Disentangled Mode-Specific Representations for Tensor Time Series via Contrastive Learning

Multi-mode tensor time series (TTS) can be found in many domains, such as search engines and environmental monitoring systems. Learning representations of a TTS benefits various applications, but it is also challenging since the complexities inherent in the tensor hinder the realization of rich representations. In this paper, we propose a novel representation learning method designed specifically for TTS, namely MoST. Specifically, MoST uses a tensor slicing approach to reduce the complexity of the TTS structure and learns representations that can be disentangled into individual non-temporal modes. Each representation captures mode-specific features, which are the relationship between variables within the same mode, and mode-invariant features, which are in common in representations of different modes. We employ a contrastive learning framework to learn parameters; the loss function comprises two parts intended to learn representation in a mode-specific way and mode-invariant way, effectively exploiting disentangled representations as augmentations. Extensive experiments on real-world datasets show that MoST consistently outperforms the state-of-the-art methods in terms of classification and forecasting accuracy. Code is available at https://github.com/KoheiObata/MoST.

Selective Denoising Diffusion Model for Time Series Anomaly Detection

Time series anomaly detection (TSAD) has been an important area of research for decades, with reconstruction-based methods, mostly based on generative models, gaining popularity and demonstrating success. Diffusion models have recently attracted attention due to their advanced generative capabilities. Existing diffusion-based methods for TSAD rely on a conditional strategy, which reconstructs input instances from white noise with the aid of the conditioner. However, this poses challenges in accurately reconstructing the normal parts, resulting in suboptimal detection performance. In response, we propose a novel diffusion-based method, named AnomalyFilter, which acts as a selective filter that only denoises anomaly parts in the instance while retaining normal parts. To build such a filter, we mask Gaussian noise during the training phase and conduct the denoising process without adding noise to the instances. The synergy of the two simple components greatly enhances the performance of naive diffusion models. Extensive experiments on five datasets demonstrate that AnomalyFilter achieves notably low reconstruction error on normal parts, providing empirical support for its effectiveness in anomaly detection. AnomalyFilter represents a pioneering approach that focuses on the noise design of diffusion models specifically tailored for TSAD.

Robust and Explainable Detector of Time Series Anomaly via Augmenting Multiclass Pseudo-Anomalies

Unsupervised anomaly detection in time series has been a pivotal research area for decades. Current mainstream approaches focus on learning normality, on the assumption that all or most of the samples in the training set are normal. However, anomalies in the training set (i.e., anomaly contamination) can be misleading. Recent studies employ data augmentation to generate pseudo-anomalies and learn the boundary separating the training samples from the augmented samples. Although this approach mitigates anomaly contamination if augmented samples mimic unseen real anomalies, it suffers from several limitations. (1) Covering a wide range of time series anomalies is challenging. (2) It disregards augmented samples that resemble normal samples (i.e., false anomalies). (3) It places too much trust in the labels of training and augmented samples. In response, we propose RedLamp, which employs diverse data augmentations to generate multiclass pseudo-anomalies and learns the multiclass boundary. Such multiclass pseudo-anomalies cover a wide variety of time series anomalies. We conduct multiclass classification using soft labels, which prevents the model from being overconfident and ensures its robustness against contaminated/false anomalies. The learned latent space is inherently explainable as it is trained to separate pseudo-anomalies into multiclasses. Extensive experiments demonstrate the effectiveness of RedLamp in anomaly detection and its robustness against anomaly contamination.

Mining of Switching Sparse Networks for Missing Value Imputation in Multivariate Time Series

Multivariate time series data suffer from the problem of missing values, which hinders the application of many analytical methods. To achieve the accurate imputation of these missing values, exploiting inter-correlation by employing the relationships between sequences (i.e., a network) is as important as the use of temporal dependency, since a sequence normally correlates with other sequences. Moreover, exploiting an adequate network depending on time is also necessary since the network varies over time. However, in real-world scenarios, we normally know neither the network structure nor when the network changes beforehand. Here, we propose a missing value imputation method for multivariate time series, namely MissNet, that is designed to exploit temporal dependency with a state-space model and inter-correlation by switching sparse networks. The network encodes conditional independence between features, which helps us understand the important relationships for imputation visually. Our algorithm, which scales linearly with reference to the length of the data, alternatively infers networks and fills in missing values using the networks while discovering the switching of the networks. Extensive experiments demonstrate that MissNet outperforms the state-of-the-art algorithms for multivariate time series imputation and provides interpretable results.

Dynamic Multi-Network Mining of Tensor Time Series

Subsequence clustering of time series is an essential task in data mining, and interpreting the resulting clusters is also crucial since we generally do not have prior knowledge of the data. Thus, given a large collection of tensor time series consisting of multiple modes, including timestamps, how can we achieve subsequence clustering for tensor time series and provide interpretable insights? In this paper, we propose a new method, Dynamic Multi-network Mining (DMM), that converts a tensor time series into a set of segment groups of various lengths (i.e., clusters) characterized by a dependency network constrained with l1-norm. Our method has the following properties. (a) Interpretable: it characterizes the cluster with multiple networks, each of which is a sparse dependency network of a corresponding non-temporal mode, and thus provides visible and interpretable insights into the key relationships. (b) Accurate: it discovers the clusters with distinct networks from tensor time series according to the minimum description length (MDL). (c) Scalable: it scales linearly in terms of the input data size when solving a non-convex problem to optimize the number of segments and clusters, and thus it is applicable to long-range and high-dimensional tensors. Extensive experiments with synthetic datasets confirm that our method outperforms the state-of-the-art methods in terms of clustering accuracy. We then use real datasets to demonstrate that DMM is useful for providing interpretable insights from tensor time series.