Sparse Representation of High Dimensional Data for Classification

In this thesis we propose the use of sparse Principal Component Analysis (PCA) for representing high dimensional data for classification. Sparse transformation reduces the data volume/dimensionality without loss of critical information, so that it can be processed efficiently and assimilated by a human. We obtained sparse representation of high dimensional dataset using Sparse Principal Component Analysis (SPCA) and Direct formulation of Sparse Principal Component Analysis (DSPCA). Later we performed classification using k Nearest Neighbor (kNN) Method and compared its result with regular PCA. The experiments were performed on hyperspectral data and various datasets obtained from University of California, Irvine (UCI) machine learning dataset repository. The results suggest that sparse data representation is desirable because sparse representation enhances interpretation. It also improves classification performance with certain number of features and in most of the cases classification performance is similar to regular PCA

Multi-Classifiers And Decision Fusion For Robust Statistical Pattern Recognition With Applications To Hyperspectral Classification

In this dissertation, a multi-classifier, decision fusion framework is proposed for robust classification of high dimensional data in small-sample-size conditions. Such datasets present two key challenges. (1) The high dimensional feature spaces compromise the classifiers’ generalization ability in that the classifier tends to overit decision boundaries to the training data. This phenomenon is commonly known as the Hughes phenomenon in the pattern classification community. (2) The small-sample-size of the training data results in ill-conditioned estimates of its statistics. Most classifiers rely on accurate estimation of these statistics for modeling training data and labeling test data, and hence ill-conditioned statistical estimates result in poorer classification performance. This dissertation tests the efficacy of the proposed algorithms to classify primarily remotely sensed hyperspectral data and secondarily diagnostic digital mammograms, since these applications naturally result in very high dimensional feature spaces and often do not have sufficiently large training datasets to support the dimensionality of the feature space. Conventional approaches, such as Stepwise LDA (S-LDA) are sub-optimal, in that they utilize a small subset of the rich spectral information provided by hyperspectral data for classification. In contrast, the approach proposed in this dissertation utilizes the entire high dimensional feature space for classification by identifying a suitable partition of this space, employing a bank-of-classifiers to perform “local” classification over this partition, and then merging these local decisions using an appropriate decision fusion mechanism. Adaptive classifier weight assignment and nonlinear pre-processing (in kernel induced spaces) are also proposed within this framework to improve its robustness over a wide range of fidelity conditions. Experimental results demonstrate that the proposed framework results in significant improvements in classification accuracies (as high as a 12% increase) over conventional approaches

Multi-Classifiers And Decision Fusion For Robust Statistical Pattern Recognition With Applications To Hyperspectral Classification

In this dissertation, a multi-classifier, decision fusion framework is proposed for robust classification of high dimensional data in small-sample-size conditions. Such datasets present two key challenges. (1) The high dimensional feature spaces compromise the classifiers’ generalization ability in that the classifier tends to overit decision boundaries to the training data. This phenomenon is commonly known as the Hughes phenomenon in the pattern classification community. (2) The small-sample-size of the training data results in ill-conditioned estimates of its statistics. Most classifiers rely on accurate estimation of these statistics for modeling training data and labeling test data, and hence ill-conditioned statistical estimates result in poorer classification performance. This dissertation tests the efficacy of the proposed algorithms to classify primarily remotely sensed hyperspectral data and secondarily diagnostic digital mammograms, since these applications naturally result in very high dimensional feature spaces and often do not have sufficiently large training datasets to support the dimensionality of the feature space. Conventional approaches, such as Stepwise LDA (S-LDA) are sub-optimal, in that they utilize a small subset of the rich spectral information provided by hyperspectral data for classification. In contrast, the approach proposed in this dissertation utilizes the entire high dimensional feature space for classification by identifying a suitable partition of this space, employing a bank-of-classifiers to perform “local” classification over this partition, and then merging these local decisions using an appropriate decision fusion mechanism. Adaptive classifier weight assignment and nonlinear pre-processing (in kernel induced spaces) are also proposed within this framework to improve its robustness over a wide range of fidelity conditions. Experimental results demonstrate that the proposed framework results in significant improvements in classification accuracies (as high as a 12% increase) over conventional approaches

Cartographie de paramètres forestiers par fusion évidentielle de données géospatiales multi-sources application aux peuplements forestiers en régénération et feuillus matures du Sud du Québec

Foresters are faced with difficulties to obtain sub-polygon information with the mapping methods available nowadays. The main objective of this work consisted in the development of new methods able to improve the map accuracy of regenerating forest stands and mature forest stands in the South of Québec, Canada. The Dempster-Shafer Theory (DST) and the Dezert-Smarandache Theory (DSmT) showed their ability to integrate multiple heterogenous data sources to go further than the classical classification procedures like the maximum likelihood or the spectral unmixing, in terms of map accuracy. Improvement on the ability to map regenerating stands, passed from 82.7% with the maximum likelihood method to 91.1% with the Free DSm model with a total transfer of the mass of the"Union" class to the"Intersection" class (+ 8.4%). For the mature stands, the improvement passed from 63.8% with the K nearest neighbour to 79.5% with the DST according to a classical belief structuration and the hybrid decision rule for which the conflict threshold was fixed at 10% (+ 15.7%). Our results with DST and a bayesian belief structuration showed the difficulty to model the uncertainty in the fusion process. This is probably due to the lack of scientific knowledge about the influence of the biophysical and climatic parameters on the mapped forest stands and to the necessity to model specifically the uncertainty for each source. Our work showed concrete improvement when mapping forest stands with DST which is encouraging to continue explorating the fundamental principle of the proposed hybrid decision rule. This means a particular focus on the difference between the fused masses of each potential class after the fusion, to choose the best hypothesis