrinsic dimension estimation experiments.