Given real-time sensor data streams obtained from machines, how can we continuously predict when a machine failure will occur? This work aims to continuously forecast the timing of future events by analyzing multi-sensor data streams. A key characteristic of real-world data streams is their dynamic nature, where the underlying patterns evolve over time. To address this, we present TimeCast, a dynamic prediction framework designed to adapt to these changes and provide accurate, real-time predictions of future event time. Our proposed method has the following properties: (a) Dynamic: it identifies the distinct time-evolving patterns (i.e., stages) and learns individual models for each, enabling us to make adaptive predictions based on pattern shifts. (b) Practical: it finds meaningful stages that capture time-varying interdependencies between multiple sensors and improve prediction performance; (c) Scalable: our algorithm scales linearly with the input size and enables online model updates on data streams. Extensive experiments on real datasets demonstrate that TimeCast provides higher prediction accuracy than state-of-the-art methods while finding dynamic changes in data streams with a great reduction in computational time.

With the rapid development of web services, large amounts of time series data are generated and accumulated across various domains such as finance, healthcare, and online platforms. As such data often co-evolves with multiple variables interacting with each other, estimating the time-varying dependencies between variables (i.e., the dynamic network structure) has become crucial for accurate modeling. However, real-world data is often represented as tensor time series with multiple modes, resulting in large, entangled networks that are hard to interpret and computationally intensive to estimate. In this paper, we propose Kronecker Time-Varying Graphical Lasso (KTVGL), a method designed for modeling tensor time series. Our approach estimates mode-specific dynamic networks in a Kronecker product form, thereby avoiding overly complex entangled structures and producing interpretable modeling results. Moreover, the partitioned network structure prevents the exponential growth of computational time with data dimension. In addition, our method can be extended to stream algorithms, making the computational time independent of the sequence length. Experiments on synthetic data show that the proposed method achieves higher edge estimation accuracy than existing methods while requiring less computation time. To further demonstrate its practical value, we also present a case study using real-world data. Our source code and datasets are available at https://github.com/Higashiguchi-Shingo/KTVGL.

Large quantities of social activity data, such as weekly web search volumes and the number of new infections with infectious diseases, reflect peoples' interests and activities. It is important to discover temporal patterns from such data and to forecast future activities accurately. However, modeling and forecasting social activity data streams is difficult because they are high-dimensional and composed of multiple time-varying dynamics such as trends, seasonality, and interest diffusion. In this paper, we propose D-Tracker, a method for continuously capturing time-varying temporal patterns within social activity tensor data streams and forecasting future activities. Our proposed method has the following properties: (a) Interpretable: it incorporates the partial differential equation into a tensor decomposition framework and captures time-varying temporal patterns such as trends, seasonality, and interest diffusion between locations in an interpretable manner; (b) Automatic: it has no hyperparameters and continuously models tensor data streams fully automatically; (c) Scalable: the computation time of D-Tracker is independent of the time series length. Experiments using web search volume data obtained from GoogleTrends, and COVID-19 infection data obtained from COVID-19 Open Data Repository show that our method can achieve higher forecasting accuracy in less computation time than existing methods while extracting the interest diffusion between locations. Our source code and datasets are available at https://github.com/Higashiguchi-Shingo/D-Tracker.

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.

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.

Many web applications, such as search engines and social network services, are continuously producing a huge number of events with a multi-order tensor form, {count;query, location, …, timestamp}, and so how can we discover important trends to enables us to forecast long-term future events? Can we interpret any relationships between events that determine the trends from multi-aspect perspectives? Real-world online activities can be composed of (1) many time-changing interactions that control trends, for example, competition/cooperation to gain user attention, as well as (2) seasonal patterns that covers trends. To model the shifting trends via interactions, namely dynamic interactions over tensor streams, in this paper, we propose a streaming algorithm, DISMO, that we designed to discover Dynamic Interactions and Seasonality in a Multi-Order tensor. Our approach has the following properties. (a) Interpretable: it incorporates interpretable non-linear differential equations in tensor factorization so that it can reveal latent interactive relationships and thus generate future events effectively; (b) Dynamic: it can be aware of shifting trends by switching multi-aspect factors while summarizing their characteristics incrementally; and (c) Automatic: it finds every factor automatically without losing forecasting accuracy. Extensive experiments on real datasets demonstrate that our algorithm extracts interpretable interactions between data attributes, while simultaneously providing improved forecasting accuracy and a great reduction in computational time.

