Seizure warning algorithm based on optimization and nonlinear dynamics

There is growing evidence that temporal lobe seizures are preceded by a preictal transition, characterized by a gradual dynamical change from asymptomatic interictal state to seizure. We herein report the first prospective analysis of the online automated algorithm for detecting the preictal transition in ongoing EEG signals. Such, the algorithm constitutes a seizure warning system. The algorithm estimates STL_max, a measure of the order or disorder of the signal, of EEG signals recorded from individual electrode sites. The optimization techniques were employed to select critical brain electrode sites that exhibit the preictal transition for the warning of epileptic seizures. Specifically, a quadratically constrained quadratic 0-1 programming problem is formulated to identify critical electrode sites. The automated seizure warning algorithm was tested in continuous, long-term EEG recordings obtained from 5 patients with temporal lobe epilepsy. For individual patient, we use the first half of seizures to train the parameter settings, which is evaluated by ROC (Receiver Operating Characteristic) curve analysis. With the best parameter setting, the algorithm applied to all cases predicted an average of 91.7% of seizures with an average false prediction rate of 0.196 per hour. These results indicate that it may be possible to develop automated seizure warning devices for diagnostic and therapeutic purposes.Mathematics Subject Classification (1991):20E28, 20G40, 20C20     

Electroencephalogram (EEG) time series classification: Applications in epilepsy

Epilepsy is among the most common brain disorders. Approximately 25–30% of epilepsy patients remain unresponsive to anti-epileptic drug treatment, which is the standard therapy for epilepsy. In this study, we apply optimization-based data mining techniques to classify the brain's normal and epilepsy activity using intracranial electroencephalogram (EEG), which is a tool for evaluating the physiological state of the brain. A statistical cross validation and support vector machines were implemented to classify the brain's normal and abnormal activities. The results of this study indicate that it may be possible to design and develop efficient seizure warning algorithms for diagnostic and therapeutic purposes. Research was partially supported by the Rutgers Research Council grant-202018, the NSF grants DBI-980821, CCF-0546574, IIS-0611998, and NIH grant R01-NS-39687-01A1.     

Sparse optimization in feature selection: application in neuroimaging

Feature selection plays an important role in the successful application of machine learning techniques to large real-world datasets. Avoiding model overfitting, especially when the number of features far exceeds the number of observations, requires selecting informative features and/or eliminating irrelevant ones. Searching for an optimal subset of features can be computationally expensive. Functional magnetic resonance imaging (fMRI) produces datasets with such characteristics creating challenges for applying machine learning techniques to classify cognitive states based on fMRI data. In this study, we present an embedded feature selection framework that integrates sparse optimization for regularization (or sparse regularization) and classification. This optimization approach attempts to maximize training accuracy while simultaneously enforcing sparsity by penalizing the objective function for the coefficients of the features. This process allows many coefficients to become zero, which effectively eliminates their corresponding features from the classification model. To demonstrate the utility of the approach, we apply our framework to three different real-world fMRI datasets. The results show that regularized classifiers yield better classification accuracy, especially when the number of initial features is large. The results further show that sparse regularization is key to achieving scientifically-relevant generalizability and functional localization of classifier features. The approach is thus highly suited for analysis of fMRI data.     

Mathematical programming approaches for dual multicast routing problem with multilayer risk cost

This paper addresses a dual multicast routing problem with shared risk link group (SRLG) diverse costs (DMR-SRLGD) that arises from large-scale distribution of realtime multicast data (e.g., internet protocol TV, videocasting, online games, stock price update). The goal of this problem is to find two redundant multicast trees, each from one of the two sources to every destination at a minimum cost. The cost of the problem contains two parts: the multicast routing cost and the shard common risk cost. Such common risk could cause the failures of multiple links simultaneously. Therefore, the DMR-SRLGD ensures the availability and reliability of multicast service. We formulate an edge-based model for the DMR-SRLGD. In addition, we also propose a path-based model that rises from the Dantzig-Wolfe decomposition of the edge-based model, and develop a column-generation framework to solve the linear relaxation of the path-based formulation. We then employ a branch-and-price solution method to find integer solutions to DMR-SRLGD. We also extend both edge-based and path-based models to handle the complex quality of service requirements. The computational results show the edge-based model is superior than the path-based model for the easy and small test instances, whereas the path-based model provides better solutions in a timely fashion for hard or large test instances.     

A multicast problem with shared risk cost

In this paper, we study a minimum cost multicast problem on a network with shared risk link groups (SRLGs). Each SRLG contains a set of arcs with a common risk, and there is a cost associated with it. The objective of the problem is to find a multicast tree from the source to a set of destinations with minimum transmission cost and risk cost. We present a basic model for the multicast problem with shared risk cost (MCSR) based on the well-known multicommodity flow formulation for the Steiner tree problem (Goemans and Myung in Networks 1:19–28, 1993; Polzin and Daneshmand in Discrete Applied Mathematics 112(1–3): 241–261, 2001). We propose a set of strong valid inequalities to tighten the linear relaxation of the basic model. We also present a mathematical model for undirected MCSR. The computational results of real life test instances demonstrate that the new valid inequalities significantly improve the linear relaxation bounds of the basic model, and reduce the total computation time by half in average.     

An improved linearization technique for a class of quadratic 0-1 programming problems

The recent research on linearization techniques for solving 0-1 quadratic programming problems focuses on providing concise models and tightening constraint bounds. In this paper, we propose a computational enhancement for a linearization technique to make the linearized model much faster to solve. We investigate the computational performance of the proposed approach, by comparing it with other linearization techniques on a class of 0-1 quadratic programming problems. We can further speed up the proposed technique by heuristically tightening the constraint bounds, as demonstrated by solving the uncapacitated single allocation p-hub median problem using the Civil Aeronautics Board data.     

A new linearization technique for multi-quadratic 0-1 programming problems

We consider the reduction of multi-quadratic 0-1 programming problems to linear mixed 0-1 programming problems. In this reduction, the number of additional continuous variables is O(kn) (n is the number of initial 0-1 variables and k is the number of quadratic constraints). The number of 0-1 variables remains the same.     

Multicriteria variable selection for classification of production batches

In many industrial processes hundreds of noisy and correlated process variables are collected for monitoring and control purposes. The goal is often to correctly classify production batches into classes, such as good or failed, based on the process variables. We propose a method for selecting the best process variables for classification of process batches using multiple criteria including classification performance measures (i.e., sensitivity and specificity) and the measurement cost. The method applies Partial Least Squares (PLS) regression on the training set to derive an importance index for each variable. Then an iterative classification/elimination procedure using k-Nearest Neighbor is carried out. Finally, Pareto analysis is used to select the best set of variables and avoid excessive retention of variables. The method proposed here consistently selects process variables important for classification, regardless of the batches included in the training data. Further, we demonstrate the advantages of the proposed method using six industrial datasets.     

Bounds of redundant multicast routing problem with SRLG-diverse constraints: edge,path and tree models

This paper proposes three classes of alternative mathematical programming models (i.e., edge-based, path-based, and tree-based) for redundant multicast routing problem with shared risk link group (SRLG)-diverse constraints (RMR-SRLGD). The goal of RMR-SRLGD problem is to find two redundant multicast trees, each from one of the two sources to every destination, at a minimum cost while ensuring the paths from the two sources to a destination do not share any common risks. Such risk could cause the failures of multiple links simultaneously. Therefore, the RMR-SRLGD problem ensures the availability and reliability of multicast services. We investigated and compared the theoretical bounds of the linear programming (LP) relaxation for all models. We also summarized a hierarchy relationship of the tightness of LP bounds for the proposed models.