A Novel Approach on Linear Discriminant Analysis (LDA)

Linear Discriminant Analysis (LDA) is a method used for dimension reduction and classification. By reducing the dimensions of data interpretation it becomes easier. A new LDA-based coordinate transformation (LDA-CT) approach has been developed that does not depend on the statistical nature of data distribution so that it is more robust to the influence of outliers. This approach transforms data from the old coordinates to the new coordinates so that an optimal gradient is obtained which maximizes the separation distance of the two groups in the projection space. Synthetic data are used to test the performance of this new LDA approach compared to existing LDA performance. The experimental results using synthetic data without and with outliers show that compared to the existing LDA, this new approach is able to make generalizations better and more robustly against the influence of outliers. For data that can be separated linearly, the LDA-CT Optimal method is able to separate classes as far as 0.705390519 better than existing LDA which only separates as far as 0.33440611. For data with outliers, LDA-CT Optimal accuracy is better than existing LDA with 91.67% compared to 75%.