Affine Feature Extraction: A Generalization of the Fukunaga-Koontz Transformation

Abstract

Dimension reduction methods are often applied in machine learning and data mining problems. Linear subspace methods are the commonly used ones, such as principal component analysis (PCA), Fisher’s linear discriminant analysis (FDA), et al. In this paper, we describe a novel feature extraction method for binary classification problems. Instead of finding linear subspaces, our method finds lower- dimensional affine subspaces for data observations. Our method can be understood as a generalization of the Fukunaga-Koontz Transformation. We show that the proposed method has a closed-form solution and thus can be solved very efficiently. Also we investigate the information-theoretical properties of the new method and study the relationship of our method with other methods. The experimental results show that our method, as PCA and FDA, can be used as another preliminary data-exploring tool to help solve machine learning and data mining problems.KeywordsFeature ExtractionPartial Little SquareIndependent Component AnalysisLinear SubspaceIndependent Component AnalysisThese 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.