Linear Discriminant Analysis

What is Linear Discriminant Analysis? Linear Discriminant Analysis Explained

Linear Discriminant Analysis (LDA) is a dimensionality reduction technique commonly used in machine learning and pattern recognition. It aims to find a linear transformation of the data that maximizes the separation between different classes while preserving the discriminative information.

Here are some key points about Linear Discriminant Analysis (LDA):

Supervised dimensionality reduction: LDA is a supervised learning algorithm that requires labeled data. It assumes that the data points are labeled with their corresponding classes or categories. LDA aims to find a projection that maximizes the separation between classes in the reduced-dimensional space.

Discriminative power: LDA focuses on capturing the discriminative information between classes rather than preserving the overall variance of the data. It seeks to find a projection that minimizes the within-class scatter (variance within each class) and maximizes the between-class scatter (variance between different classes).

Linear transformation: LDA seeks a linear transformation of the original features to a lower-dimensional space. The transformed features, called discriminant functions or linear discriminants, are a linear combination of the original features. The number of discriminant functions is equal to the number of classes minus one.

Dimensionality reduction: LDA reduces the dimensionality of the data by projecting it onto a subspace spanned by the discriminant functions. This reduces the number of features while maximizing the separability between classes. The reduced-dimensional representation can be used for classification or visualization purposes.

Fisher’s criterion: LDA optimizes Fisher’s criterion, which is defined as the ratio of between-class scatter to within-class scatter. Maximizing this criterion ensures that the classes are well-separated in the reduced space, making it easier to classify new, unseen examples.

Normality assumption: LDA assumes that the data follows a multivariate normal distribution within each class. This assumption is essential for estimating the scatter matrices accurately and achieving optimal separation between classes.

Applications: LDA is widely used in various fields, including face recognition, object recognition, text categorization, and bioinformatics. It can be applied to problems where the goal is to reduce the dimensionality of the data while preserving the discriminative information between classes.

Comparison with PCA: LDA is often compared with Principal Component Analysis (PCA), another dimensionality reduction technique. While PCA focuses on capturing the overall variance in the data, LDA emphasizes the separation between classes. PCA is unsupervised and does not consider class labels, while LDA leverages class information to maximize class separability.

LDA is a valuable technique for dimensionality reduction and feature extraction in supervised learning tasks. It provides a lower-dimensional representation of the data that maximizes the discrimination between classes. By identifying the most discriminative features, LDA can improve classification performance and facilitate data visualization.