Applying Linear Discriminant Analysis to Trading Data

Summary

The article explains Linear Discriminant Analysis (LDA) as a supervised method for reducing feature dimensions while retaining information that separates labeled classes. It describes calculating within-class and between-class scatter matrices, solving an eigenvalue problem, selecting leading eigenvectors, and projecting observations into a lower-dimensional space. The discussion also outlines a reusable implementation with fit and transform operations, plus regularization to help stabilize matrix calculations.

The author presents LDA alongside Principal Component Analysis (PCA), which reduces dimensions without using class labels, and says the two methods are compared on a sample dataset and in a strategy tester. The supplied text includes methodological details but omits much of the comparison and its results, so it does not establish which method performs better for trading. LDA relies on assumptions including normally distributed features and shared class covariance, and the article also cautions that scaling transformed features can affect model behavior and interpretability. Any trading application therefore needs validation on relevant data.

Key ideas

• LDA uses class labels to find projections that separate groups while reducing feature dimensions.
• Its calculation compares within-class scatter with between-class scatter through an eigenvalue problem.
• The leading eigenvectors form a projection used to transform training data and later observations.
• Regularization is included to make matrix calculations less error-prone.
• LDA's distribution and covariance assumptions, along with feature scaling choices, can limit how well it applies to a dataset.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.