l1 Major Component Detection and Analysis (11 MCDA) in Three and Higher Dimensional Spaces
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 19, 2014
- Accession Number
- AD1074507
Entities
People
- Jian Luo
- John E. Lavery
- Shu-cherng Fang
- Zhibin Deng
Organizations
- North Carolina State University