Today, in the class, we were introduced to the concept of Discriminant analysis. It is basically a method to find a linear combination of features which characterize or separate two or more classes of objects or events. It is closely related to ANOVA and Regression Analysis, which also attempt to express one dependent variable as a linear combination of other features or measurements. It is also closely related to the Principal Component Analysis (PCA) and Factor Analysis in that both look for linear combinations of variables which best explains the data.

There are various applications of Discriminant analysis and one of them was taught in class, that was whether a person would default on his bank loan or not. Others include bankruptcy prediction, face recognition, marketing applications, etc. I am going to primarily talk about the facial recognition software application.

Facial recognition software uses a combination of PCA and Linear Discriminant Analysis (LDA) to identify the facial features. PCA is used in this case to approximate the original data with lower dimensional feature vectors. LDA produces an optimal linear Discriminant function which maps the input into classification space in which the class identification of the sample is decided on the basis of some metric such as the Euclidean distance. A pure LDA based system faces some problems in the facial recognition and thus it is combined with PCA.

To process the face images, geometric normalization of the principal components is done. Then the LDA is done on the principal components using the eigenvectors which are the components of PCA. Through this technique we can identify the facial features up to a greater accuracy.

Thus, we can see that Discriminant Analysis forms an important integral component of facial recognition.

Thanks and Regards,

Mittul Desai (13146)

Operations Group 1

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