Masking Strategies for Image Manifolds

We consider the problem of selecting an optimal mask for an image manifold, i.e., choosing a subset of the pixels of the image that preserves the manifold's geometric structure present in the original data. Such masking implements a form of compressive sensing through emerging imaging sensor platforms for which the power expense grows with the number of pixels acquired. Our goal is for the manifold learned from masked images to resemble its full image counterpart as closely as possible. More precisely, we show that one can indeed accurately learn an image manifold without having to consider a large majority of the image pixels. In doing so, we consider two masking methods that preserve the local and global geometric structure of the manifold, respectively. In each case, the process of finding the optimal masking pattern can be cast as a binary integer program, which is computationally expensive but can be approximated by a fast greedy algorithm. Numerical experiments show that the relevant manifold structure is preserved through the data-dependent masking process, even for modest mask sizes

Contribution to Graph-based Manifold Learning with Application to Image Categorization.

122 pLos algoritmos de aprendizaje de variedades basados en grafos (Graph,based manifold) son técnicas que han demostrado ser potentes herramientas para la extracción de características y la reducción de la dimensionalidad en los campos de reconomiento de patrones, visión por computador y aprendizaje automático. Estos algoritmos utilizan información basada en las similitudes de pares de muestras y del grafo ponderado resultante para revelar la estructura geométrica intrínseca de la variedad

Contribution to Graph-based Manifold Learning with Application to Image Categorization.

122 pLos algoritmos de aprendizaje de variedades basados en grafos (Graph,based manifold) son técnicas que han demostrado ser potentes herramientas para la extracción de características y la reducción de la dimensionalidad en los campos de reconomiento de patrones, visión por computador y aprendizaje automático. Estos algoritmos utilizan información basada en las similitudes de pares de muestras y del grafo ponderado resultante para revelar la estructura geométrica intrínseca de la variedad

Contribution to supervised representation learning: algorithms and applications.

278 p.In this thesis, we focus on supervised learning methods for pattern categorization. In this context, itremains a major challenge to establish efficient relationships between the discriminant properties of theextracted features and the inter-class sparsity structure.Our first attempt to address this problem was to develop a method called "Robust Discriminant Analysiswith Feature Selection and Inter-class Sparsity" (RDA_FSIS). This method performs feature selectionand extraction simultaneously. The targeted projection transformation focuses on the most discriminativeoriginal features while guaranteeing that the extracted (or transformed) features belonging to the sameclass share a common sparse structure, which contributes to small intra-class distances.In a further study on this approach, some improvements have been introduced in terms of theoptimization criterion and the applied optimization process. In fact, we proposed an improved version ofthe original RDA_FSIS called "Enhanced Discriminant Analysis with Class Sparsity using GradientMethod" (EDA_CS). The basic improvement is twofold: on the first hand, in the alternatingoptimization, we update the linear transformation and tune it with the gradient descent method, resultingin a more efficient and less complex solution than the closed form adopted in RDA_FSIS.On the other hand, the method could be used as a fine-tuning technique for many feature extractionmethods. The main feature of this approach lies in the fact that it is a gradient descent based refinementapplied to a closed form solution. This makes it suitable for combining several extraction methods andcan thus improve the performance of the classification process.In accordance with the above methods, we proposed a hybrid linear feature extraction scheme called"feature extraction using gradient descent with hybrid initialization" (FE_GD_HI). This method, basedon a unified criterion, was able to take advantage of several powerful linear discriminant methods. Thelinear transformation is computed using a descent gradient method. The strength of this approach is thatit is generic in the sense that it allows fine tuning of the hybrid solution provided by different methods.Finally, we proposed a new efficient ensemble learning approach that aims to estimate an improved datarepresentation. The proposed method is called "ICS Based Ensemble Learning for Image Classification"(EM_ICS). Instead of using multiple classifiers on the transformed features, we aim to estimate multipleextracted feature subsets. These were obtained by multiple learned linear embeddings. Multiple featuresubsets were used to estimate the transformations, which were ranked using multiple feature selectiontechniques. The derived extracted feature subsets were concatenated into a single data representationvector with strong discriminative properties.Experiments conducted on various benchmark datasets ranging from face images, handwritten digitimages, object images to text datasets showed promising results that outperformed the existing state-ofthe-art and competing methods

Unsupervised spectral sub-feature learning for hyperspectral image classification

Spectral pixel classification is one of the principal techniques used in hyperspectral image (HSI) analysis. In this article, we propose an unsupervised feature learning method for classification of hyperspectral images. The proposed method learns a dictionary of sub-feature basis representations from the spectral domain, which allows effective use of the correlated spectral data. The learned dictionary is then used in encoding convolutional samples from the hyperspectral input pixels to an expanded but sparse feature space. Expanded hyperspectral feature representations enable linear separation between object classes present in an image. To evaluate the proposed method, we performed experiments on several commonly used HSI data sets acquired at different locations and by different sensors. Our experimental results show that the proposed method outperforms other pixel-wise classification methods that make use of unsupervised feature extraction approaches. Additionally, even though our approach does not use any prior knowledge, or labelled training data to learn features, it yields either advantageous, or comparable, results in terms of classification accuracy with respect to recent semi-supervised methods

High Dimensional Data Set Analysis Using a Large-Scale Manifold Learning Approach

Because of technological advances, a trend occurs for data sets increasing in size and dimensionality. Processing these large scale data sets is challenging for conventional computers due to computational limitations. A framework for nonlinear dimensionality reduction on large databases is presented that alleviates the issue of large data sets through sampling, graph construction, manifold learning, and embedding. Neighborhood selection is a key step in this framework and a potential area of improvement. The standard approach to neighborhood selection is setting a fixed neighborhood. This could be a fixed number of neighbors or a fixed neighborhood size. Each of these has its limitations due to variations in data density. A novel adaptive neighbor-selection algorithm is presented to enhance performance by incorporating sparse ℓ 1-norm based optimization. These enhancements are applied to the graph construction and embedding modules of the original framework. As validation of the proposed ℓ1-based enhancement, experiments are conducted on these modules using publicly available benchmark data sets. The two approaches are then applied to a large scale magnetic resonance imaging (MRI) data set for brain tumor progression prediction. Results showed that the proposed approach outperformed linear methods and other traditional manifold learning algorithms