A Simple Iterative Algorithm for Parsimonious Binary Kernel Fisher Discrimination

By applying recent results in optimization theory variously known as optimization transfer or majorize/minimize algorithms, an algorithm for binary, kernel, Fisher discriminant analysis is introduced that makes use of a non-smooth penalty on the coefficients to provide a parsimonious solution. The problem is converted into a smooth optimization that can be solved iteratively with no greater overhead than iteratively re-weighted least-squares. The result is simple, easily programmed and is shown to perform, in terms of both accuracy and parsimony, as well as or better than a number of leading machine learning algorithms on two well-studied and substantial benchmarks

A robust high-sensitivity algorithm for automated detection of proteins in two-dimensional electrophoresis gels

The automated interpretation of two-dimensional gel electrophoresis images used in protein separation and analysis presents a formidable problem in the detection and characterization of ill-defined spatial objects. We describe in this paper a hierarchical algorithm that provides a robust, high-sensitivity solution to this problem, which can be easily adapted to a variety of experimental situations. The software implementation of this algorithm functions as part of a complete package designed for general protein gel analysis applications

Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problems

Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify its solution. Deriving efficient strategies which jointly brings into play the primal and the dual problems is however a more recent idea which has generated many important new contributions in the last years. These novel developments are grounded on recent advances in convex analysis, discrete optimization, parallel processing, and non-smooth optimization with emphasis on sparsity issues. In this paper, we aim at presenting the principles of primal-dual approaches, while giving an overview of numerical methods which have been proposed in different contexts. We show the benefits which can be drawn from primal-dual algorithms both for solving large-scale convex optimization problems and discrete ones, and we provide various application examples to illustrate their usefulness

Measuring Blood Glucose Concentrations in Photometric Glucometers Requiring Very Small Sample Volumes

Glucometers present an important self-monitoring tool for diabetes patients and therefore must exhibit high accu- racy as well as good usability features. Based on an invasive, photometric measurement principle that drastically reduces the volume of the blood sample needed from the patient, we present a framework that is capable of dealing with small blood samples, while maintaining the required accuracy. The framework consists of two major parts: 1) image segmentation; and 2) convergence detection. Step 1) is based on iterative mode-seeking methods to estimate the intensity value of the region of interest. We present several variations of these methods and give theoretical proofs of their convergence. Our approach is able to deal with changes in the number and position of clusters without any prior knowledge. Furthermore, we propose a method based on sparse approximation to decrease the computational load, while maintaining accuracy. Step 2) is achieved by employing temporal tracking and prediction, herewith decreasing the measurement time, and, thus, improving usability. Our framework is validated on several real data sets with different characteristics. We show that we are able to estimate the underlying glucose concentration from much smaller blood samples than is currently state-of-the- art with sufficient accuracy according to the most recent ISO standards and reduce measurement time significantly compared to state-of-the-art methods