Njeunje, Franck Olivier NdjakouWith the increasing amount of raw data generation produced every day, it has become pertinent to develop new techniques for data representation, analyses, and interpretation. Motivated by real-world applications, there is a trending interest in techniques such as dimensionality reduction, wavelet decomposition, and classication methods that allow for better understanding of data. This thesis details the development of a new non-linear dimension reduction technique based on transport model by advection. We provide a series of computational experiments, and practical applications in hyperspectral images to illustrate the strength of our algorithm. In wavelet decomposition, we construct a novel Haar approximation technique for functions f in the Lp-space, 0 < p < 1, such that the approximants have support contained in the support of f. Furthermore, a classification algorithm to study tissue-specific deoxyribonucleic acids (DNA) is constructed using the support vector machine. In magnetic resonance imaging, we provide an extension of the T2-store-T2 magnetic resonance relaxometry experiment used in the analysis of magnetization signal from 2 to N exchanging sites, where N >= 2.enDissertationApplied mathematicsComputer scienceStatisticsClassificationData representationDimension reductionMachine LearninUnsupervised LearningWavelet decomposition