Classification of compressive sampling data improved with singular value decomposition based preconditioning

Compressive Sensing (CS) and Compressive Classification (CC) are the methods targetting transmission, storage, and information extraction fields of data that progressively demand innovative solutions due to the rapid increase in the amount of data transferred, stored, and processed in the modern world. CS enables lossless reconstruction with high probability with fewer samples than is required in the Shannon sampling theorem. In connection with that gain, CC, which runs on the measurement space generated by CS, provides economy in computation and advantages in operation. In the literature, it is well known the number of samples required for reconstruction and the amount of data to be transmitted/stored reduce by applying preconditioning (PC) to the measurement matrix (MM) in CS. In addition, MM enhancement via the Singular Value Decomposition (SVD) and reconstruction performance relation are also experimentally studied in the literature. Merging MM enhancement via the SVD approach and PC by reformulation is the first contribution in this thesis. At the same time, the other contributions are; naming this combined approach as SVD-PC, analytical proof of reduction of the number of required samples in reconstruction by applying SVD-PC in CS, development of two Monte Carlo simulations for probing the proven outcome of SVD-PC, experimental investigation of the effects of SVD-PC on CC via utilizing three different classification methods (K-Nearest Neighbours (KNN), Random Forest (RF) and Support Vector Machines (SVM)) over five different data sets (MNIST, Fashion MNIST, Chinese MNIST, Sign MNIST, and WARD). One of the findings obtained in the thesis is a precise definition of the effect of SVD-PC on CC performance cannot be made according to the results. Another finding from the observations in this thesis is that, KNN gives better results than the other two methods in classifying the data produced by CS. Moreover, as for classification with KNN, another finding is that CS seems like a close alternative to Principal Component Analysis (PCA) for 25% and 50% compression ratios in dimension reduction. Another exemplary finding in the thesis is that the precision and recall performances of RF are adversely affected by the dimension reduction before classification, with a few exceptions.