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.

The study of model bias and variance with respect to decision boundaries is critically important in supervised learning and artificial intelligence. There is generally a tradeoff between the two, as fine-tuning of the decision boundary of a classification model to accommodate more boundary training samples (i.e., higher model complexity) may improve training accuracy (i.e., lower bias) but hurt generalization against unseen data (i.e., higher variance). By focusing on just classification boundary fine-tuning and model complexity, it is difficult to reduce both bias and variance. To overcome this dilemma, we take a different perspective and investigate a new approach to handle inaccuracy and uncertainty in the training data labels, which are inevitable in many applications where labels are conceptual entities and labeling is performed by human annotators. The process of classification can be undermined by uncertainty in the labels of the training data; extending a boundary to accommodate an inaccurately labeled point will increase both bias and variance. Our novel method can reduce both bias and variance by estimating the pointwise label uncertainty of the training set and accordingly adjusting the training sample weights such that those samples with high uncertainty are weighted down and those with low uncertainty are weighted up. In this way, uncertain samples have a smaller contribution to the objective function of the model’s learning algorithm and exert less pull on the decision boundary. In a real-world physical activity recognition case study, the data present many labeling challenges, and we show that this new approach improves model performance and reduces model variance.

Unsupervised semantic segmentation in the time series domain is a much studied problem due to its potential to detect unexpected regularities and regimes in poorly understood data. However, the current techniques have several shortcomings, which have limited the adoption of time series semantic segmentation beyond academic settings for four primary reasons. First, most methods require setting/learning many parameters and thus may have problems generalizing to novel situations. Second, most methods implicitly assume that all the data is segmentable and have difficulty when that assumption is unwarranted. Thirdly, many algorithms are only defined for the single dimensional case, despite the ubiquity of multi-dimensional data. Finally, most research efforts have been confined to the batch case, but online segmentation is clearly more useful and actionable. To address these issues, we present a multi-dimensional algorithm, which is domain agnostic, has only one, easily-determined parameter, and can handle data streaming at a high rate. In this context, we test the algorithm on the largest and most diverse collection of time series datasets ever considered for this task and demonstrate the algorithm's superiority over current solutions.

The article Domain agnostic online semantic segmentation for multi-dimensional time series, written by Shaghayegh Gharghabi, Chin-Chia Michael Yeh, Yifei Ding, Wei Ding, Paul Hibbing, Samuel LaMunion, Andrew Kaplan, Scott E. Crouter, Eamonn Keogh was originally published electronically on the publisher’s internet portal (currently SpringerLink) on 25 September 2018 without open access.

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.