Multivariate time series classification is an important task with widespread domains of applications. Recently, deep neural networks (DNN) have achieved state-of-the-art performance in time series classification. However, they often require large expert-labeled training datasets which can be infeasible in practice. In few-shot settings, i.e. only a limited number of samples per class are available in training data, DNNs show a significant drop in testing accuracy and poor generalization ability. In this paper, we propose to address these problems from an optimization and a loss function perspective. Specifically, we propose a new learning framework named COSCO consisting of a sharpness-aware minimization (SAM) optimization and a Prototypical loss function to improve the generalization ability of DNN for multivariate time series classification problems under few-shot setting. Our experiments demonstrate our proposed method outperforms the existing baseline methods. Our source code is available at: https://github.com/JRB9/COSCO.

Recent rapid development of sensor technology has allowed massive time series data to be collected and set foundation for the development of data-driven services and applications. During the process, data sharing is often required to allow modelers to perform specific time series data mining tasks based on the need of data owner. The high resolution of time series data brings new challenges in privacy protection, as meaningful information in high-resolution data shifts from concrete point values to shape-based patterns. Numerous research efforts have found that long shape-based patterns could contain more sensitive information and may potentially be extracted and misused by a malicious modeler. However, the privacy issue for time series patterns is surprisingly seldom explored in privacy-preserving literature. In this work, we consider a new privacy preserving problem: preventing malicious inference on long shape-based patterns while preserving short segment information to maintain utility task performance. To mitigate the challenge, we investigate an alternative approach by sharing Matrix Profile (MP), a versatile data structure that supports many time series data mining tasks. We found that while MP can prevent the concrete shape leakage, the canonical correlation in MP index can still reveal the location of sensitive long pattern information. Based on this observation, we design two attacks named Location Attack and Entropy Attack to extract the pattern location from MP. To further protect MP from these two attacks, we propose a Privacy-Aware Matrix Profile (PMP) via perturbing the local correlation and breaking the canonical correlation in MP index vector. We evaluate our proposed PMP against baseline noise-adding methods through quantitative analysis and real-world case study to show the effectiveness of the proposed method. Our source code is available at https://github.com/lzhang18/PMP.

Time series motif discovery has been a fundamental task to identify meaningful repeated patterns in time series. Recently, time series chains (TSCs) were introduced as an expansion of time series motifs to identify the continuous evolving patterns in time series data. TSCs are shown to be able to reveal latent continuous evolving trends in the time series, and identify precursors of unusual events in complex systems. However, existing TSC definitions lack the ability to accurately cover the evolving part of a time series: the discovered chains can be easily cut by noise and can include non-evolving patterns, making them impractical in real-world applications. In this work, we introduce a new TSC definition based on an incremental nearest neighbor concept which can better locate the evolving patterns while excluding the non-evolving ones, and propose two new quality metrics to rank the discovered chains. With extensive empirical evaluations, we demonstrate that the proposed TSC definition is significantly more robust to noise than the state of the art, and the top ranked chains discovered can reveal meaningful regularities in a variety of real world datasets.

Time series chain (TSC) is a recently introduced concept that captures the evolving patterns in large scale time series. Informally, a time series chain is a temporally ordered set of subsequences, in which consecutive subsequences in the chain are similar to one another, but the last and the first subsequences maybe be dissimilar. Time series chain has the great potential to reveal latent unusual evolving trend in the time series, or identify precursor of important events in a complex system. Unfortunately, existing definitions of time series chains only consider finding chains in a single time series. As a result, they are likely to miss unexpected evolving patterns in interrupted time series, or across two related time series. To address this limitation, in this work, we introduce a new definition called Joint Time Series Chain, which is specially designed for the task of finding unexpected evolving trend across interrupted time series or two related time series. Our definition focuses on mitigating the robustness issues caused by the gap or interruption in the time series. We further propose an effective ranking criterion to identify the best chain. We demonstrate that our proposed approach outperforms existing TSC work in locating unusual evolving patterns through extensive empirical evaluations. We further demonstrate the utility of our work with a real-life manufacturing application from Intel.

Finding anomalous subsequence in a long time series is a very important but difficult problem. Existing state-of-the-art methods have been focusing on searching for the subsequence that is the most dissimilar to the rest of the subsequences; however, they do not take into account the background patterns that contain the anomalous candidates. As a result, such approaches are likely to miss local anomalies. We introduce a new definition named semantic discord, which incorporates the context information from larger subsequences containing the anomaly candidates. We propose an efficient algorithm with a derived lower bound that is up to 3 orders of magnitude faster than the brute force algorithm in real world data. We demonstrate that our method significantly outperforms the state-of-the-art methods in locating anomalies by extensive experiments. We further explain the interpretability of semantic discord.