SummerTime seeks to summarize global time-series signals and provides a fixed-length, robust representation of the variable-length time series. Many machine learning methods 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. Existing methods such as sliding windows can lose minority local information. Summarization conducted by the 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. By making use of variational methods, GMM converges to a more robust mixture, meaning the clusters are more resistant to noise and overfitting. Further, the model is naturally capable of converging to an appropriate cluster count. We validate our method on a challenging real-world dataset, an imbalanced physical activity dataset with a variable-length time series structure. We compare our results to state-of-the-art studies and show high-quality improvement by classifying with only the summarization.

Physical activity consists complex behavior, typically structured in bouts which can consist of one continuous movement (e.g. exercise) or many sporadic movements (e.g. household chores). Each bout can be represented as a block of feature vectors corresponding to the same activity type. This paper introduces a general distance metric technique to use this block representation to first predict activity type, and then uses the predicted activity to estimate energy expenditure within a novel framework. This distance metric, dubbed Bipart, learns block-level information from both training and test sets, combining both to form a projection space which materializes block-level constraints. Thus, Bipart provides a space which can improve the bout classification performance of all classifiers. We also propose an energy expenditure estimation framework which leverages activity classification in order to improve estimates. Comprehensive experiments on waist-mounted accelerometer data, comparing Bipart against many similar methods as well as other classifiers, demonstrate the superior activity recognition of Bipart, especially in low-information experimental settings.