A time-varying distance based interval-valued functional principal component analysis method – A case study of consumer price index
Functional principal component analysis (FPCA) is an extension of conventional principal component analysis (PCA) that allows the processing of functional data. Besides the reduction in dimensionality that is inherent to PCA, FPCA relies on fewer assumptions and offers a greater ability to visualize...
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| Published in | Information sciences Vol. 589; pp. 94 - 116 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
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Elsevier Inc
01.04.2022
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| ISSN | 0020-0255 1872-6291 |
| DOI | 10.1016/j.ins.2021.12.113 |
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| Abstract | Functional principal component analysis (FPCA) is an extension of conventional principal component analysis (PCA) that allows the processing of functional data. Besides the reduction in dimensionality that is inherent to PCA, FPCA relies on fewer assumptions and offers a greater ability to visualize the functional data. Thus, FPCA can be used in, for example, social, economic, and medical research. However, the existing FPCA methods are sensitive to outliers, and underperform when extracting features from interval-valued functional data. At the same time, the existing PCA methods for interval-valued functional data suffer from inconsistency in the interpretation of the principal components, and substantial information loss. Therefore, this paper proposes an interval-valued functional principal component analysis (IFPCA) method based on the time-varying distance function. The time-varying distance function containing information on the midpoint and radius is constructed to mitigate information loss. The novel IFPCA method is also able to solve the problem of the inconsistent interpretation of the principal components. The effectiveness of the method is verified by considering the case of the consumer price index. |
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| AbstractList | Functional principal component analysis (FPCA) is an extension of conventional principal component analysis (PCA) that allows the processing of functional data. Besides the reduction in dimensionality that is inherent to PCA, FPCA relies on fewer assumptions and offers a greater ability to visualize the functional data. Thus, FPCA can be used in, for example, social, economic, and medical research. However, the existing FPCA methods are sensitive to outliers, and underperform when extracting features from interval-valued functional data. At the same time, the existing PCA methods for interval-valued functional data suffer from inconsistency in the interpretation of the principal components, and substantial information loss. Therefore, this paper proposes an interval-valued functional principal component analysis (IFPCA) method based on the time-varying distance function. The time-varying distance function containing information on the midpoint and radius is constructed to mitigate information loss. The novel IFPCA method is also able to solve the problem of the inconsistent interpretation of the principal components. The effectiveness of the method is verified by considering the case of the consumer price index. |
| Author | Wang, Kaili Zhang, Chonghui Balezentis, Tomas Sun, Lirong Xu, Lini |
| Author_xml | – sequence: 1 givenname: Lirong surname: Sun fullname: Sun, Lirong organization: School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China – sequence: 2 givenname: Kaili surname: Wang fullname: Wang, Kaili organization: School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China – sequence: 3 givenname: Lini surname: Xu fullname: Xu, Lini organization: School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China – sequence: 4 givenname: Chonghui surname: Zhang fullname: Zhang, Chonghui organization: School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China – sequence: 5 givenname: Tomas surname: Balezentis fullname: Balezentis, Tomas organization: Lithuanian Centre for Social Sciences, 03220 Vilnius, Lithuania |
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| Cites_doi | 10.1111/j.1467-9868.2010.00769.x 10.1109/ACCESS.2020.2968339 10.1007/s11634-013-0158-y 10.1016/j.chemolab.2003.11.005 10.24963/ijcai.2018/390 10.1080/01621459.2015.1016225 10.1080/01621459.2016.1273115 10.1109/TGRS.2018.2876123 10.1109/LGRS.2017.2783879 10.1111/rssc.12376 10.1214/08-AOAS206 10.1080/01621459.2013.788980 10.1002/cem.868 10.1016/j.csda.2007.05.024 10.1016/j.ejor.2021.02.010 10.1111/biom.12236 10.1016/j.csda.2014.04.012 10.1016/j.ins.2007.05.027 10.1002/sam.10118 10.1016/j.ejor.2015.04.038 10.1111/j.1467-9868.2005.00530.x 10.1007/BF02789706 10.1109/TCYB.2015.2389653 10.3233/JIFS-169058 10.1006/jmva.2001.2027 10.1007/s00180-013-0399-4 10.1016/0166-0462(78)90024-8 |
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| Keywords | Feature extraction Multivariate statistics Interval-valued functional data Time-varying distance function Functional principal component analysis |
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| SubjectTerms | Feature extraction Functional principal component analysis Interval-valued functional data Multivariate statistics Time-varying distance function |
| Title | A time-varying distance based interval-valued functional principal component analysis method – A case study of consumer price index |
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