Solving Noisy ICA Using Multivariate Wavelet Denoising with an Application to Noisy Latent Variables Regression

Abstract

A novel approach to solve the independent component analysis (ICA) model in the presence of noise is proposed. We use wavelets as natural denoising tools to solve the noisy ICA model. To do this, we use a multivariate wavelet denoising algorithm allowing spatial and temporal dependency. We propose also using a statistical approach, named nested design of experiments, to select the parameters such as wavelet family and thresholding type. This technique helps us to select more convenient combination of the parameters. This approach could be extended to many other problems in which one needs to choose parameters between many choices. The performance of the proposed method is illustrated on the simulated data and promising results are obtained. Also, the suggested method applied in latent variables regression in the presence of noise on real data. The good results confirm the ability of multivariate wavelet denoising to solving noisy ICA.

Keywords:

• Independent component analysis
• Denoising
• Wavelet transform
• Design of experiment
• Regression

Mathematics Subject Classification:

• 62M20
• 62M10
• 62G99
• 65T60

Notes

This condition can be relaxed in many situations.

We use the Matlab efficient code named fastmcd available from ftp://win-ftp.uia.ac.be/pub/software/statis/newfiles/fastmcdm.gz.