The estimation of the gradient of a density function, with applications in pattern recognition

Authors:
K. Fukunaga;L. Hostetler
Affiliations:
-;-
Venue:
IEEE Transactions on Information Theory
Year:
2006

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Abstract

Nonparametric density gradient estimation using a generalized kernel approach is investigated. Conditions on the kernel functions are derived to guarantee asymptotic unbiasedness, consistency, and uniform consistency of the estimates. The results are generalized to obtain a simple mcan-shift estimate that can be extended in ak-nearest-neighbor approach. Applications of gradient estimation to pattern recognition are presented using clustering and intrinsic dimensionality problems, with the ultimate goal of providing further understanding of these problems in terms of density gradients.