A Better Alternative to Piecewise Linear Time Series Segmentation

Time series are difficult to monitor, summarize and predict. Segmentation organizes time series into few intervals having uniform characteristics (flatness, linearity, modality, monotonicity and so on). For scalability, we require fast linear time algorithms. The popular piecewise linear model can determine where the data goes up or down and at what rate. Unfortunately, when the data does not follow a linear model, the computation of the local slope creates overfitting. We propose an adaptive time series model where the polynomial degree of each interval vary (constant, linear and so on). Given a number of regressors, the cost of each interval is its polynomial degree: constant intervals cost 1 regressor, linear intervals cost 2 regressors, and so on. Our goal is to minimize the Euclidean (l_2) error for a given model complexity. Experimentally, we investigate the model where intervals can be either constant or linear. Over synthetic random walks, historical stock market prices, and electrocardiograms, the adaptive model provides a more accurate segmentation than the piecewise linear model without increasing the cross-validation error or the running time, while providing a richer vocabulary to applications. Implementation issues, such as numerical stability and real-world performance, are discussed.Comment: to appear in SIAM Data Mining 200

Nonlinear Stochastic Modeling and Analysis of Cardiovascular System Dynamics - Diagnostic and Prognostic Applications

The purpose of this investigation is to develop monitoring, diagnostic and prognostic schemes for cardiovascular diseases by studying the nonlinear stochastic dynamics underlying complex heart system. The employment of a nonlinear stochastic analysis combined with wavelet representations can extract effective cardiovascular features, which will be more sensitive to the pathological dynamics instead of the extraneous noises. While conventional statistical and linear systemic approaches have limitations for capturing signal variations resulting from changes in the cardiovascular system states. The research methodology includes signal representation using optimal wavelet function design, feature extraction using nonlinear recurrence analysis, and local recurrence modeling for state prediction.Industrial Engineering & Managemen

Efficient and secured wireless monitoring systems for detection of cardiovascular diseases

Cardiovascular Disease (CVD) is the number one killer for modern era. Majority of the deaths associated with CVD can entirely be prevented if the CVD struck person is treated with urgency. This thesis is our effort in minimizing the delay associated with existing tele-cardiology application. We harnessed the computational power of modern day mobile phones to detect abnormality in Electrocardiogram (ECG). If abnormality is detected, our innovative ECG compression algorithm running on the patient's mobile phone compresses and encrypts the ECG signal and then performs efficient transmission towards the doctors or hospital services. According to the literature, we have achieved the highest possible compression ratio of 20.06 (95% compression) on ECG signal, without any loss of information. Our 3 layer permutation cipher based ECG encoding mechanism can raise the security strength substantially higher than conventional AES or DES algorithms. If in near future, a grid of supercomputers can compare a trillion trillion trillion (1036) combinations of one ECG segment (comprising 500 ECG samples) per second for ECG morphology matching, it will take approximately 9.333 X 10970 years to enumerate all the combinations. After receiving the compressed ECG packets the doctor's mobile phone or the hospital server authenticates the patient using our proposed set of ECG biometric based authentication mechanisms. Once authenticated, the patients are diagnosed with our faster ECG diagnosis algorithms. In a nutshell, this thesis contains a set of algorithms that can save a CVD affected patient's life by harnessing the power of mobile computation and wireless communication