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Principal Component Analysis
• PCA is a powerful tool for analyzing data.
• It is a way of identifying patterns in data, and expressing the data in such a way as to highlight their similarities and differences.
• Principal component analysis (PCA) involves a mathematical procedure that transforms a number of possibly correlated variables into a smaller number of uncorrelated variables called principal components.
• Principal Components Analysis is a method that reduces data dimensionality by performing a covariance analysis between factors.
• One of the main applications of the PCA in Computer Vision is in facial recognition.
• By means of PCA one can transform each original image of the training set into a corresponding Eigen face
Eigen Face Generation
• Each Eigen face represents only certain features of the face, which may or may not be present in the original image.
• If the feature is present in the original image to a higher degree, the share of the corresponding Eigen face in the” sum” of the Eigen faces should be greater.
• First, the original images of the training set are transformed in to a set of Eigen faces E.
• An eigenvector of a matrix is a vector such that, if multiplied with the matrix, the result is always an integer multiple of that vector. This integer value is the corresponding Eigen value of the eigenvector
• Eigenvectors possess following properties:
• They can be determined only for square matrices
• There are n eigenvectors (and corresponding Eigen values) in a n × n matrix.
• All eigenvectors are perpendicular, i.e. at right angle with each other.
Steps Required for PCA Algorithm
Requirements
Operating System
• Linux (32-bit)
• Mac OS X (Intel 32-bit)
• Mac OS X (Intel 64-bit)
• Windows (32-bit)
• Windows (64-bit)
Hardware Requirements:
• CPU 32 bit intel core duo Pentium IV processor with 1.86GHz or similar
• 512 MB RAM
• Disk Space 510 MB
Expected Output:
Eigen faces of the given training