Denoising by Singular Value Decomposition and Its Application to Electronic Nose Data Processing

This paper analyzes the role of singular value decomposition (SVD) in denoising sensor array data of electronic nose systems. It is argued that the SVD decomposition of raw data matrix distributes additive noise over orthogonal singular directions representing both the sensor and the odor variables. The noise removal is done by truncating the SVD matrices up to a few largest singular value components, and then reconstructing a denoised data matrix by using the remaining singular vectors. In electronic nose systems this method seems to be very effective in reducing noise components arising from both the odor sampling and delivery system and the sensors electronics. The feature extraction by principal component analysis based on the SVD denoised data matrix is seen to reduce separation between samples of the same class and increase separation between samples of different classes. This is beneficial for improving classification efficiency of electronic noses by reducing overlap between classes in feature space. The efficacy of SVD denoising method in electronic nose data analysis is demonstrated by analyzing five data sets available in public domain which are based on surface acoustic wave (SAW) sensors, conducting composite polymer sensors and the tin-oxide sensors arrays.