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Proceedings Paper

A maximum entropy kernel density estimator with applications to function interpolation and texture segmentation
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Paper Abstract

In this paper, we develop a new algorithm to estimate an unknown probability density function given a finite data sample using a tree shaped kernel density estimator. The algorithm formulates an integrated squared error based cost function which minimizes the quadratic divergence between the kernel density and the Parzen density estimate. The cost function reduces to a quadratic programming problem which is minimized within the maximum entropy framework. The maximum entropy principle acts as a regularizer which yields a smooth solution. A smooth density estimate enables better generalization to unseen data and offers distinct advantages in high dimensions and cases where there is limited data. We demonstrate applications of the hierarchical kernel density estimator for function interpolation and texture segmentation problems. When applied to function interpolation, the kernel density estimator improves performance considerably in situations where the posterior conditional density of the dependent variable is multimodal. The kernel density estimator allows flexible non parametric modeling of textures which improves performance in texture segmentation algorithms. We demonstrate performance on a text labeling problem which shows performance of the algorithm in high dimensions. The hierarchical nature of the density estimator enables multiresolution solutions depending on the complexity of the data. The algorithm is fast and has at most quadratic scaling in the number of kernels.

Paper Details

Date Published: 2 February 2006
PDF: 13 pages
Proc. SPIE 6065, Computational Imaging IV, 60650N (2 February 2006); doi: 10.1117/12.640740
Show Author Affiliations
Nikhil Balakrishnan M.D., Univ. of Illinois at Chicago (United States)
St. Francis Hospital of Evanston (United States)
Dan Schonfeld, Univ. of Illinois at Chicago (United States)

Published in SPIE Proceedings Vol. 6065:
Computational Imaging IV
Charles A. Bouman; Eric L. Miller; Ilya Pollak, Editor(s)

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