Abstract
Principal Component Analysis (PCA) is one of the most popular techniques for dimensionality reduction of multivariate data points with application areas covering many branches of science. However, conventional PCA handles the multivariate data in a discrete manner only, i.e., the covariance matrix represents only sample data points rather than higher-order data representations.
In this paper we extend conventional PCA by proposing techniques for constructing the covariance matrix of uniformly sampled continuous regions in parameter space. These regions include polytops defined by convex combinations of sample data, and polyhedral regions defined by intersection of half spaces. The applications of these ideas in practice are simple and shown to be very effective in providing much superior generalization properties than conventional PCA for appearance-based recognition applications.
This work was done while A.S. was a visiting faculty at Stanford University.
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Keywords
- Covariance Matrix
- Independent Component Analysis
- Principal Vector
- False Detection Rate
- Principal Component Analysis Approach
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Levin, A., Shashua, A. (2002). Principal Component Analysis over Continuous Subspaces and Intersection of Half-Spaces. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds) Computer Vision — ECCV 2002. ECCV 2002. Lecture Notes in Computer Science, vol 2352. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47977-5_42
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DOI: https://doi.org/10.1007/3-540-47977-5_42
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