SVD-clustering, a general image-analyzing method explained and demonstrated on model and Raman micro-spectroscopic maps

An image analyzing method (SVD-clustering) is presented. Amplitude vectors of SVD factorization (V-1...V-i) were introduced into the imaging of the distribution of the corresponding U-i basis-spectra. Since each V-i vector contains each point of the map, plotting them along the X, Y, Z dimensions of the map reconstructs the spatial distribution of the corresponding U-i basis-spectrum. This gives valuable information about the first, second, etc. higher-order deviations present in the map. We extended SVD with a clustering method, using the significant V-i vectors from the V-T matrix as coordinates of image points in a n(e)-dimensional space (n(e) is the effective rank of the data matrix). This way every image point had a corresponding coordinate in the n(e)-dimensional space and formed a point set. Clustering was applied to this point set. SVD-clustering is universal; it is applicable to any measurement where data are recorded as a function of an external parameter (time, space, temperature, concentration, species, etc.). Consequently, our method is not restricted to spectral imaging, it can find application in many different 2D and 3D image analyses. Using SVD-clustering, we have shown on models the theoretical possibilities and limitations of the method, especially in the context of creating, meaning/interpreting of cluster spectra. Then for real-world samples, two examples are presented, where we were able to reveal minute alterations in the samples (changing cation ratios in minerals, differently structured cellulose domains in plant root) with spatial resolution.