Partial least squares discriminant analysis: A dimensionality reduction method to classify hyperspectral data

The recent development of more sophisticated spectroscopic methods allows acqui- sition of high dimensional datasets from which valuable information may be extracted using multivariate statistical analyses, such as dimensionality reduction and automatic classification (supervised and unsupervised). In this work, a supervised classification through a partial least squares discriminant analysis (PLS-DA) is performed on the hy- perspectral data. The obtained results are compared with those obtained by the most commonly used classification approaches

Partial least squares discriminant analysis: A dimensionality reduction method to classify hyperspectral data

The recent development of more sophisticated spectroscopic methods allows acquisition of high dimensional datasets from which valuable information may be extracted using multivariate statistical analyses, such as dimensionality reduction and automatic classification (supervised and unsupervised). In this work, a supervised classification through a partial least squares discriminant analysis (PLS-DA) is performed on the hy- perspectral data. The obtained results are compared with those obtained by the most commonly used classification approaches

Inferring Multiple Graphical Structures

Gaussian Graphical Models provide a convenient framework for representing dependencies between variables. Recently, this tool has received a high interest for the discovery of biological networks. The literature focuses on the case where a single network is inferred from a set of measurements, but, as wetlab data is typically scarce, several assays, where the experimental conditions affect interactions, are usually merged to infer a single network. In this paper, we propose two approaches for estimating multiple related graphs, by rendering the closeness assumption into an empirical prior or group penalties. We provide quantitative results demonstrating the benefits of the proposed approaches. The methods presented in this paper are embeded in the R package 'simone' from version 1.0-0 and later

Gradient Hard Thresholding Pursuit for Sparsity-Constrained Optimization

Hard Thresholding Pursuit (HTP) is an iterative greedy selection procedure for finding sparse solutions of underdetermined linear systems. This method has been shown to have strong theoretical guarantee and impressive numerical performance. In this paper, we generalize HTP from compressive sensing to a generic problem setup of sparsity-constrained convex optimization. The proposed algorithm iterates between a standard gradient descent step and a hard thresholding step with or without debiasing. We prove that our method enjoys the strong guarantees analogous to HTP in terms of rate of convergence and parameter estimation accuracy. Numerical evidences show that our method is superior to the state-of-the-art greedy selection methods in sparse logistic regression and sparse precision matrix estimation tasks

Statistical and Stochastic Learning Algorithms for Distributed and Intelligent Systems

In the big data era, statistical and stochastic learning for distributed and intelligent systems focuses on enhancing and improving the robustness of learning models that have become pervasive and are being deployed for decision-making in real-life applications including general classification, prediction, and sparse sensing. The growing prospect of statistical learning approaches such as Linear Discriminant Analysis and distributed Learning being used (e.g., community sensing) has raised concerns around the robustness of algorithm design. Recent work on anomalies detection has shown that such Learning models can also succumb to the so-called \u27edge-cases\u27 where the real-life operational situation presents data that are not well-represented in the training data set. Such cases have been the primary reason for quite a few mis-classification bottleneck problems recently. Although initial research has begun to address scenarios with specific Learning models, there remains a significant knowledge gap regarding the detection and adaptation of learning models to \u27edge-cases\u27 and extreme ill-posed settings in the context of distributed and intelligent systems. With this motivation, this dissertation explores the complex in several typical applications and associated algorithms to detect and mitigate the uncertainty which will substantially reduce the risk in using statistical and stochastic learning algorithms for distributed and intelligent systems

Ill-conditioning and multicollinearity

AbstractIt is well known that unstability of solutions to small changes in inputs causes many problems in numerical computations. Existence, uniqueness and stability of solutions are important features of mathematical problems. Problems that fail to satisfy these conditions are called ill-posed. The purpose of this study is to remind briefly some methods of solution to ill-posed problems and to see the impacts or connections of these techniques to some statistical methods