When the instances number is smaller than dimensions of the input data, the within-class scatter matrix is singular, which is also named the Small Sample Size (SSS) problem [1].
[1]K. Fukunaga, Introduction to Statistical Patten Recognition, Academic Press, 1990.
When the data dimensionality is larger than the sample size,which is the case for many high-dimensional and low sample size data, all of the three scatter matrices are singular and the
classical LDA cannot be applied directly. This is known as the singularity or undersampled problem in LDA.
参考文献：叶杰平大师的Generalized Linear Discriminant Analysis: A Unified Framework and Efficient Model Selection的1770页
发表于：IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 19, NO. 10, OCTOBER 2008