Algorithms 2014, 7(3), 429-443; doi:10.3390/a7030429
Article

1 Major Component Detection and Analysis (ℓ1 MCDA) in Three and Higher Dimensional Spaces

1,2email, 2,3email, 2email and 2,* email
Received: 21 May 2014; in revised form: 21 July 2014 / Accepted: 23 July 2014 / Published: 19 August 2014
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract: Based on the recent development of two dimensional ℓ1 major component detection and analysis (ℓ1 MCDA), we develop a scalable ℓ1 MCDA in the n-dimensional space to identify the major directions of star-shaped heavy-tailed statistical distributions with irregularly positioned “spokes” and “clutters”. In order to achieve robustness and efficiency, the proposed ℓ1 MCDA in n-dimensional space adopts a two-level median fit process in a local neighbor of a given direction in each iteration. Computational results indicate that in terms of accuracy ℓ1 MCDA is competitive with two well-known PCAs when there is only one major direction in the data, and ℓ1 MCDA can further determine multiple major directions of the n-dimensional data from superimposed Gaussians or heavy-tailed distributions without and with patterned artificial outliers. With the ability to recover complex spoke structures with heavy-tailed noise and clutter in the data, ℓ1 MCDA has potential to generate better semantics than other methods.
Keywords: multidimensional heavy-tailed distribution; ℓ1-norm; major component; n-dimensional; outlier; pattern recognition; robust principal component analysis
PDF Full-text Download PDF Full-Text [1519 KB, Updated Version, uploaded 20 August 2014 16:13 CEST]
The original version is still available [1519 KB, uploaded 19 August 2014 14:32 CEST]

Export to BibTeX |
EndNote


MDPI and ACS Style

Deng, Z.; Lavery, J.E.; Fang, S.-C.; Luo, J. ℓ1 Major Component Detection and Analysis (ℓ1 MCDA) in Three and Higher Dimensional Spaces. Algorithms 2014, 7, 429-443.

AMA Style

Deng Z, Lavery JE, Fang S-C, Luo J. ℓ1 Major Component Detection and Analysis (ℓ1 MCDA) in Three and Higher Dimensional Spaces. Algorithms. 2014; 7(3):429-443.

Chicago/Turabian Style

Deng, Zhibin; Lavery, John E.; Fang, Shu-Cherng; Luo, Jian. 2014. "ℓ1 Major Component Detection and Analysis (ℓ1 MCDA) in Three and Higher Dimensional Spaces." Algorithms 7, no. 3: 429-443.

Algorithms EISSN 1999-4893 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert