A simple explanation of what is LDA Classification

 

I am finding it hard to understand the process of Linear discriminant analysis (LDA), and I was wondering if someone could explained it with a simple step by step process in English. I understand LDA is closely related to principal component analysis (PCA). but I have no idea how it gives all the probabilities with a grate precision. And how the training data is related to the actual dataset. I have refer few documents and i don't get much idea. It make more confusing and complicated.

PCA (Principal Component Analysis) is unsupervised or what is the same, it does not use class-label information. Therefore, discriminative information is not necessarily preserve.

  • Minimizes the projection error.

  • Maximizes the variance of projected points.

    Example: Reducing the number of features of a face (Face detection).

    • LDA (Linear Discriminant Analysis): A PCA that takes class-labels into consideration, hence, it's supervised.

  • Maximizes distance between classes.

  • Minimizes distance within classes.

    Example: Separating faces into male and female clusters (Face recognition).

    • LDA与PCA

    With regar to the step by step process, you can easily find an implementation in Google.

    Regarding the classification:

  • Project input x into PCA subspace U, and calculate its projection a
  • Project a into LDA subspace V
  • Find the class with the closest center

    • In simple words, project the input x and then check from which cluster center is closer.

    Image from K. Etemad, R. Chellapa, Discriminant analysis for recognition of human faces. J. Opt. Soc. Am. A,Vol. 14, No. 8, August 1997

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