Jump-sparse and sparse recovery using Potts functionals

We recover jump-sparse and sparse signals from blurred incomplete data corrupted by (possibly non-Gaussian) noise using inverse Potts energy functionals. We obtain analytical results (existence of minimizers, complexity) on inverse Potts functionals and provide relations to sparsity problems. We then propose a new optimization method for these functionals which is based on dynamic programming and the alternating direction method of multipliers (ADMM). A series of experiments shows that the proposed method yields very satisfactory jump-sparse and sparse reconstructions, respectively. We highlight the capability of the method by comparing it with classical and recent approaches such as TV minimization (jump-sparse signals), orthogonal matching pursuit, iterative hard thresholding, and iteratively reweighted $\ell^1$ minimization (sparse signals)

Partial Least Squares: A Versatile Tool for the Analysis of High-Dimensional Genomic Data

Partial Least Squares (PLS) is a highly efficient statistical regression technique that is well suited for the analysis of high-dimensional genomic data. In this paper we review the theory and applications of PLS both under methodological and biological points of view. Focusing on microarray expression data we provide a systematic comparison of the PLS approaches currently employed, and discuss problems as different as tumor classification, identification of relevant genes, survival analysis and modeling of gene networks

Improving discrimination of Raman spectra by optimising preprocessing strategies on the basis of the ability to refine the relationship between variance components

Discrimination of the samples into predefined groups is the issue at hand in many fields, such as medicine, environmental and forensic studies, etc. Its success strongly depends on the effectiveness of groups separation, which is optimal when the group means are much more distant than the data within the groups, i.e. the variation of the group means is greater than the variation of the data averaged over all groups. The task is particularly demanding for signals (e.g. spectra) as a lot of effort is required to prepare them in a way to uncover interesting features and turn them into more meaningful information that better fits for the purpose of data analysis. The solution can be adequately handled by using preprocessing strategies which should highlight the features relevant for further analysis (e.g. discrimination) by removing unwanted variation, deteriorating effects, such as noise or baseline drift, and standardising the signals. The aim of the research was to develop an automated procedure for optimising the choice of the preprocessing strategy to make it most suitable for discrimination purposes. The authors propose a novel concept to assess the goodness of the preprocessing strategy using the ratio of the between-groups to within-groups variance on the first latent variable derived from regularised MANOVA that is capable of exposing the groups differences for highly multidimensional data. The quest for the best preprocessing strategy was carried out using the grid search and much more efficient genetic algorithm. The adequacy of this novel concept, that remarkably supports the discrimination analysis, was verified through the assessment of the capability of solving two forensic comparison problems - discrimination between differently-aged bloodstains and various car paints described by Raman spectra - using likelihood ratio framework, as a recommended tool for discriminating samples in the forensics

Some Recent Advances in Measurement Error Models and Methods

A measurement error model is a regression model with (substantial) measurement errors in the variables. Disregarding these measurement errors in estimating the regression parameters results in asymptotically biased estimators. Several methods have been proposed to eliminate, or at least to reduce, this bias, and the relative efficiency and robustness of these methods have been compared. The paper gives an account of these endeavors. In another context, when data are of a categorical nature, classification errors play a similar role as measurement errors in continuous data. The paper also reviews some recent advances in this field

A Simple Flood Forecasting Scheme Using Wireless Sensor Networks

This paper presents a forecasting model designed using WSNs (Wireless Sensor Networks) to predict flood in rivers using simple and fast calculations to provide real-time results and save the lives of people who may be affected by the flood. Our prediction model uses multiple variable robust linear regression which is easy to understand and simple and cost effective in implementation, is speed efficient, but has low resource utilization and yet provides real time predictions with reliable accuracy, thus having features which are desirable in any real world algorithm. Our prediction model is independent of the number of parameters, i.e. any number of parameters may be added or removed based on the on-site requirements. When the water level rises, we represent it using a polynomial whose nature is used to determine if the water level may exceed the flood line in the near future. We compare our work with a contemporary algorithm to demonstrate our improvements over it. Then we present our simulation results for the predicted water level compared to the actual water level.Comment: 16 pages, 4 figures, published in International Journal Of Ad-Hoc, Sensor And Ubiquitous Computing, February 2012; V. seal et al, 'A Simple Flood Forecasting Scheme Using Wireless Sensor Networks', IJASUC, Feb.201