TitleMathematical optimization methods for clustering and classification with biological and medical applications
NameChou, Chun-An (author), Chaovalitwongse, Wanpracha Art (chair), Boros, Endre (internal member), Jeong, Myong-K. (internal member), Pham, Hoang (outside member), Berger-Wolf, Tanya Y. (outside member), Rutgers University, Graduate School - New Brunswick,
SubjectIndustrial and Systems Engineering,
DescriptionThe focus of the dissertation is on the development of effective combinatorial optimization approaches for both large-scale clustering and classification problems in data mining with high computational complexity by massive biological and medical data. In the first part, we study an important clustering problem in computational and population biology, namely sibling reconstruction problem. The problem is mathematically considered a special case of capacitated clustering problem. A mathematical optimization model is proposed to establish the sibling relationships (i.e., groups of siblings) based on the biological concept of combinatorial constraints and similarity likelihood of genetic data. Both exact and heuristic solution approaches are developed, which enable the problem to be solved comparably and outperform other existing combinatorial and statistical approaches significantly. In the second part, we develop new combinatorial and pattern-based optimization approaches in the framework of Logical Analysis of Data (LAD) for binary classification. In the framework, while patterns are the building blocks for the LAD classification model, a new mathematical optimization model is proposed for generating decisive and high-quality patterns. Moreover, a column generation framework, where the proposed pattern generation approach is employed, is developed to build an “optimal” LAD classifier such that the classification accuracy and computational efficiency are improved. In the third part, we investigate feature selection that has two-fold advantages in classification problems with massive data: data reduction and noise reduction. First, we formulate a quadratic program by using statistical information (relevancy and redundancy) of features as inputs to select critical features that are favorable for classifiers. Second, we propose a new pattern-based optimization approach using a decomposed nearest neighbor rule for direct classification. The preliminary results show the potential for the improvement in data reduction and classification accuracy.
NoteIncludes bibliographical references
Noteby Chun-An Chou
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.