Novel quadratic programming approach for time series clustering with biomedical application

Fundamental problems in data mining mainly involve discrete decisions based on numerical analyses of data (e.g., class assignment, feature selection, data categorization, identifying outlier samples). These decision-making problems in data mining are combinatorial in nature and can naturally be formulated as discrete optimization problems. One of the most widely studied problems in data mining is clustering. In this paper, we propose a new optimization model for hierarchical clustering based on quadratic programming and later show that this model is compact and scalable. Application of this clustering technique in epilepsy, the second most common brain disorder, is a case point in this study. In our empirical study, we will apply the proposed clustering technique to treatment problems in epilepsy through the brain dynamics analysis of electroencephalogram (EEG) recordings. This study is a proof of concept of our hypothesis that epileptic brains tend to be more synchronized (clustered) during the period before a seizure than a normal period. The results of this study suggest that data mining research might be able to revolutionize current diagnosis and treatment of epilepsy as well as give a greater understanding of brain functions (and other complex systems) from a system perspective. This work was partially supported by the NSF grant CCF 0546574 and Rutgers Research Council grant-202018.