Variable selection for the multicategory SVM via adaptive sup-norm regularization

The Support Vector Machine (SVM) is a popular classification paradigm in machine learning and has achieved great success in real applications. However, the standard SVM can not select variables automatically and therefore its solution typically utilizes all the input variables without discrimination. This makes it difficult to identify important predictor variables, which is often one of the primary goals in data analysis. In this paper, we propose two novel types of regularization in the context of the multicategory SVM (MSVM) for simultaneous classification and variable selection. The MSVM generally requires estimation of multiple discriminating functions and applies the argmax rule for prediction. For each individual variable, we propose to characterize its importance by the supnorm of its coefficient vector associated with different functions, and then minimize the MSVM hinge loss function subject to a penalty on the sum of supnorms. To further improve the supnorm penalty, we propose the adaptive regularization, which allows different weights imposed on different variables according to their relative importance. Both types of regularization automate variable selection in the process of building classifiers, and lead to sparse multi-classifiers with enhanced interpretability and improved accuracy, especially for high dimensional low sample size data. One big advantage of the supnorm penalty is its easy implementation via standard linear programming. Several simulated examples and one real gene data analysis demonstrate the outstanding performance of the adaptive supnorm penalty in various data settings.Comment: Published in at http://dx.doi.org/10.1214/08-EJS122 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

Modeling and analysis of a reverse supply chain network for lead-acid battery manufacturing.

The North American lead-acid battery industry gains its environmental edge from its employment of closed-loop life cycle production. Nowadays, the typical new lead-acid battery contains 60 to 80 percent recycled lead and plastics. In this thesis, the closed-loop supply chain of a lead-acid battery manufacturing process has been investigated which extends the traditional supply chain to the entire product life cycle. A new tactical planning model has been developed for the entire closed-loop manufacturing process including purchasing, production, and end-of-life product return and recycling. The model is a multi-objective, multi-echelon mixed integer linear programming model, which minimizes the total costs and the total transportation pollution emissions, subject to structural and functional constraints. Decisions are made regarding material procurement, production, recycling and inventory levels, and the transportation modes between the echelons. Sensitivity analysis has been performed to evaluate the integration with third party outsourcing, changes in parameters and design options.* *This dissertation is a compound document (contains both a paper copy and a CD as part of the dissertation).Dept. of Industrial and Manufacturing Systems Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2006 .Z435. Source: Masters Abstracts International, Volume: 45-01, page: 0440. Thesis (M.A.Sc.)--University of Windsor (Canada), 2006