662 research outputs found
Independent Process Analysis without A Priori Dimensional Information
Recently, several algorithms have been proposed for independent subspace
analysis where hidden variables are i.i.d. processes. We show that these
methods can be extended to certain AR, MA, ARMA and ARIMA tasks. Central to our
paper is that we introduce a cascade of algorithms, which aims to solve these
tasks without previous knowledge about the number and the dimensions of the
hidden processes. Our claim is supported by numerical simulations. As a
particular application, we search for subspaces of facial components.Comment: 9 pages, 2 figure
A matrix-pencil approach to blind separation of colored nonstationary signals
For many signal sources such as speech with distinct, nonwhite power spectral densities, second-order statistics of the received signal mixture can be exploited for signal separation. Without knowledge on noise correlation matrix, we propose a simple and yet effective signal extraction method for signal source separation under unknown temporally white noise. This new and unbiased signal extractor is derived from the matrix pencil formed between output autocorrelation matrices at different delays. Based on the matrix pencil, an ESPRIT-type algorithm is derived to get an optimal solution in least square sense. Our method is well suited for systems with colored sensor noises and for nonstationary signals. © 2000 IEEE.published_or_final_versio
Robustifying Independent Component Analysis by Adjusting for Group-Wise Stationary Noise
We introduce coroICA, confounding-robust independent component analysis, a
novel ICA algorithm which decomposes linearly mixed multivariate observations
into independent components that are corrupted (and rendered dependent) by
hidden group-wise stationary confounding. It extends the ordinary ICA model in
a theoretically sound and explicit way to incorporate group-wise (or
environment-wise) confounding. We show that our proposed general noise model
allows to perform ICA in settings where other noisy ICA procedures fail.
Additionally, it can be used for applications with grouped data by adjusting
for different stationary noise within each group. Our proposed noise model has
a natural relation to causality and we explain how it can be applied in the
context of causal inference. In addition to our theoretical framework, we
provide an efficient estimation procedure and prove identifiability of the
unmixing matrix under mild assumptions. Finally, we illustrate the performance
and robustness of our method on simulated data, provide audible and visual
examples, and demonstrate the applicability to real-world scenarios by
experiments on publicly available Antarctic ice core data as well as two EEG
data sets. We provide a scikit-learn compatible pip-installable Python package
coroICA as well as R and Matlab implementations accompanied by a documentation
at https://sweichwald.de/coroICA/Comment: equal contribution between Pfister and Weichwal
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