2019/11/27 by Chengyuan Wu, Wu, Chengyuan, Carol Anne Hargreaves +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Vision and Imaging #Algebraic Topology (math.AT) #Algorithm #Artificial intelligence #Computer science #Data mining #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Geometry #Machine Learning (cs.LG) #Machine learning #Mathematics #Multivariate statistics #Point (geometry) #Point cloud #Rotation (mathematics) #Series (stratigraphy) #Signal Processing (eess.SP) #Time series #Topological and Geometric Data Analysis #Topological data analysis #Translation (biology) #Window (computing) #cs.LG #eess.SP #electronic engineering #information engineering #math.AT
paper · pdf · doi:10.48550/arxiv.1911.12082
published in arXiv (Cornell University) (Cornell University) · 18 pages, to appear in Journal of Experimental & Theoretical Artificial Intelligence
openalex publication_date 2019/11/27 · arxiv created 2020/12/26 · arxiv updated 2020/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We develop a framework for analyzing multivariate time series using topological data analysis (TDA) methods. The proposed methodology involves converting the multivariate time series to point cloud data, calculating Wasserstein distances between the persistence diagrams and using the k-nearest neighbors algorithm (k-NN) for supervised machine learning. Two methods (symmetry-breaking and anchor points) are also introduced to enable TDA to better analyze data with heterogeneous features that are sensitive to translation, rotation, or choice of coordinates. We apply our methods to room occupancy detection based on 5 time-dependent variables (temperature, humidity, light, CO2 and humidity ratio). Experimental results show that topological methods are effective in predicting room occupancy during a time window. We also apply our methods to an Activity Recognition dataset and obtained good results.