Physiological Signal Analysis: A Topo-Geometric Perspective.

EMRANI, SABA. Physiological Signal Analysis: A Topo-Geometric Perspective. (Under the direction of Dr. Hamid Krim.) The first goal of this dissertation is to find evidence of periodicity in data with low computational complexity and high accuracy. We propose a framework for exploiting the intrinsic topology of signals to detect “quasi-harmonic” behaviors with minimal processing of data. Using delay-coordinate embeddings, we transform the time-domain signal into a point cloud, whose topology reflects the periodic behavior of the signal. We use persistent homology for robust analysis of the point clouds of delay-coordinate embeddings. To discover the proper delay, we propose an autocorrelation like (ACL) function of the signals. In order to reduce the computational complexity of the algorithm, persistent homology is employed to determine the underlying manifold of the point cloud, and the Euler characteristic provides a fast computation of topology of the resulting manifold. We apply the introduced approach to analyze breathing sound signals for wheeze detection. Experiments have been carried out to substantiate the capabilities of the proposed methods. We then use this method to identifying cell-cycle regulated genes in short gene expression microarray data. This novel technique for gene data analysis is accurate and robust to noise, missing data points and time varying sampling intervals. Our experiments using Yeast Saccharomyces cerevisiae dataset validates the effectiveness of the proposed method. We subsequently invoke one more dimension to the point cloud and utilize three dimensional delay embedding for spectral estimation of highly transient data. We present a new framework for estimating different frequencies in highly non-stationary piece-wise periodic signals with time varying amplitude and phase. The goal of this study is to enumerate and estimate the frequencies in wheezes as a premise to essential diagnostic knowledge. Three dimensional delay embedding of the introduced model constructs a union of intersecting planes where each plane corresponds to one frequency. The equation of each plane only depend on the associated frequency, and is used to calculate the tone in each segment. Sparse subspace clustering technique is utilized to find the segmentation of the data, and the points in each cluster are used to compute the normal vectors. In the presence of white Gaussian noise, principal component analysis is used to robustly perform this computation. Experimental results demonstrate the effectiveness of the proposed framework in detecting different frequencies. We next propose a new framework based on topological signal processing for extracting the characteristic points of pulse pressure waves, and test this framework on real data. Specifically, using the persistence diagram, we locate key characteristic points on the pressure wave, and use these points both for AIx calculation and pulse validation. We show that the novel persistence-based analysis robustly produces AIx values that are not statistically different from those computed using traditional derivative-based techniques. Finally, we further the delay embedding framework to multiple time series for extraction of causal interactions. We propose a geometric model-free causality measure based on multivariate delay embedding that can efficiently detect linear and nonlinear causal interactions between time series with no prior information. We then exploit the proposed causal interaction measure in real MEG data analysis. The results are used to construct effective connectivity maps of brain activity to decode different categories of visual stimuli. Moreover, we discovered that the MEGbased effective connectivity maps as a response to structured images exhibit more geometric patterns, as disclosed by analyzing the evolution of toplogical structures of the underlying networks using persistent homology. © Copyright 2016 by Saba Emrani