A new polynomial-time algorithm for linear programming
Combinatorica
Introduction to operations research, 4th ed.
Introduction to operations research, 4th ed.
Information Processing Letters
Algorithms for clustering data
Algorithms for clustering data
Integer and combinatorial optimization
Integer and combinatorial optimization
Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
Introduction to the theory of neural computation
Introduction to the theory of neural computation
Advances in neural information processing systems 2
Network programming
Machine Learning
Bilinear separation of two sets in n-space
Computational Optimization and Applications
The nature of statistical learning theory
The nature of statistical learning theory
The KDD process for extracting useful knowledge from volumes of data
Communications of the ACM
Improved generalization via tolerant training
Journal of Optimization Theory and Applications
Fundamentals of Artificial Neural Networks
Fundamentals of Artificial Neural Networks
Mathematics of Generalization: Proceedings: SFI-CNLS Workshop on Formal Approaches to Supervised Learning (1992: Santa Fe, N. M.)
Readings in Machine Learning
Knowledge Acquisition Via Incremental Conceptual Clustering
Machine Learning
Feature Selection Via Mathematical Programming
INFORMS Journal on Computing
Approximation schemes for Euclidean k-medians and related problems
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Parsimonious Least Norm Approximation
Computational Optimization and Applications
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part I
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part II
The analysis of a simple k-means clustering algorithm
Proceedings of the sixteenth annual symposium on Computational geometry
A method of truncated codifferential with application to some problems of cluster analysis
Journal of Global Optimization
An Efficient k-Means Clustering Algorithm: Analysis and Implementation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Constructing Boosting Algorithms from SVMs: An Application to One-Class Classification
IEEE Transactions on Pattern Analysis and Machine Intelligence
Clustering Data Streams: Theory and Practice
IEEE Transactions on Knowledge and Data Engineering
A new approximate maximal margin classification algorithm
The Journal of Machine Learning Research
Learning adaptive kernels for model diagnosis
Design and application of hybrid intelligent systems
Dual Characterizations of Set Containments with Strict Convex Inequalities
Journal of Global Optimization
A Genetic Algorithm Using Hyper-Quadtrees for Low-Dimensional K-means Clustering
IEEE Transactions on Pattern Analysis and Machine Intelligence
A scalable decision tree system and its application in pattern recognition and intrusion detection
Decision Support Systems
Journal of Management Information Systems
Accurately learning from few examples with a polyhedral classifier
Computational Optimization and Applications
A genetic algorithm that exchanges neighboring centers for k-means clustering
Pattern Recognition Letters
Multi-group support vector machines with measurement costs: A biobjective approach
Discrete Applied Mathematics
Stability of the intersection of solution sets of semi-infinite systems
Journal of Computational and Applied Mathematics
On the stable containment of two sets
Journal of Global Optimization
Dual characterizations of the set containments with strict cone-convex inequalities in Banach spaces
Journal of Global Optimization
Smoothing Newton Method for L1 Soft Margin Data Classification Problem
ICCS 2009 Proceedings of the 9th International Conference on Computational Science
The hyperbolic smoothing clustering method
Pattern Recognition
A scalable decision tree system and its application in pattern recognition and intrusion detection
Decision Support Systems
An optimization-based approach to patient grouping for acute healthcare in Australia
ICCS'03 Proceedings of the 2003 international conference on Computational science: PartIII
Quantization-based clustering algorithm
Pattern Recognition
Minimum sum-of-squares clustering by DC programming and DCA
ICIC'09 Proceedings of the Intelligent computing 5th international conference on Emerging intelligent computing technology and applications
Operations Research Letters
A reduced support vector machine approach for interval regression analysis
Information Sciences: an International Journal
New and efficient DCA based algorithms for minimum sum-of-squares clustering
Pattern Recognition
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Mathematical programming approaches to three fundamental problemswill be described: feature selection, clustering and robustrepresentation. The feature selection problem considered is that ofdiscriminating between two sets while recognizing irrelevant andredundant features and suppressing them. This creates a lean modelthat often generalizes better to new unseen data. Computationalresults on real data confirm improved generalization of leanermodels. Clustering is exemplified by the unsupervised learning ofpatterns and clusters that may exist in a given database and is auseful tool for knowledge discovery in databases (KDD). Amathematical programming formulation of this problem is proposed thatis theoretically justifiable and computationally implementable in afinite number of steps. A resulting k-Median Algorithm is utilized todiscover very useful survival curves for breast cancer patients froma medical database. Robust representation is concerned withminimizing trained model degradation when applied to new problems. Anovel approach is proposed that purposely tolerates a small error inthe training process in order to avoid overfitting data that maycontain errors. Examples of applications of these concepts aregiven.