An Extension of Functional PCA to Interval-Valued Functional Data

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  • 区間値関数データに対する主成分分析法の提案
  • クカンチ カンスウ データ ニ タイスル シュセイブン ブンセキホウ ノ テイアン

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Abstract

We discuss an extension of Functional Principal Component Analysis (Functional PCA) to Symbolic Data Analysis (SDA).<BR>SDA proposed by Diday is a new approach for analyzing datasets which are too large and complex to handle with conventional methods. In SDA, an observation is represented by symbolic concept including numerical, interval-valued and modal-valued data. Symbolic PCA methods have been studied as dimension reduction techniques, which are mainly applied to interval-valued data.<BR>Another approach for a huge variety of datasets is Functional Data Analysis (FDA), developed by Ramsay. In FDA, each data is characterized by real-valued functions, rather than by a vector and/or a matrix whose components are real-values. We can analyze datasets effectively with FDA if observations are identified as discretized functions. We can apply FDA, for instance, to time series, spectrometric data, weather data, etc. <BR>In this paper, we introduce an idea of interval-valued functional data with a pair of functions, an upper function and a lower function, and extend an FDA method to the framework of SDA. In particular, we propose an interval-valued functional PCA method based on interval-valued PCA methods. We apply our method to actual data and show its effectiveness.

Journal

  • Ouyou toukeigaku

    Ouyou toukeigaku 39 (1), 21-33, 2010

    Japanese Society of Applied Statistics

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