Helpful examples of using Discriminant Analysis machine learning algorithms in scikit-learn.
Discriminant Analysis algorithms are used for classification tasks and involve finding a linear combination of features that best separates two or more classes. The two main types are Linear Discriminant Analysis (LDA) and Quadratic Discriminant Analysis (QDA).
Linear Discriminant Analysis (LDA): LDA assumes that the different classes generate data based on Gaussian distributions with a common covariance matrix but different means. It aims to find a linear decision boundary that maximizes the separation between the classes by projecting the data onto a lower-dimensional space. LDA is effective when class distributions are approximately normal and homoscedastic (having the same covariance matrix).
Quadratic Discriminant Analysis (QDA): QDA is an extension of LDA that relaxes the assumption of a common covariance matrix, allowing each class to have its own covariance matrix. This results in a quadratic decision boundary, which can model more complex class structures. QDA is more flexible than LDA and can handle situations where class distributions have different variances, but it requires more parameters and thus more data to estimate these parameters reliably.
Both LDA and QDA are powerful tools for classification, particularly when the assumptions about the data distributions hold true. They provide interpretable models and are computationally efficient, making them suitable for high-dimensional datasets.