Kernel Maximum Autocorrelation Factor and Minimum Noise Fraction Transformations

—This paper introduces kernel versions of maximum autocorrelation factor (MAF) analysis and minimum noise fraction (MNF) analysis. The kernel versions are based upon a dual formulation also termed Q-mode analysis in which the data enter into the analysis via inner products in the Gram matrix only. In the kernel version, the inner products of the original data are replaced by inner products between nonlinear mappings into higher dimensional feature space. Via kernel substitution also known as the kernel trick these inner products between the mappings are in turn replaced by a kernel function and all quantities needed in the analysis are expressed in terms of this kernel function. This means that we need not know the nonlinear mappings explicitly. Kernel principal component analysis (PCA), kernel MAF, and kernel MNF analyses handle nonlinearities by implicitly transforming data into high (even infinite) dimensional feature space via the kernel function and then performing a linear ana...

• Type: Journal
• Year: 2011
• Where: TIP
• Authors: Allan Aasbjerg Nielsen
• Keywords: Analysis, Inner Products, Kernel Version, TIP 2011