Treatment of Noise in Multivariate Data Analysis Techniques.
Event details
| Date | 27.05.2011 |
| Hour | 10:15 |
| Speaker | Pr. S. Narasimhan, Chemical Engineering Workshop, Indian Institute of Technology Madras, India. |
| Location |
MEC2405
|
| Category | Conferences - Seminars |
The last decade has seen an explosion in the quantum of data available on different systems. This has led to a growth in the development and use of techniques for mining this data for extracting valuable information. The spectrum of applications include speech and image processing, biomedical signal processing, bioinformatics, envirometrics and chemometrics. Several multivariate data analysis techniques such as Principal Components Analysis (PCA) and its variants, Non-negative Matrix Factorization (NMF), Independent Components Analysis (ICA) etc. are among the popular techniques being currently used. Despite the fact that the data obtained in many of the above applications contain a significant amount of noise, relatively less effort has been directed at treating noise in a systematic and theoretically rigorous manner. Methods such as NMF and ICA are developed from a deterministic viewpoint, and typically PCA is used as a pre-processing technique for dealing with noise. The purpose of this talk is to first review the conditions under which PCA is an optimal technique for denoising data. The Iterative PCA (IPCA) method, which we have developed for dealing with heteroscedastic errors in a rigorous manner, by estimating both the noise parameters and the regression model simultaneously, is also discussed. IPCA is further integrated with functional PCA for developing a powerful combined univariate-multivariate denoising technique. The use of the proposed approach in developing more accurate multivariate calibration models and as a pre-processing technique for accurate extraction of source signals from mixtures is illustrated.
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