Independent component analysis, a new concept?
Signal Processing - Special issue on higher order statistics
A fast fixed-point algorithm for independent component analysis
Neural Computation
The Geometry of Algorithms with Orthogonality Constraints
SIAM Journal on Matrix Analysis and Applications
High-order contrasts for independent component analysis
Neural Computation
Kernel independent component analysis
The Journal of Machine Learning Research
Kernel Methods for Measuring Independence
The Journal of Machine Learning Research
Expert Systems with Applications: An International Journal
Sparse spectral clustering method based on the incomplete Cholesky decomposition
Journal of Computational and Applied Mathematics
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A new kernel based contrast function for independent component analysis (ICA) is proposed. This criterion corresponds to a regularized correlation measure in high dimensional feature spaces induced by kernels. The formulation is a multivariate extension of the least squares support vector machine (LS-SVM) formulation to kernel canonical correlation analysis (CCA). The regularization is incorporated naturally in the primal problem leading to a dual generalized eigenvalue problem. The smallest generalized eigenvalue is a measure of correlation in the feature space and a measure of independence in the input space. Due to the primal-dual nature of the proposed approach, the measure of independence can also be extended to out-of-sample points which is important for model selection ensuring statistical reliability of the proposed measure. Computational issues due to the large size of the matrices involved in the eigendecomposition are tackled via the incomplete Cholesky factorization. Simulations with toy data, images and speech signals show improved performance on the estimation of independent components compared with existing kernel-based contrast functions.