R Code to Accompany “Principal Component Analysis and Optimization: A Tutorial”

This data accompanies Principal Component Analysis and Optimization: A Tutorial by Robert Reris and J. Paul Brooks, presented at the 2015 INFORMS Computing Society Conference, Operations Research and Computing: Algorithms and Software for Analytics, Richmond, Virginia January 11-13, 2015. The data contains R code, output, and comments that follow the examples for principal component analysis in the paper

The Support Vector Machine and Mixed Integer Linear Programming: Ramp Loss SVM with L1-Norm Regularization

The support vector machine (SVM) is a flexible classification method that accommodates a kernel trick to learn nonlinear decision rules. The traditional formulation as an optimization problem is a quadratic program. In efforts to reduce computational complexity, some have proposed using an L1-norm regularization to create a linear program (LP). In other efforts aimed at increasing the robustness to outliers, investigators have proposed using the ramp loss which results in what may be expressed as a quadratic integer programming problem (QIP). In this paper, we consider combining these ideas for ramp loss SVM with L1-norm regularization. The result is four formulations for SVM that each may be expressed as a mixed integer linear program (MILP). We observe that ramp loss SVM with L1-norm regularization provides robustness to outliers with the linear kernel. We investigate the time required to find good solutions to the various formulations using a branch and bound solver

R Code to Accompany “Principal Component Analysis and Optimization: A Tutorial”

This data accompanies Principal Component Analysis and Optimization: A Tutorial by Robert Reris and J. Paul Brooks, presented at the 2015 INFORMS Computing Society Conference, Operations Research and Computing: Algorithms and Software for Analytics, Richmond, Virginia January 11-13, 2015. The data contains R code, output, and comments that follow the examples for principal component analysis in the paper

Children’s tolerance of word-form variation

How much morphological variation can children tolerate when identifying familiar words? This is an important question in the context of the acquisition of richly inflected languages where identical word forms occur far less frequently than in English. To address this question, we compared children’s (N = 96, mean age 4;1, range 2;11–5;1) and adults’ (N = 96, mean age 21 years) tolerance of word-onset modifications (e.g., for stug: wug and wastug) and pseudoaffixes (e.g., kostug and stugko) in a labelextension task. Word-form modifications were repeated within each experiment to establish productive inflectional patterns. In two experiments, children and adults exhibited similar strategies: they were more tolerant of prefixes (wastug) than substitutions of initial consonants (wug), and more tolerant of suffixes (stugko) than prefixes (kostug). The findings point to word-learning strategies as being flexible and adaptive to morphological patterns in languages

Principal Component Analysis and Optimization: A Tutorial

This data accompanies Principal Component Analysis and Optimization: A Tutorial by Robert Reris and J. Paul Brooks, presented at the 2015 INFORMS Computing Society Conference, Operations Research and Computing: Algorithms and Software for Analytics, Richmond, Virginia January 11-13, 2015. The data contains R code, output, and comments that follow the examples for principal component analysis in the paper

Analysis of the Consistency of a Mixed Integer Programming-based Multi-Category Constrained Discriminant Model

Classification is concerned with the development of rules for the allocation of observations to groups, and is a fundamental problem in machine learning. Much of previous work on classification models investigates two-group discrimination. Multi-category classification is less-often considered due to the tendency of generalizations of two-group models to produce misclassification rates that are higher than desirable. Indeed, producing “good” two-group classification rules is a challenging task for some applications, and producing good multi-category rules is generally more difficult. Additionally, even when the “optimal” classification rule is known, inter-group misclassification rates may be higher than tolerable for a given classification model. We investigate properties of a mixed-integer programming based multi-category classification model that allows for the pre-specification of limits on inter-group misclassification rates. The mechanism by which the limits are satisfied is the use of a reserved judgment region, an artificial category into which observations are placed whose attributes do not sufficiently indicate membership to any particular group. The method is shown to be a consistent estimator of a classification rule with misclassification limits, and performance on simulated and real-world data is demonstrated

Outlier-Resistant L1 Orthogonal Regression via the Reformulation-Linearization Technique

Assessing the linear relationship between a set of continuous predictors and a continuous response is a well-studied problem in statistics and data mining. L2-based methods such as ordinary least squares and orthogonal regression can be used to determine this relationship. However, both of these methods become impaired when influential values are present. This problem becomes compounded when outliers confound standard diagnostics. This work proposes an L1-norm orthogonal regression method (L1OR) formulated as a nonconvex optimization problem. Solution strategies for finding globally optimal solutions are presented. Simulation studies are conducted to assess the resistance of the method to outliers and the consistency of the method. The method is also applied to real-world data arising from an environmental science application

Technical aspects of amyloid imaging for Alzheimer's disease

[11C]Pittsburgh Compound B positron emission tomography has now been extensively used to evaluate the amyloid load in different types of dementia and has become a powerful research tool in the field of neurodegenerative diseases. In the present short review we discuss the properties of amyloid imaging agent [11C]Pittsburgh Compound B, the different modalities of molecular imaging, image processing and data analysis, and newer amyloid imaging agents