A Novel Hybrid Dimensionality Reduction Method using Support Vector Machines and Independent Component Analysis

Due to the increasing demand for high dimensional data analysis from various applications such as electrocardiogram signal analysis and gene expression analysis for cancer detection, dimensionality reduction becomes a viable process to extracts essential information from data such that the high-dimensional data can be represented in a more condensed form with much lower dimensionality to both improve classification accuracy and reduce computational complexity. Conventional dimensionality reduction methods can be categorized into stand-alone and hybrid approaches. The stand-alone method utilizes a single criterion from either supervised or unsupervised perspective. On the other hand, the hybrid method integrates both criteria. Compared with a variety of stand-alone dimensionality reduction methods, the hybrid approach is promising as it takes advantage of both the supervised criterion for better classification accuracy and the unsupervised criterion for better data representation, simultaneously. However, several issues always exist that challenge the efficiency of the hybrid approach, including (1) the difficulty in finding a subspace that seamlessly integrates both criteria in a single hybrid framework, (2) the robustness of the performance regarding noisy data, and (3) nonlinear data representation capability. This dissertation presents a new hybrid dimensionality reduction method to seek projection through optimization of both structural risk (supervised criterion) from Support Vector Machine (SVM) and data independence (unsupervised criterion) from Independent Component Analysis (ICA). The projection from SVM directly contributes to classification performance improvement in a supervised perspective whereas maximum independence among features by ICA construct projection indirectly achieving classification accuracy improvement due to better intrinsic data representation in an unsupervised perspective. For linear dimensionality reduction model, I introduce orthogonality to interrelate both projections from SVM and ICA while redundancy removal process eliminates a part of the projection vectors from SVM, leading to more effective dimensionality reduction. The orthogonality-based linear hybrid dimensionality reduction method is extended to uncorrelatedness-based algorithm with nonlinear data representation capability. In the proposed approach, SVM and ICA are integrated into a single framework by the uncorrelated subspace based on kernel implementation. Experimental results show that the proposed approaches give higher classification performance with better robustness in relatively lower dimensions than conventional methods for high-dimensional datasets

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

Multivariate Analysis Applications in X-ray Diffraction

: Multivariate analysis (MA) is becoming a fundamental tool for processing in an efficient way the large amount of data collected in X-ray diffraction experiments. Multi-wedge data collections can increase the data quality in case of tiny protein crystals; in situ or operando setups allow investigating changes on powder samples occurring during repeated fast measurements; pump and probe experiments at X-ray free-electron laser (XFEL) sources supply structural characterization of fast photo-excitation processes. In all these cases, MA can facilitate the extraction of relevant information hidden in data, disclosing the possibility of automatic data processing even in absence of a priori structural knowledge. MA methods recently used in the field of X-ray diffraction are here reviewed and described, giving hints about theoretical background and possible applications. The use of MA in the framework of the modulated enhanced diffraction technique is described in detail