| Principal Component Analysis has been extensively used in the computer vision field as a method of capturing orthogonal axes of large variability in high-dimensional data sets. Computer vision scientists have come up with reconstructive models which capture the most distinguished features of a human face using Principal Component Analysis, known as "Eigenfaces". Several papers have approached the problem of facial recognition using standard PCA, however very few provide a detailed comparison on the different non-linear kernels which can be used in place of the traditional linear approach. The aim of this paper is to introduce several non-linear kernel functions to the human recognition problem, by working with a set of radial basis kernels, a logarithmic kernel, a Cauchy kernel, and a polynomial kernel. We perform a model assessment for each kernel using a parameter tuning method which minimizes reconstruction error, and display reconstruction plots for each kernel method. We also capture influential physical features of the images in the high-dimensional space (the Eigenface) for each kernel and compare reconstructed and original images, by capturing the Frebenius (L2) norm between test and original image data. |