Given a huge, online stream of time-evolving events with multiple attributes, such as online shopping logs: (item, price, brand, time), how can we summarize large, dynamic high-order tensor streams? How can we see any hidden patterns, rules, and anomalies? Our answer is to focus on two types of patterns, i.e., “regimes” and “components”, over high-order tensor streams, for which we present an efficient and effective method, namely CubeScope. Specifically, it identifies any sudden discontinuity and recognizes distinct dynamical patterns, “regimes” (e.g., weekday/weekend/holiday patterns). In each regime, it also performs multi-way summarization for all attributes (e.g., item, price, brand, and time) and discovers hidden “components” representing latent groups (e.g., item/brand groups) and their relationship. Thanks to its concise but effective summarization, CubeScope can also detect the sudden appearance of anomalies and identify the types of anomalies that occur in practice.

Given a large, semi-infinite collection of co-evolving epidemiological data containing the daily counts of cases/deaths/recovered in multiple locations, how can we incrementally monitor current dynamical patterns and forecast future behavior? The world faces the rapid spread of infectious diseases such as SARS-CoV-2 (COVID-19), where a crucial goal is to predict potential future outbreaks and pandemics, as quickly as possible, using available data collected throughout the world. In this paper, we propose a new streaming algorithm, EPICAST, which is able to model, understand and forecast dynamical patterns in large co-evolving epidemiological data streams. Our proposed method is designed as a dynamic and flexible system, and is based on a unified non-linear differential equation. Our method has the following properties: (a) Effective: it operates on large co-evolving epidemiological data streams, and captures important world-wide trends, as well as location-specific patterns. It also performs real-time and long-term forecasting; (b) Adaptive: it incrementally monitors current dynamical patterns, and also identifies any abrupt changes in streams; (c) Scalable: our algorithm does not depend on data size, and thus is applicable to very large data streams. In extensive experiments on real datasets, we demonstrate that EPICAST outperforms the best existing state-of-the-art methods as regards accuracy and execution speed.

Given a large time-evolving event series such as Google web-search logs, which are collected according to various aspects, i.e., timestamps, locations and keywords, how accurately can we forecast their future activities? How can we reveal significant patterns that allow us to long-term forecast from such complex tensor streams? In this paper, we propose a streaming method, namely, CubeCast, that is designed to capture basic trends and seasonality in tensor streams and extract temporal and multi-dimensional relationships between such dynamics. Our proposed method has the following properties: (a) it is effective: it finds both trends and seasonality and summarizes their dynamics into simultaneous non-linear latent space. (b) it is automatic: it automatically recognizes and models such structural patterns without any parameter tuning or prior information. (c) it is scalable: it incrementally and adaptively detects shifting points of patterns for a semi-infinite collection of tensor streams. Extensive experiments that we conducted on real datasets demonstrate that our algorithm can effectively and efficiently find meaningful patterns for generating future values, and outperforms the state-of-the-art algorithms for time series forecasting in terms of forecasting accuracy and computational time.

Given a large volume of multi-dimensional data streams, such as that produced by IoT applications, finance and online web-click logs, how can we discover typical patterns and compress them into compact models? In addition, how can we incrementally distinguish multiple patterns while considering the information obtained from a pattern found in a streaming setting? In this paper, we propose a streaming algorithm, namely StreamScope, that is designed to find intuitive patterns efficiently from event streams evolving over time. Our proposed method has the following properties: (a) it is effective: it operates on semi-infinite collections of co-evolving streams and summarizes all the streams into a set of multiple discrete segments grouped by their similarities. (b) it is automatic: it automatically and incrementally recognizes such patterns and generates models for each of them if necessary; (c) it is scalable: the complexity of our method does not depend on the length of the data streams. Our extensive experiments on real data streams demonstrate that StreamScope can find meaningful patterns and achieve great improvements in terms of computational time and memory space over its full batch method competitors.