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Principal component analysis for probabilistic symbolic data: a more generic and accurate algorithm

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Abstract

In the symbolic data framework, probabilistic symbolic data are considered as those whose components are random variables with general probability distributions. Intervals (or uniform distributions), histograms (or empirical distributions), Gaussian distribution and Chi-squared distribution are all the special cases of them. The existing approaches devoted to the subject have a common shortcoming since they can not obtain the distributions of linear combinations (i.e., principal components) of random variables especially for not identically distributed ones. This paper will overcome the shortcoming by providing an exact probability density function for each principal component by using the inversion theorem. Further, the paper defines a covariance matrix for probabilistic symbolic data and presents a new principal component analysis based on this variance–covariance structure. The effectiveness of the proposed method is illustrated by a simulated numerical experiment, and two real-life cases including clustering of oils and fats data, and evaluation of indexed journals of Science Citation Index.

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Acknowledgments

The authors are grateful to the Editor and anonymous reviewers for their insightful comments which have helped to improve the quality of this paper. This work was supported by the National Natural Science Foundation of China (Grant Nos. 71031001, 70771004, 71371019), and the Program for New Century Excellent Talents in University, by Ministry of Education of China (Grant No. NCET-12-0026).

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Authors and Affiliations

  1. School of Economics and Management, Beihang University, Beijng , 100191, China

    Meiling Chen, Huiwen Wang & Zhongfeng Qin

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  1. Meiling Chen
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  2. Huiwen Wang
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  3. Zhongfeng Qin
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Correspondence to Zhongfeng Qin.

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Chen, M., Wang, H. & Qin, Z. Principal component analysis for probabilistic symbolic data: a more generic and accurate algorithm. Adv Data Anal Classif 9, 59–79 (2015). https://doi.org/10.1007/s11634-014-0178-2

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  • DOI: https://doi.org/10.1007/s11634-014-0178-2

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