Marginal Fisher Analysis Based on Matrix Exponential Transformation
Jinrong He · Chinese Journal of Computers · 2014
Marginal Fisher Analysis is a classical supervised linear dimensionality reduction method which has been widely applied in high-dimensional data classification tasks.Since Marginal Fisher Analysis involves matrix inversion operation which may lead to matrix singularity problem in numerical computation,especially when the number of samples is less than the dimensionality of sample,which is called small sample size problem.Principal Component Analysis can be used for data preprocessing to overcome singularity problem,however,it may lose some discrimination information in samples.For dealing with these limitations,according to the non-singularity of matrix exponential,we apply matrix exponential transformation on scatter matrix in Marginal Fisher Analysis,and then the singularity problem in matrix inversion operation is overcame.Theoretical analysis shows that this method is equivalent to Null Space Marginal Fisher Analysis,which can extract information in the null space of intra-class scatter matrix,and then the discriminantability of algorithm is enhanced.Data visualization and face recognition experiments show that the proposed method can effectively extract the potential discriminative information of sample to improve classification performance.