Kernel Canonical Correlation Research Articles

Detecting genetic associations with brain imaging phenotypes in Alzheimer's disease via a novel structured KCCA approach.

Neuroimaging genetics has become an important research topic since it can reveal complex associations between genetic variants (i.e. single nucleotide polymorphisms (SNPs) and the structures or functions of the human brain. However, existing kernel mapping is difficult to directly use the sparse representation method in the kernel feature space, which makes it difficult for most existing sparse canonical correlation analysis (SCCA) methods to be directly promoted in the kernel feature space. To bridge this gap, we adopt a novel alternating projected gradient approach, gradient KCCA (gradKCCA) model to develop a powerful model for exploring the intrinsic associations among genetic markers, imaging quantitative traits (QTs) of interest. Specifically, this model solves kernel canonical correlation (KCCA) with an additional constraint that projection directions have pre-images in the original data space, a sparsity-inducing variant of the model is achieved through controlling the [Formula: see text]-norm of the preimages of the projection directions. We evaluate this model using Alzheimer's disease Neuroimaging Initiative (ADNI) cohort to discover the relationships among SNPs from Alzheimer's disease (AD) risk gene APOE, imaging QTs extracted from structural magnetic resonance imaging (MRI) scans. Our results show that the algorithm not only outperforms the traditional KCCA method in terms of Root Mean Square Error (RMSE) and Correlation Coefficient (CC) but also identify the meaningful and relevant biomarkers of SNPs (e.g. rs157594 and rs405697), which are positively related to right Postcentral and right SupraMarginal brain regions in this study. Empirical results indicate its promising capability in revealing biologically meaningful neuroimaging genetics associations and improving the disease-related mechanistic understanding of AD.

Blind Identification of SIMO Wiener Systems Based on Kernel Canonical Correlation Analysis

We consider the problem of blind identification and equalization of single-input multiple-output (SIMO) nonlinear channels. Specifically, the nonlinear model consists of multiple single-channel Wiener systems that are excited by a common input signal. The proposed approach is based on a well-known blind identification technique for linear SIMO systems. By transforming the output signals into a reproducing kernel Hilbert space (RKHS), a linear identification problem is obtained, which we propose to solve through an iterative procedure that alternates between canonical correlation analysis (CCA) to estimate the linear parts, and kernel canonical correlation (KCCA) to estimate the memoryless nonlinearities. The proposed algorithm is able to operate on systems with as few as two output channels, on relatively small data sets and on colored signals. Simulations are included to demonstrate the effectiveness of the proposed technique.