Optimal scaling by alternating length-constrained nonnegative least squares, with application to distance-based analysis

An important feature of distance-based principal components analysis, is that the variables can be optimally transformed. For monotone spline transformation, a nonnegative least-squares problem with a length constraint has to be solved in each iteration. As an alternative algorithm to Lawson and Hanson (1974), we propose the Alternating Length-Constrained Non-Negative Least-Squares (ALC-NNLS) algorithm, which minimizes the nonnegative least-squares loss function over the parameters under a length constraint, by alternatingly minimizing over one parameter while keeping the others fixed. Several properties of the new algorithm are discussed. A Monte Carlo study is presented which shows that for most cases in distance-based principal components analysis, ALC-NNLS performs as good as the method of Lawson and Hanson or sometimes even better in terms of the quality of the solution. Supported by The Netherlands Organization for Scientific Research (NWO) by grant nr. 030-56403 for the “PIONEER” project “Subject Oriented Multivariate Analysis” to the third author. We would like to thank the anonymous referees for their valuable remarks that have improved the quality of this paper.     

A Classification Framework using a Diverse Intensified Strawberry Optimized Neural Network (DISON) for Clinical Decision-making

A novel classification framework for clinical decision making that uses an Extremely Randomized Tree (ERT) based feature selection and a Diverse Intensified Strawberry Optimized Neural network (DISON) is proposed. DISON is a Feed Forward Artificial Neural Network where the optimization of weights and bias is done using a two phase training strategy. Two algorithms namely Strawberry Plant Optimization (SPO) algorithm and Gradient-descent Back-propagation algorithm are used sequentially to identify the optimum weights and bias. The novel two phase training method and the stochastic duplicate-elimination strategy of SPO helps in addressing the issue of local optima associated with conventional neural networks. The relevant attributes are selected based on the feature importance values computed using an ERT classifier.Vertebral Column, Pima Indian diabetes (PID), Cleveland Heart disease (CHD) and Statlog Heart disease (SHD) datasets from the University of California Irvine machine learning repository are used for experimentation. The framework has achieved an accuracy of 87.17% for Vertebral Column, 90.92% for PID, 93.67% for CHD and 94.5% for SHD. The classifier performance has been compared with existing works and is found to be competitive in terms of accuracy, sensitivity and specificity. Wilcoxon test confirms the statistical superiority of the proposed method.     

On the Determination of Minimal Facets and Edges of a Polyhedral Set

In this paper we investigate the image of a polyhedral set under a linear map. Moreover, we present an algorithm for the determination of so-called minimal facets and certain minimal irredundant proper edges of a convex polyhedral set in ℝ³. © 1997 John Wiley & Sons, Ltd.     

Pareto simulated annealing—a metaheuristic technique for multiple-objective combinatorial optimization

This paper presents a multiple-objective metaheuristic procedure—Pareto simulated annealing. The goal of the procedure is to find in a relatively short time a good approximation of the set of efficient solutions of a multiple-objective combinatorial optimization problem. The procedure uses a sample, of so-called generating solutions. Each solution explores its neighbourhood in a way similar to that of classical simulated annealing. Weights of the objectives, used for their local aggregation, are tuned in each iteration in order to assure a tendency for approaching the efficient solutions set while maintaining a uniform distribution of the generating solutions over this set. A computational experiment shows that the method is a better tool for approximating the efficient set than some previous proposals. © 1998 John Wiley & Sons, Ltd.     

Feedback functions, optimization, and the relation of response rate to reinforcer rate

The present experiment arranged a series of inverted U-shaped feedback functions relating reinforcer rate to response rate to test whether responding was consistent with an optimization account or with a one-to-one relation of response rate to reinforcer rate such as linear system theory's rate equation or Herrnstein's hyperbola. Reinforcer rate was arranged according to a quadratic equation with a maximum at a unique response rate. The experiment consisted of two phases, during which 6 Long Evans rats lever pressed for food. In the first phase of the experiment, the rats responded on six fixed-interval-plus-quadratic-feedback schedules, and in the second phase the rats responded on three variable-interval-plus-quadratic-feedback schedules. Responding in both phases was inconsistent with a one-to-one relation of response rate to reinforcer rate. Instead, different response rates were obtained at equivalent reinforcer rates. Responding did vary directly with the vertex of the feedback function in both phases, a finding consistent with optimization of reinforcer rate. The present results suggest that the feedback function relating reinforcer rate to response rate imposed by a reinforcement schedule can be an important determinant of behavior. Furthermore, the present experiment illustrates the benefit of arranging feedback functions to investigate assumptions about the variables that control schedule performance.     

Compact integer-programming models for extracting subsets of stimuli from confusion matrices

This paper presents an integer linear programming formulation for the problem of extracting a subset of stimuli from a confusion matrix. The objective is to select stimuli such that total confusion among the stimuli is minimized for a particular subset size. This formulation provides a drastic reduction in the number of variables and constraints relative to a previously proposed formulation for the same problem. An extension of the formulation is provided for a biobjective problem that considers both confusion and recognition in the objective function. Demonstrations using an empirical interletter confusion matrix from the psychological literature revealed that a commercial branch-and-bound integer programming code was always able to identify optimal solutions for both the single-objective and biobjective formulations within a matter of seconds. A further extension and demonstration of the model is provided for the extraction of multiple subsets of stimuli, wherein the objectives are to maximize similarity within subsets and minimize similarity between subsets.     

A global optimization approach for generating efficient points for multiobjective concave fractional programs

In this article, we present a global optimization approach for generating efficient points for multiobjective concave fractional programming problems. The main work of the approach involves solving an instance of a concave multiplicative fractional program (W̄). Problem (W̄) is a global optimization problem for which no known algorithms are available. Therefore, to render the approach practical, we develop and validate a branch and bound algorithm for globally solving problem (W̄). To illustrate the performance of the global optimization approach, we use it to generate efficient points for a sample multiobjective concave fractional program. Copyright © 2006 John Wiley & Sons, Ltd.     

A Comparison of Heuristic Procedures for Minimum Within-Cluster Sums of Squares Partitioning

Perhaps the most common criterion for partitioning a data set is the minimization of the within-cluster sums of squared deviation from cluster centroids. Although optimal solution procedures for within-cluster sums of squares (WCSS) partitioning are computationally feasible for small data sets, heuristic procedures are required for most practical applications in the behavioral sciences. We compared the performances of nine prominent heuristic procedures for WCSS partitioning across 324 simulated data sets representative of a broad spectrum of test conditions. Performance comparisons focused on both percentage deviation from the “best-found” WCSS values, as well as recovery of true cluster structure. A real-coded genetic algorithm and variable neighborhood search heuristic were the most effective methods; however, a straightforward two-stage heuristic algorithm, HK-means, also yielded exceptional performance. A follow-up experiment using 13 empirical data sets from the clustering literature generally supported the results of the experiment using simulated data. Our findings have important implications for behavioral science researchers, whose theoretical conclusions could be adversely affected by poor algorithmic performances.     

生命进化动力之哲学思考

对生命进化的本质问题作了新的哲学思考,提出进化的本质是物种在生存的驱动下生存效率的优化过程,是原始细胞自主性与环境选择的双向过程。同时提出推动物种进化的动力在于生存资源稀缺性与物种自私性之间的矛盾和多细胞物种效率优化过程中自身的局部利益与整体利益之间的矛盾。