Kernel PCA and de-noising in feature spaces
Proceedings of the 1998 conference on Advances in neural information processing systems II
Cluster Analysis of Biomedical Image Time-Series
International Journal of Computer Vision
Slow feature analysis: unsupervised learning of invariances
Neural Computation
In Search of Non-Gaussian Components of a High-Dimensional Distribution
The Journal of Machine Learning Research
Estimating non-gaussian subspaces by characteristic functions
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
Uniqueness of non-gaussian subspace analysis
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
A blind source separation technique using second-order statistics
IEEE Transactions on Signal Processing
Colored subspace analysis: dimension reduction based on a signal's autocorrelation structure
IEEE Transactions on Circuits and Systems Part I: Regular Papers
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With the advent of high-throughput data recording methods in biology and medicine, the efficient identification of meaningful subspaces within these data sets becomes an increasingly important challenge. Classical dimension reduction techniques such as principal component analysis often do not take the large statistics of the data set into account, and thereby fail if the signal space is for example of low power but meaningful in terms of some other statistics. With 'colored subspace analysis', we propose a method for linear dimension reduction that evaluates the time structure of the multivariate observations. We differentiate the signal subspace from noise by searching for a subspace of nontrivially autocorrelated data; algorithmically we perform this search by joint low-rank approximation. In contrast to blind source separation approaches we however do not require the existence of sources, so the model is applicable to any wide-sense stationary time series without restrictions. Moreover, since the method is based on second-order time structure, it can be efficiently implemented even for large dimensions. We conclude with an application to dimension reduction of functional MRI recordings.