Nian Yan

Nonlinear Classification by Linear Programming with Signed Fuzzy Measures

Linear programming (LP) based models provide good solutions to classification problem especially when the data is linearly separable. The assumption of LP classification models is: the contributions from all attributes towards the classification model are the sum of contributions of each attribute. This assumption leads to a weakness of LP classification models when data is linearly inseparable. The concept of signed fuzzy measure is introduced and utilized in LP approach in order to enhance the classification power through capturing all possible interactions among any two or more attributes. The use of the Choquet integral with respect to a signed fuzzy measure on LP model is able to separate the data that is finearly inseparable.

Multiple Criteria Mathematical Programming and Data Mining

Recently, researchers have extensively applied quadratic programming into classification, known as V. Vapniks Support Vector Machine, as well as various applications. However, using optimization techniques to deal with data separation and data analysis goes back to more than forty years ago. Since 1998, the authors and their colleagues extended such a research idea into classification via multiple criteria linear programming (MCLP) and multiple criteria quadratic programming (MQLP). The purpose of the paper is to share our research results and promote the research interests in the community of computational sciences. These methods are different from statistics, decision tree induction, and neural networks. In this paper, starting from the basics of Multiple Criteria Linear Programming (MCLP), we further discuss penalized MCLP Multiple Criteria Quadratic Programming (MCQP), Multiple Criteria Fuzzy Linear Programming, Multi-Group Multiple Criteria Mathematical Programming, as well as regression method by Multiple Criteria Linear Programming. A brief summary of applications of Multiple Criteria Mathematical Programming is also provided.

An Optimization-Based Classification Approach with the Non-additive Measure

Optimization-based classification approaches have well been used for decision making problems, such as classification in data mining. It considers that the contributions from all the attributes for the classification model equals to the joint individual contribution from each attribute. However, the impact from the interactions among attributes is ignored because of linearly or equally aggregation of attributes. Thus, we introduce the generalized Choquet integral with respect to the non-additive measure as the attributes aggregation tool to the optimization-based approaches in classification problem. Also, the boundary for classification is optimized in our proposed model compared with previous optimization-based models. The experimental result of two real life data sets shows the significant improvement of using the non-additive measure in data mining.

A non-linear multi-regression model based on the Choquet integral with a quadratic core

Signed efficiency measures with relevant non-linear integrals can be used to treat data that have strong interaction among contributions from various attributes towards a certain objective attribute. The Choquet integral is the most common non-linear integral. The non-linear multi-regression based on the Choquet integral can well describe the non-linear relation how the objective attribute depends on the predictive attributes. This research is to extend the non-linear multi-regression model from using a linear core to adopting a quadratic core in the Choquet integral. It can describe some more complex interaction among attributes and, therefore, can significantly improve the accuracy of non-linear multi-regression. The unknown parameters of the model involve the coefficients in the quadratic core and the values of the signed efficiency measure. They should be optimally determined via a genetic algorithm based on the given data. The results of the new model are compared with that of the linear core as well...

A family of optimization based data mining methods

An extensive review for the family of multi-criteria programming data mining models is provided in this paper. These models are introduced in a systematic way according to the evolution of the multi-criteria programming. Successful applications of these methods to real world problems are also included in detail. This survey paper can serve as an introduction and reference repertory of multi-criteria programming methods helping researchers in data mining.

Multiple Criteria Nonlinear Programming Classification with the Non-additive Measure

Multiple criteria linear/nonlinear programming has well been used for decision making problems, such as classification and prediction. In these applications, usually only contributions from the attributes towards a certain target, such as classification, are considered (using weighted sum), while the impact from the interactions among attributes is simply ignored, resulting a model of linear aggregation of attributes. However, interaction among attributes could be a very important factor for more accurate classification. Taking interaction among attributes into consideration, in this paper we review the concept of the Choquet integral, and apply the Choquet integral with respect to non-additive measure as the attributes aggregation tool for multiple criteria nonlinear programming. We have applied our method in credit cardholders’ behaviors classification problems. The experimental results on two real life data sets show the significant improvement of using the non-additive measure in data mining.

A Nonlinear Multiregression Model Based on the Choquet Integral with a Quadratic Core

Signed efficiency measures with relevant nonlinear integrals can be used to treat data that have strong interaction among contributions from various attributes towards a certain objective attribute. The Choquet integral is the most common nonlinear integral. The nonlinear multiregression based on the Choquet integral can well describe the nonlinear relation how the objective attribute depends on the predictive attributes. This research is to extend the nonlinear multiregression model from using a linear core to adopting a quadratic core in the Choquet integral. It can describe some more complex interaction among attributes and, therefore, can significantly improve the accuracy of nonlinear multiregression. The unknown parameters of the model involve the coefficients in the quadratic core and the values of the signed efficiency measure. They should be optimally determined via a genetic algorithm based on the given data. The results of the new model are compared with that of the linear core as well as the classic linear multiregression that can be solved by an algebraic method.

Using k-Interactive Measure in Optimization-Based Data Mining

Optimization-based methods have been used for data separation in different domains and applications since 1960s. The commonality of those methods is to separate data by minimizing the overlapping between the groups and regard contribution from all the attributes toward the target of classification is the sum of every single attribute. However, the interaction among the attributes in the data is not considered at all. The theory of non-additive measures is used to describe those interactions. The consideration of the interactions is a breakthrough for dealing with the nonlinearity of data. Through the non-additive measure has been successfully utilized in optimization-based classification, it increases the computation cost as well as the quadratic programming models particularly designed for dealing with the nonlinearity. In this paper, we proposed the optimization-based classification method with the signed k-interactive measure. The experimental results shows that it successfully reduced the computation but retained the classification power.

Bound for the L2 Norm of Random Matrix and Succinct Matrix Approximation

This work furnished a sharper bound of exponential form for the L 2 norm of an arbitrary shaped random matrix. Based on the newly elaborated bound, a non-uniform sampling method was developed to succinctly approximate a matrix with a sparse binary one and hereby to relieve the computation loads in both time and storage. This method is not only pass-efficient but query-efficient also since the whole process can be completed in one pass over the input matrix and the sampling and quantizing are naturally combined in a single step.