Maximum Likelihood Estimation of Intrinsic Dimension

Part of Advances in Neural Information Processing Systems 17 (NIPS 2004)

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Elizaveta Levina, Peter Bickel


We propose a new method for estimating intrinsic dimension of a dataset derived by applying the principle of maximum likelihood to the distances between close neighbors. We derive the estimator by a Poisson process approximation, assess its bias and variance theo- retically and by simulations, and apply it to a number of simulated and real datasets. We also show it has the best overall performance compared with two other intrinsic dimension estimators.