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Linear Discriminant Analysis (LDA) is a dimensionality reduction and classification method. It finds low-dimensional subspace with the strongest class separation and uses it to perform classification. Use this tag for quadratic DA (QDA) too.
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LDA vs. perceptron
As AdamO suggests in the above comment, you can't really do better than read Chapter 4 of The Elements of Statistical Learning (which I will call HTF) which compares LDA with other linear classificati …