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Linear Discriminant Analysis (LDA) is a supervised machine learning technique used for dimensionality reduction and classification. It seeks to find a linear combination of features that maximizes the separation between different classes or categories in a labeled dataset. LDA identifies new variables, called linear discriminants, that capture the most discriminative information in the data, making it easier to classify data points into their respective classes while reducing the dimensionality of the feature space. It is particularly useful when you have multiple classes and want to transform your data into a lower-dimensional space that preserves class-related variations.

In Linear Discriminant Analysis, the random variables X and Y typically refer to the features or attributes of your dataset, where X represents the features or attributes, and Y represents the class labels or target variable. LDA is a supervised dimensionality reduction and classification technique that seeks to find a linear combination of features (X) that best separates different classes or categories (Y) in a dataset.

Here's how LDA works:

1. Input Data: You start with a labeled dataset where each data point is associated with both a set of features (X) and a class label (Y). For example, in a two-class classification problem, Y may take on two values, like 0 and 1, to represent the two classes.

2. Dimensionality Reduction: LDA aims to reduce the dimensionality of the feature space (X) while preserving the discriminative information between different classes (Y). It does this by finding linear combinations of features (X) that maximize the separation between classes.

3. Linear Discriminants: LDA computes linear combinations of features, known as linear discriminants, that maximize the ratio of the between-class variance to the within-class variance. These linear discriminants are the new variables that represent the data in a lower-dimensional space.

4. Classification: Once you have obtained these linear discriminants, you can use them for classification tasks. LDA can be used for both dimensionality reduction and classification simultaneously. It seeks to project the data onto a lower-dimensional space where the classes are well-separated, making classification tasks easier.

Therefore, in LDA, X represents the original features or attributes, and Y represents the class labels or categories you are trying to discriminate between. The goal of LDA is to find linear combinations of X (the linear discriminants) that maximize the separation between the classes represented by Y. These linear discriminants are determined through LDA's mathematical computations and are used for dimensionality reduction and classification purposes.

Table 3964. Applications and related concepts of Linear Discriminant Analysis.

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