Principal Component Analysis (PCA) and Factor Analysis (FA) are common multivariate techniques used for dimensionality reduction. With these techniques it is expected to identify actual number of dimensions while accounting almost all observed variability. Standard PCA is based either on correlation matrix (CORM) or covariance matrix (COVM). When it is based on CORM, scale dependency can be removed but inherent variability cannot be preserved. On the other hand, when PCA is based on COVM, inherent variability can be preserved but scale dependency cannot be removed. As a solution to this issue, this paper suggests scaling each indicator by its mean, resulting in new mean equal to 1 and standard deviation equal to the coefficient of variance (CV). This leads to PCs, which are scale independent while retaining the observed variability. The computation of PCs and factors under the suggested method is derived in the study. The procedure is illustrated using the lowest level administrative division census data of Western province of Sri Lanka.
| Published in | American Journal of Theoretical and Applied Statistics (Volume 6, Issue 2) |
| DOI | 10.11648/j.ajtas.20170602.13 |
| Page(s) | 90-94 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2017. Published by Science Publishing Group |
Scaling Indicators, Coefficient of Variation, Multivariate Techniques, Dimensional Reduction, Computation of PCAs and Factors
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APA Style
Priyadarshana Dharmawardena, Raphel Ouseph Thattil, Sembakutti Samita. (2017). Scale Independent Principal Component Analysis and Factor Analysis with Preserved Inherent Variability of the Indicators. American Journal of Theoretical and Applied Statistics, 6(2), 90-94. https://doi.org/10.11648/j.ajtas.20170602.13
ACS Style
Priyadarshana Dharmawardena; Raphel Ouseph Thattil; Sembakutti Samita. Scale Independent Principal Component Analysis and Factor Analysis with Preserved Inherent Variability of the Indicators. Am. J. Theor. Appl. Stat. 2017, 6(2), 90-94. doi: 10.11648/j.ajtas.20170602.13
AMA Style
Priyadarshana Dharmawardena, Raphel Ouseph Thattil, Sembakutti Samita. Scale Independent Principal Component Analysis and Factor Analysis with Preserved Inherent Variability of the Indicators. Am J Theor Appl Stat. 2017;6(2):90-94. doi: 10.11648/j.ajtas.20170602.13
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Download@article{10.11648/j.ajtas.20170602.13,
author = {Priyadarshana Dharmawardena and Raphel Ouseph Thattil and Sembakutti Samita},
title = {Scale Independent Principal Component Analysis and Factor Analysis with Preserved Inherent Variability of the Indicators},
journal = {American Journal of Theoretical and Applied Statistics},
volume = {6},
number = {2},
pages = {90-94},
doi = {10.11648/j.ajtas.20170602.13},
url = {https://doi.org/10.11648/j.ajtas.20170602.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20170602.13},
abstract = {Principal Component Analysis (PCA) and Factor Analysis (FA) are common multivariate techniques used for dimensionality reduction. With these techniques it is expected to identify actual number of dimensions while accounting almost all observed variability. Standard PCA is based either on correlation matrix (CORM) or covariance matrix (COVM). When it is based on CORM, scale dependency can be removed but inherent variability cannot be preserved. On the other hand, when PCA is based on COVM, inherent variability can be preserved but scale dependency cannot be removed. As a solution to this issue, this paper suggests scaling each indicator by its mean, resulting in new mean equal to 1 and standard deviation equal to the coefficient of variance (CV). This leads to PCs, which are scale independent while retaining the observed variability. The computation of PCs and factors under the suggested method is derived in the study. The procedure is illustrated using the lowest level administrative division census data of Western province of Sri Lanka.},
year = {2017}
}
TY - JOUR T1 - Scale Independent Principal Component Analysis and Factor Analysis with Preserved Inherent Variability of the Indicators AU - Priyadarshana Dharmawardena AU - Raphel Ouseph Thattil AU - Sembakutti Samita Y1 - 2017/03/02 PY - 2017 N1 - https://doi.org/10.11648/j.ajtas.20170602.13 DO - 10.11648/j.ajtas.20170602.13 T2 - American Journal of Theoretical and Applied Statistics JF - American Journal of Theoretical and Applied Statistics JO - American Journal of Theoretical and Applied Statistics SP - 90 EP - 94 PB - Science Publishing Group SN - 2326-9006 UR - https://doi.org/10.11648/j.ajtas.20170602.13 AB - Principal Component Analysis (PCA) and Factor Analysis (FA) are common multivariate techniques used for dimensionality reduction. With these techniques it is expected to identify actual number of dimensions while accounting almost all observed variability. Standard PCA is based either on correlation matrix (CORM) or covariance matrix (COVM). When it is based on CORM, scale dependency can be removed but inherent variability cannot be preserved. On the other hand, when PCA is based on COVM, inherent variability can be preserved but scale dependency cannot be removed. As a solution to this issue, this paper suggests scaling each indicator by its mean, resulting in new mean equal to 1 and standard deviation equal to the coefficient of variance (CV). This leads to PCs, which are scale independent while retaining the observed variability. The computation of PCs and factors under the suggested method is derived in the study. The procedure is illustrated using the lowest level administrative division census data of Western province of Sri Lanka. VL - 6 IS - 2 ER -
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