In this paper the exact linear relation between the leading eigenvectors of the modularity matrix and the singular vectors of an uncentered data matrix is developed. Based on this analysis the concept of a modularity component is defined, and its properties are developed. It is shown that modularity component analysis can be used to cluster data similar to how traditional principal component analysis is used except that modularity component analysis does not require data centering.
| Published in | American Journal of Applied Mathematics (Volume 4, Issue 2) |
| DOI | 10.11648/j.ajam.20160402.15 |
| Page(s) | 99-104 |
| 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), 2016. Published by Science Publishing Group |
Data Clustering, Graph Partitioning, Modularity Matrix, Principal Component Analysis
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APA Style
Hansi Jiang, Carl Meyer. (2016). Modularity Component Analysis versus Principal Component Analysis. American Journal of Applied Mathematics, 4(2), 99-104. https://doi.org/10.11648/j.ajam.20160402.15
ACS Style
Hansi Jiang; Carl Meyer. Modularity Component Analysis versus Principal Component Analysis. Am. J. Appl. Math. 2016, 4(2), 99-104. doi: 10.11648/j.ajam.20160402.15
AMA Style
Hansi Jiang, Carl Meyer. Modularity Component Analysis versus Principal Component Analysis. Am J Appl Math. 2016;4(2):99-104. doi: 10.11648/j.ajam.20160402.15
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Download@article{10.11648/j.ajam.20160402.15,
author = {Hansi Jiang and Carl Meyer},
title = {Modularity Component Analysis versus Principal Component Analysis},
journal = {American Journal of Applied Mathematics},
volume = {4},
number = {2},
pages = {99-104},
doi = {10.11648/j.ajam.20160402.15},
url = {https://doi.org/10.11648/j.ajam.20160402.15},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20160402.15},
abstract = {In this paper the exact linear relation between the leading eigenvectors of the modularity matrix and the singular vectors of an uncentered data matrix is developed. Based on this analysis the concept of a modularity component is defined, and its properties are developed. It is shown that modularity component analysis can be used to cluster data similar to how traditional principal component analysis is used except that modularity component analysis does not require data centering.},
year = {2016}
}
TY - JOUR T1 - Modularity Component Analysis versus Principal Component Analysis AU - Hansi Jiang AU - Carl Meyer Y1 - 2016/04/11 PY - 2016 N1 - https://doi.org/10.11648/j.ajam.20160402.15 DO - 10.11648/j.ajam.20160402.15 T2 - American Journal of Applied Mathematics JF - American Journal of Applied Mathematics JO - American Journal of Applied Mathematics SP - 99 EP - 104 PB - Science Publishing Group SN - 2330-006X UR - https://doi.org/10.11648/j.ajam.20160402.15 AB - In this paper the exact linear relation between the leading eigenvectors of the modularity matrix and the singular vectors of an uncentered data matrix is developed. Based on this analysis the concept of a modularity component is defined, and its properties are developed. It is shown that modularity component analysis can be used to cluster data similar to how traditional principal component analysis is used except that modularity component analysis does not require data centering. VL - 4 IS - 2 ER -
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