A Statistical Matrix Representation Using Sliced Orthogonal Nonlinear Correlations for Pattern Recognition

摘要

In pattern recognition, the choice of features to be detected is a critical factor to determine the success or failure of a method; much research has gone into finding the best features for particular tasks. When images are detected by digital cameras, they are usually acquired as rectangular arrays of pixels, so the initial features are pixel values. Some methods use those pixel values directly for processing, for instance in normal matched filtering, whereas other methods execute some degree of pre-processing, such as binarizing the pixel values. An important tool for pattern recognition is the correlation matrix between objects and its zero-mean cousin, the covariance matrix. Because the curse of dimensionality plagues so many pattern recognition procedures, a variety of methods for dimensionality reduction have been proposed. One of the classical statistical procedures is the principal component analysis. This method (known in the communication theory literature the Karhunen-Loeve expansion ) finds a lower-dimensional representation that accounts for the variance of the features. The diagonalization of the correlation or covariance matrix is significant for image processing, because among other advantages, it implies the decomposition of images into independent components, it minimizes entropy, it minimizes the mean squared error when some terms are removed, and it is related to principal value decomposition and to factor analysis. Unfortunately the diagonalization of large matrices corresponding to the covariance matrices of images with many pixels is often beyond the capacity of even today's powerful computers. So it is clear that finding an image decomposition that easily diagonalizes a correlation matrix is of interest; in this paper, we introduce such a decomposition, which we then use in order to see some familiar pattern recognition techniques in a new light, and to propose a new and powerful approach to pattern recognition. The correlation matrix that we propose should not be confused with the classical covariance matrix between objects. Our correlation matrix is between the non-linerly transformed features of two objects.