Linear Discriminant Analysis LDA – Fun and Easy Machine Learning

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Linear Discriminant Analysis LDA - Fun and Easy Machine Learning

Linear Discriminant Analysis LDA – Fun and Easy Machine Learning

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Linear Discriminant Analysis (LDA) is most commonly used as dimensionality reduction technique in the pre-processing step for pattern-classification and machine learning applications. The goal is to project a dataset onto a lower-dimensional space with good class-separability in order avoid over-fitting (“curse of dimensionality”) and also reduce computational costs.

Ronald A. Fisher formulated the Linear Discriminant in 1936, and it also has some practical uses as classifier. The original Linear discriminant or Fisher Linear Discriminant Analysis was described for a 2-class problem, and it was then later generalized as “multi-class Linear Discriminant Analysis” or “Multiple Discriminant Analysis” by C. R. Rao in 1948 for his research “The utilization of multiple measurements in problems of biological classification”
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There are many possible techniques for classification of data. Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA) are two commonly used techniques for data classification and dimensionality reduction.
PCA finds the most accurate data representation in a lower dimensional space. It projects data in the directions of maximum variance. However the directions of maximum variance may be not be useful for classification.

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Fisher’s Linear Discriminant Analysis or just LDA projects to a line which it inherently preserves direction useful for data classification. The main idea of LDA is to find projection to a line so that samples from different classes are well separated.

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