Discriminant Functions with Covariance

Covariance-enhanced discriminant analysis.

Linear discriminant analysis has been widely used to characterize or separate multiple classes via linear combinations of features. However, the high dimensionality of features from modern biological experiments defies traditional discriminant analysis techniques. Possible interfeature correlations present additional challenges and are often underused in modelling. In this paper, by incorporati...

COVARIANCE MATRIX OF MULTIVARIATE REWARD PROCESSES WITH NONLINEAR REWARD FUNCTIONS

Multivariate reward processes with reward functions of constant rates, defined on a semi-Markov process, first were studied by Masuda and Sumita, 1991. Reward processes with nonlinear reward functions were introduced in Soltani, 1996. In this work we study a multivariate process , , where are reward processes with nonlinear reward functions respectively. The Laplace transform of the covar...

Pairwise-Covariance Linear Discriminant Analysis

In machine learning, linear discriminant analysis (LDA) is a popular dimension reduction method. In this paper, we first provide a new perspective of LDA from an information theory perspective. From this new perspective, we propose a new formulation of LDA, which uses the pairwise averaged class covariance instead of the globally averaged class covariance used in standard LDA. This pairwise (av...

Supplementary material to: Covariance-Enhanced Discriminant Analysis

Supplementary material for “ Covariance - Enhanced discriminant analysis ”

Proof of Theorem 1. The proof is summarized in the following three steps. First, we prove Qn(ω, μ∗,Ω∗) ≥ Qn(ω, μ∗,Ω∗) for ‖ω(1) − ω∗ (1)‖2 = Op(n). In Step 2, we show that Qn(ω, μ ∗,Ω∗) ≥ Qn(ω, μ∗,Ω) for ‖Ω− Ω‖F = Op{(pn + an) log pn/n}. In Step 3, we prove that Qn(ω, μ∗,Ω) ≥ Qn(ω, μ,Ω) for ‖μ − μ‖2 = Op(pn log pn/n). The following are the details. 20 Step 1. Let ∆ω(1) = ω(1) − ω∗ (1), and h(ω(...