Relative distances between homology groups to assess persistent defects in time series

Abstract

It is common to consider a data-intensive strategy to be an appropriate way to develop systemic analyses in biology and physiology. Therefore, options for data collection, sampling, standardization, visualization, and interpretation determine how causes are identified in time series to build mathematical models. However, there are often biases in the collected data that can affect the validity of the model: while collecting enough large datasets seems to be a good strategy for reducing the bias of the collected data, persistent and dynamical anomalies in the data structure can affect the overall validity of the model. In this work we present a methodology based on the definition of homological groups to evaluate persistent anomalies in the structure of the sampled time series. In this evaluation relevant patterns in the combination of different time series are clustered and grouped to customize the identification of causal relationships between parameters. We test this methodology on data collected from patients using mobile sensors to test the response to physical exercise in real-world conditions and outside the lab. With this methodology we plan to obtain a patient stratification of the time series to customize models in medicine.