Some developments in multivariate image analysis

Multivariate image analysis (MIA), one of the successful chemometric applications, now is used widely in different areas of science and industry. Introduced in late 80s it has became very popular with hyperspectral imaging, where MIA is one of the most efficient tools for exploratory analysis and classification. MIA considers all image pixels as objects and their color values (or spectrum in the case of hyperspectral images) as variables. So it gives data matrices with hundreds of thousands samples in the case of laboratory scale images and even more for aerial photos, where the number of pixels could be up to several million. The main MIA tool for exploratory analysis is score density plot – all pixels are projected into principal component space and on the corresponding scores plots are colorized according to their density (how many pixels are crowded in the unit area of the plot). Looking for and analyzing patterns on these plots and the original image allow to do interactive analysis, to get some hidden information, build a supervised classification model, and much more. In the present work several alternative methods to original principal component analysis (PCA) for building the projection subspace have been considered in respect to MIA purposes. First of all, Robust PCA has been applied to several images with and without outliers. Being proposed as a method to deal with high-dimensional data, it suits the needs of MIA very well. Also several non-linear methods have been tried, including Principal Curves and Kernel PCA with different kernel functions. For some of the cases non-linear methods allowed to improve the results significantly giving scores plots where the pixels are organized more effectively according to the nature of the depicted areas and their properties. The detailed comparison of the methods using several examples will be shown.