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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.

In recent years, a massive amount of time-stamped sensor data has been generated and collected by many Internet of Things (IoT) applications, such as advanced automobiles and health care devices. Given such a large collection of complex sensor sequences, which consists of multiple attributes (e.g., sensor, user, timestamp), how can we automatically find important dynamic time-series patterns and the points of variation? How can we summarize all the complex sensor sequences, and achieve a meaningful segmentation? Also, can we see any hidden user-specific differences and outliers? In this paper we present CUBEMARKER, an efficient and effective method for capturing such multi-aspect features in sensor sequences. CUBEMARKER performs multi-way summarization for all attributes, namely, sensors, users, and time, and specifically it extracts multi-aspect features, such as important time-series patterns (i.e., time-aspect features) and hidden groups of users (i.e., user-aspect features), in complex sensor sequences. Our proposed method has the following advantages: (a) It is effective: it extracts multi-aspect features from complex sensor sequences and enables the efficient and effective analysis of complicated datasets; (b) It is automatic: it requires no prior training and no parameter tuning; (c) It is scalable: our method is carefully designed to be linear as regards dataset size and applicable to a large number of sensor sequences. Extensive experiments on real datasets show that CUBEMARKER is effective in that it can capture meaningful patterns for various real-world datasets, such as those obtained from smart factories, human activities, and automobiles. CUBEMARKER consistently outperforms the best state-of-the-art methods in terms of both accuracy and execution speed.

Given a large, semi-infinite collection of co-evolving data sequences (e.g., IoT/sensor streams), which contains multiple distinct dynamic time-series patterns, our aim is to incrementally monitor current dynamic patterns and forecast future behavior. We present an intuitive model, namely OrbitMap, which provides a good summary of time-series evolution in streams. We also propose a scalable and effective algorithm for fitting and forecasting time-series data streams. Our method is designed as a dynamic, interactive and flexible system, and is based on latent non-linear differential equations. Our proposed method has the following advantages: (a) It is effective: it captures important time-evolving patterns in data streams and enables real-time, long-range forecasting; (b) It is general: our model is general and practical and can be applied to various types of time-evolving data streams; (c) It is scalable: our algorithm does not depend on data size, and thus is applicable to very large sequences. Extensive experiments on real datasets demonstrate that OrbitMap makes long-range forecasts, and consistently outperforms the best existing state-of-the-art methods as regards accuracy and execution speed.

Given a large collection of co-evolving online activities, such as searches for the keywords "Xbox", "PlayStation" and "Wii", how can we find patterns and rules? Are these keywords related? If so, are they competing against each other? Can we forecast the volume of user activity for the coming month? We conjecture that online activities compete for user attention in the same way that species in an ecosystem compete for food. We present EcoWeb, (i.e., Ecosystem on the Web), which is an intuitive model designed as a non-linear dynamical system for mining large-scale co-evolving online activities. Our second contribution is a novel, parameter-free, and scalable fitting algorithm, EcoWeb-Fit, that estimates the parameters of EcoWeb. Extensive experiments on real data show that EcoWeb is effective, in that it can capture long-range dynamics and meaningful patterns such as seasonalities, and practical, in that it can provide accurate long-range forecasts. EcoWeb consistently outperforms existing methods in terms of both accuracy and execution speed.

Given a large collection of multiple time-evolving sensor sequences, how can we capture the transitions of time series patterns? How can we find individual differences between different sequences? In this paper we present CUBEMARKER, an effective method for capturing multi-aspect features of sensor sequences, which provides a compact and powerful representation of sensor behavior. Our second contribution is a novel, scalable, and parameter-free algorithm. CUBEMARKER performs two-way mining for all attributes. Specifically it discovers multi-aspect time series patterns (human motion, smart factory, etc) and groups of patterns simultaneously. Extensive experiments on real datasets show that CUBEMARKER is effective in that it can capture meaningful patterns for various real sensor datasets.

