Project DetailsIn this work we investigated a relatively new approach to signal processing, using Topological Data Analysis (TDA) methods. We first transfer the signal to a Point Cloud structure, using Sliding Window Embedding and studied global features of that cloud. By creating sequence of Simplicial Complexes with the Alpha Complex structure, we extracted information about quality topological features of the point cloud such as holes, air pockets, and their higher-order analogues. We show that a careful selection of the parameters controlling the transformation of the signal into a point cloud allows for the extraction of significant information about the signal. Further, it could lead to achieving superiority over classical Fourier analysis in the study of the difference between periodic and quasi-periodic signals.
We continued the known research on the relationship between time domain features of signals and the shape of the point cloud formed by them. In particular, we found a unique characteristic to point clouds generated by FM modulated signal. This insight can lead to an immediate distinction between an FM modulated signal and an AM modulated signal, whose topological form has already been analysed in the literature. In addition, we found out that there is a connection between the signal frequency and the angle of the point cloud in space.
Based on these insights, we built several scoring methods to identify powerful topological features and used them to create a POC for alarm detection in noisy environments. We focus on the task of distinguishing alarm sounds from noise. To check the quality of our features we use the relief algorithm and show superiority of topological features over features from the DSP world in classification of alarms from noise. We use machine learning algorithms to create KNN and SVM classifiers for detecting alarms in a noisy urban environment. Apart from results, we also addressed the problems of selecting hyper-parameters for the Sliding Window Embedding method, such as the window-length and the sampling rate. We studied the effect of these parameters and suggested a way to determine them when searching for certain features.
