Behavior Classification based on Sensor Data - Classifying time series using low-dimensional manifold representations

Abstract

This master´s thesis focuses on developing and testing methods that can automatically classify a given time series as having a certain behavior, chosen from a set of pre-specified, known behaviors. The first part of the thesis focused on finding statistical values where the empirical cumulative distribution of these values could be used for classification. The inverse of the cumulative distributions where then sampled at equally distanced sampling points and the resulting vector of sample values were treated as points in a high-dimensional Euclidean space. These points were then dimensionally reduced using projections onto a 2-dimensional manifold, where the manifold was warped in the high-dimensional Euclidean space using the elastic map and Kohonen Self-Organizing Map methodologies. The outputs from the manifold projections were then clustered using a 𝑘-nearest-neighbor algorithm. Both methodologies gave fairly good classification result for the two behaviors under consideration (86.5% / 80.3%, class 𝐶1 / 𝐶2 for elastic map, 83.6% / 78.3%, class 𝐶1 / 𝐶2 for Kohonen SOM). It was also shown that there truly were convergence in distribution for the behaviors under consideration.