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Abstract: Dimensionality reduction is a topic of recent interest. In this paper, wepresent the classification constrained dimensionality reduction CCDRalgorithm to account for label information. The algorithm can account formultiple classes as well as the semi-supervised setting. We present anout-of-sample expressions for both labeled and unlabeled data. For unlabeleddata, we introduce a method of embedding a new point as preprocessing to aclassifier. For labeled data, we introduce a method that improves the embeddingduring the training phase using the out-of-sample extension. We investigateclassification performance using the CCDR algorithm on hyper-spectral satelliteimagery data. We demonstrate the performance gain for both local and globalclassifiers and demonstrate a 10% improvement of the $k$-nearest neighborsalgorithm performance. We present a connection between intrinsic dimensionestimation and the optimal embedding dimension obtained using the CCDRalgorithm.

Author: Raviv Raich, Jose A. Costa, Steven B. Damelin, Alfred O. Hero III


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