Time Series Analysis
Time series (TS) analysis is a general term for a vast array of methods and applications. Roughly, it can be divided into two main parts. The first is acoustic or otherwise harmonic, which roughly says that there is some smoothness in the data and possibly harmonics, e.g., many types of biomedical data. The second is non-smooth or harmonic TS. This can include financial and other man-made data. For the first group, we apply heavy signal processing tools which can be viewed as feature extraction, before applying statistical and machine learning tools for obtaining the desired interpretation from the data. For the second we apply only statistical and machine learning tools.
We have perfected methods for feature extraction and dimensionality reduction, for denoising using a combination of machine learning (clustering, ICA, non-linear PCA) and signal processing(wavelet packet analysis, compressed sensing). These are used for different applications in bio-medical, acoustic (also ultrasound and infrasound) financial TS and more.
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Clustering results of 2725 beats of S1 acquired from a single subject during 29 min of Dobutamine stress test. Clusters are marked by different colors and by number labels on the y-axis. The stress level is represented by the bold black line, labeled with the test stages. The time-domain and S-transform representations of the significant clusters exhibit substantial morphological changes, strongly associated with stages of the stress test, with a return to the baseline morphology during recovery. From Amit et al., 2009