SPARSE REPRESENTATION, DISCRIMINATIVE DICTIONARIES AND PROJECTIONS FOR VISUAL CLASSIFICATION
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Developments in sensing and communication technologies have led to an explosion in the availability of visual data from multiple sources and modalities. Millions of cameras have been installed in buildings, streets, and airports around the world that are capable of capturing multimodal information such as light, depth, heat etc. These data are potentially a tremendous resource for building robust visual detectors and classifiers. However, the data are often large, mostly unlabeled and increasingly of mixed modality. To extract useful information from these heterogeneous data, one needs to exploit the underlying physical, geometrical or statistical structure across data modalities. For instance, in computer vision, the number of pixels in an image can be rather large, but most inference or representation models use only a few parameters to describe the appearance, geometry, and dynamics of a scene. This has motivated researchers to develop a number of techniques for finding a low-dimensional representation of a high-dimensional dataset. The dominant methodology for modeling and exploiting the low-dimensional structure in high dimensional data is sparse dictionary-based modeling. While discriminative dictionary learning have demonstrated tremendous success in computer vision applications, their performance is often limited by the amount and type of labeled data available for training. In this dissertation, we extend the sparse dictionary learning framework for weakly supervised learning problems such as semi-supervised learning, ambiguously labeled learning and Multiple Instance Learning (MIL). Furthermore, we present nonlinear extensions of these methods using the kernel trick. We also address the problem of choosing the optimal kernel for sparse representation-based classification using Multiple Kernel Learning (MKL) methods. Finally, in order to deal with heterogeneous multimodal data, we present a feature level fusion method based on quadratic programing. The dissertation has been divided into following four parts: 1) In the first part, we develop a discriminative non-linear dictionary learning technique which utilizes both labeled and unlabeled data for learning dictionaries. We compute a probability distribution over class labels for all the unlabeled samples which is updated together with dictionary and sparse coefficients. The algorithm is also extended for ambiguously labeled data when part of the data contains multiple labels for a training sample. 2) Using non-linear dictionaries, we present a multi-class Multiple Instance Learning (MIL) algorithm where the data is given in the form of bags. Each bag contains multiple samples, called instances, out of which at least one belongs to the class of the bag. We propose a noisy-OR model and a generalized mean-based optimization framework for learning the dictionaries in the feature space. The proposed method can be viewed as a generalized dictionary learning algorithm since it reduces to a novel discriminative dictionary learning framework when there is only one instance in each bag. 3) We propose a Multiple Kernel Learning (MKL) algorithm that is based on the Sparse Representation-based Classification (SRC) method. Taking advantage of the non-linear kernel SRC in efficiently representing the non-linearities in the high-dimensional feature space, we propose an MKL method based on the kernel alignment criteria. Our method uses a two step training method to learn the kernel weights and the sparse codes. At each iteration, the sparse codes are updated first while fixing the kernel mixing coefficients, and then the kernel mixing coefficients are updated while fixing the sparse codes. These two steps are repeated until a stopping criteria is met. 4) Finally, using a linear classification model, we study the problem of fusing information from multiple modalities. Many current recognition algorithms combine different modalities based on training accuracy but do not consider the possibility of noise at test time. We describe an algorithm that perturbs test features so that all modalities predict the same class. We enforce this perturbation to be as small as possible via a quadratic program (QP) for continuous features, and a mixed integer program (MIP) for binary features. To efficiently solve the MIP, we provide a greedy algorithm and empirically show that its solution is very close to that of a state-of-the-art MIP solver.