SummerTime: Variable-length Time SeriesSummarization with Applications to PhysicalActivity Analysis
This addresses the need for robust summarization of variable-length time series in domains like physical activity analysis, though it is incremental as it builds on existing clustering and summarization techniques.
The paper tackles the problem of applying classical machine learning methods to variable-length time series by developing SummerTime, a method that summarizes time series into fixed-length feature vectors using Gaussian Mixture models over disjoint windows, resulting in high-quality improvements in physical activity classification and more robust energy expenditure estimation.
\textit{SummerTime} seeks to summarize globally time series signals and provides a fixed-length, robust summarization of the variable-length time series. Many classical machine learning methods for classification and regression depend on data instances with a fixed number of features. As a result, those methods cannot be directly applied to variable-length time series data. One common approach is to perform classification over a sliding window on the data and aggregate the decisions made at local sections of the time series in some way, through majority voting for classification or averaging for regression. The downside to this approach is that minority local information is lost in the voting process and averaging assumes that each time series measurement is equal in significance. Also, since time series can be of varying length, the quality of votes and averages could vary greatly in cases where there is a close voting tie or bimodal distribution of regression domain. Summarization conducted by the \textit{SummerTime} method will be a fixed-length feature vector which can be used in-place of the time series dataset for use with classical machine learning methods. We use Gaussian Mixture models (GMM) over small same-length disjoint windows in the time series to group local data into clusters. The time series' rate of membership for each cluster will be a feature in the summarization. The model is naturally capable of converging to an appropriate cluster count. We compare our results to state-of-the-art studies in physical activity classification and show high-quality improvement by classifying with only the summarization. Finally, we show that regression using the summarization can augment energy expenditure estimation, producing more robust and precise results.