Corpus ID: 173990775

Independent Component Analysis based on multiple data-weighting

@article{Bedychaj2019IndependentCA,
  title={Independent Component Analysis based on multiple data-weighting},
  author={Andrzej Bedychaj and Przemysław Spurek and Lukasz Struski and Jacek Tabor},
  journal={ArXiv},
  year={2019},
  volume={abs/1906.00028}
}
Independent Component Analysis (ICA) - one of the basic tools in data analysis - aims to find a coordinate system in which the components of the data are independent. In this paper we present Multiple-weighted Independent Component Analysis (MWeICA) algorithm, a new ICA method which is based on approximate diagonalization of weighted covariance matrices. Our idea is based on theoretical result, which says that linear independence of weighted data (for gaussian weights) guarantees independence… Expand
WICA: nonlinear weighted ICA
TLDR
A new nonlinear ICA model is constructed, called WICA, which obtains better and more stable results than other algorithms and a crucial tool is given by a new efficient method of verifying nonlinear dependence with the use of computation of correlation coefficients for normally weighted data. Expand

References

SHOWING 1-10 OF 37 REFERENCES
Independent component analysis, A new concept?
  • P. Comon
  • Mathematics, Computer Science
  • Signal Process.
  • 1994
TLDR
An efficient algorithm is proposed, which allows the computation of the ICA of a data matrix within a polynomial time and may actually be seen as an extension of the principal component analysis (PCA). Expand
Fast and robust fixed-point algorithms for independent component analysis
  • A. Hyvärinen
  • Mathematics, Computer Science
  • IEEE Trans. Neural Networks
  • 1999
TLDR
Using maximum entropy approximations of differential entropy, a family of new contrast (objective) functions for ICA enable both the estimation of the whole decomposition by minimizing mutual information, and estimation of individual independent components as projection pursuit directions. Expand
Kernel independent component analysis
We present a class of algorithms for independent component analysis (ICA) which use contrast functions based on canonical correlations in a reproducing kernel Hilbert space. On the one hand, we showExpand
Fast independent component analysis algorithm with a simple closed-form solution
TLDR
WeICA substantially outperforms other state-of-the-art ICA methods with respect to time complexity, gives very good results in the case of dimension reduction and obtains satisfying restoring level. Expand
ICA based on asymmetry
TLDR
A competitive approach to ICA based on the Split Gaussian distribution, which is well adapted to asymmetric data and which works better than the classical approaches, especially in the case when the underlying density is not symmetric. Expand
Tensorial extensions of independent component analysis for multisubject FMRI analysis
TLDR
The tensor PICA approach is able to efficiently and accurately extract signals of interest in the spatial, temporal, and subject/session domain and gives simple and useful representations of multisubject/multisession FMRI data that can aid the interpretation and optimization of group FMRI studies beyond what can be achieved using model-based analysis techniques. Expand
Probabilistic independent component analysis for functional magnetic resonance imaging
TLDR
An integrated approach to probabilistic independent component analysis for functional MRI (FMRI) data that allows for nonsquare mixing in the presence of Gaussian noise is presented and compared to the spatio-temporal accuracy of results obtained from classical ICA and GLM analyses. Expand
Separation of independent sources from correlated inputs
TLDR
While spectral analysis only uses second-order properties of independent stochastic sources, a procedure based on higher-order analysis (fourth-order cross cumulants) is developed, which leads to a complete identification of the sources. Expand
Kernel ICA: An alternative formulation and its application to face recognition
TLDR
The experiment using a subset of FERET database indicates that the proposed kernel ICA method significantly outperform ICA, PCA and KPCA in terms of the total recognition rate. Expand
Spatial filtering and selection of optimized components in four class motor imagery EEG data using independent components analysis
Three independent components analysis (ICA) algorithms (Infomax, FastICA and SOBI) have been compared with other preprocessing methods in order to find out whether and to which extent spatialExpand
...
1
2
3
4
...