PROJECTION OF MULTIVARIATE DATA ONTO LOWER DIMENSIONAL SPACE BY MINIMIZING LOSS FUNCTION

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  • 損失関数最小化による多変量データの低次元空間への射影
  • ソンシツ カンスウ サイショウカ ニ ヨル タヘンリョウ データ ノ テイジゲン クウカン エ ノ シャエイ

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Homogeneity analysis which includes principal component analysis as a special case is a useful method for describing data structure on a low dimensional space. In the method the homogeneity defined by a loss function based on distance between vectors is used as a measure of homogeneity of variables. Introducing a measure based on distance between a vector and a higher dimensional space, we can extend a concept of homogeneity more broadly, that is, the loss function which defines homogeneity is based on distance between a variable vector and a low dimensional space. In this paper a new method for describing data structure on a low dimensional space is proposed by a natural extension of the concept of homogeneity. The method describes data structure on a low dimensional space by minimizing the loss function based on distances between vectors and a space.

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