Attribute graph adjusted trace ratio linear discriminant analysis for feature extraction

Trace Ratio Linear Discriminant Analysis (TRLDA) is an appealing supervised feature extraction method because it explicitly reflects the Euclidean distances between and within classes of projected samples while preserving data similarity through its orthogonal constraint. However, TRLDA fails to account for inter-attribute correlations, which may limit its discriminant capability. To overcome this limitation, we propose Attribute Graph Adjusted Trace Ratio Linear Discriminant Analysis (AGATRLDA), a novel method that incorporates attribute-level relationships into the discriminant projection matrix. In our approach, each attribute is represented as a point formed by the values of that attribute across all samples. An attribute graph is then constructed by connecting these attribute points with edges weighted according to their pairwise similarity. By integrating the Laplacian matrix of this attribute graph into the optimization framework, AGATRLDA adjusts the discriminant projection matrix to account for inter-attribute correlations. This adjustment encourages attributes with higher similarity to have more aligned coefficients in the projection matrix, thereby improving discriminative performance. Experimental results demonstrate that AGATRLDA consistently outperforms the original TRLDA method as well as several state-of-the-art feature extraction techniques, validating the benefit of incorporating inter-attribute correlations in the discriminant learning process.