Covariance-enhanced discriminant analysis

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...

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(...

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...

Repeated measures discriminant analysis 1 Discriminant Analysis for Repeated Measures Data: Effects of Mean and Covariance Misspecification on Bias and Error in Discriminant Function Coefficients

Word Count: 47 Manuscript Word Count: 4387 Repeated measures discriminant analysis 2