On Designing Invertible Pseudo Covariance Matrix for Undersampled Cases in Classification
Rashid Mahmood
University of Sargodha, Sargodha, 40100, Pakistan.
Khalid Mahmood Aamir
University of Sargodha, Sargodha, 40100, Pakistan.
Marija Milojević Jevrić *
Mathematical Institute SANU, Kneza Mihaila 36, 11000 Belgrade, Serbia.
Stojan Radenović
Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrade, Serbia and Department of Mathematics, University of Novi Pazar, Novi Pazar, Serbia.
Tehseen Zia
COMSATS Institute of Information Technology, Islamabad, 44000, Pakistan.
*Author to whom correspondence should be addressed.
Abstract
In linear discriminant analysis, determinant and inverse of the covariance matrix are required to be computed. If number of features is greater than the number of available examples, covariance matrix is no longer invertible. A common approach is to reduce dimensionality due to which some features of interest may be lost. When we are not interested in dimensionality reduction, one approach to solve such problems is to take pseudoinverse of covariance matrix which is not always possible. We propose, in such cases, to project covariance matrix onto a highly correlated space to compute pseudoinverse of the matrix. Proposed solution has been tested for classification of microarray gene expression data of colon’s tumor.
Keywords: Covariance matrix, dimensionality reduction, pseudoinverse.