An Example of Principal Component Analysis
/ November 14, 2017

Principal component analysis is a quantitatively rigorous method for achieving this simplification. The method generates a new set of variables, called principal components. Each principal component is a linear combination of the original variables. All the principal components are orthogonal to each other, so there is no redundant information. The principal components as a whole form an orthogonal basis for the space of the data. Principal component analysis : Introduction PCA is an orthogonal linear transformation that transforms the data to a new coordinate system such that greatest variance by any projection of the data comes to lie on the rst coordinate; the second greatest variance comes up in the second coordinate, and so on. Eigenfaces also known as Principal Components Analysis (PCA) find the minimum mean squared error linear subspace that maps from the original N dimensional data space into an M-dimensional feature space. By doing this, Eigenfaces (where typically M << N) achieve dimensionality reduction by using the M eigenvectors of the covariance matrix corresponding to the largest eigenvalues. The resulting basis vectors are obtained by finding the optimal basis vectors that maximize the total variance of the projected data (i.e. the set of basis vectors that best describe…

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