Given a large volume of multiple data streams, such as online web-click logs and sensor data, how can we discover typical patterns and compress them into compact models? 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 can find intuitive patterns efficiently from event streams evolving over time. Our method has the following properties: (a) Effective: It operates on semi-infinite data streams and summarizes all the streams into a set of multiple discrete segments grouped by their similarities. (b) Automatic: It automatically and incrementally recognizes such patterns and generates models for each of them if necessary. (c) Scalable: The complexity of our method does not depend on the length of the input streams. Our experiments on real datasets demonstrate that StreamsCopecan find meaningful patterns and achieve great improvements in terms of computational time and memory space over its full batch method competitors.

Given a large collection of time-evolving online user activities, such as Google Search queries for multiple keywords of various categories (celebrities, events, diseases, etc.), which consist of \(d\) keywords/activities, for \(l\) countries/locations of duration \(n\), how can we find patterns and rules? How do we go about capturing non-linear evolutions of local activities and forecasting future patterns? We also aim to achieve good monitoring of the data sequences statistically, and detection of the patterns immediately. In this paper, we present \({\varDelta \hbox {-}\textsc {SPOT}} \), a unifying analytical non-linear model for analysing large scale web search data, which is sense-making, automatic, scalable and free of parameters. \({\varDelta \hbox {-}\textsc {SPOT}} \) can also forecast long-range future dynamics of the keywords/queries. Besides, we also provide an efficient and effective fitting algorithm, which leads to novel discoveries and sense-making features, and contribute to the need of monitoring multiple co-evolving data sequences.

Given a large, online stream of multiple co-evolving event sequences, such as sensor data and Web-click logs, that contains various types of non-linear dynamic evolving patterns of different durations, how can we efficiently and effectively capture important patterns? How do we go about forecasting long-term future events? In this paper, we present REGIMECAST, an efficient and effective method for forecasting co-evolving data streams. REGIMECAST is designed as an adaptive non-linear dynamical system, which is inspired by the concept of "regime shifts" in natural dynamical systems. Our method has the following properties: (a) Effective: it operates on large data streams, captures important patterns and performs long-term forecasting; (b) Adaptive: it automatically and incrementally recognizes the latent trends and dynamic evolution patterns (i.e., regimes) that are unknown in advance; (c) Scalable: it is fast and the computation cost does not depend on the length of data streams; (d) Any-time: it provides a response at any time and generates long-range future events. Extensive experiments on real datasets demonstrate that REGIMECAST does indeed make long-range forecasts, and it outperforms state-of-the-art competitors as regards accuracy and speed.

Given a large collection of time-evolving activities, such as Google search queries, which consist of d keywords/activities for m locations of duration n, how can we analyze temporal patterns and relationships among all these activities and find location-specific trends? How do we go about capturing non-linear evolutions of local activities and forecasting future patterns? For example, assume that we have the online search volume for multiple keywords, e.g., "Nokia/Nexus/Kindle" or "CNN/BBC" for 236 countries/territories, from 2004 to 2015. Our goal is to analyze a large collection of multi-evolving activities, and specifically, to answer the following questions: (a) Is there any sign of interaction/competition between two different keywords? If so, who competes with whom? (b) In which country is the competition strong? (c) Are there any seasonal/annual activities? (d) How can we automatically detect important world-wide (or local) events? We present COMPCUBE, a unifying non-linear model, which provides a compact and powerful representation of co-evolving activities; and also a novel fitting algorithm, COMPCUBE-FIT, which is parameter-free and scalable. Our method captures the following important patterns: (B)asic trends, i.e., non-linear dynamics of co-evolving activities, signs of (C)ompetition and latent interaction, e.g., Nokia vs. Nexus, (S)easonality, e.g., a Christmas spike for iPod in the U.S. and Europe, and (D)eltas, e.g., unrepeated local events such as the U.S. election in 2008. Thanks to its concise but effective summarization, COMPCUBE can also forecast long-range future activities. Extensive experiments on real datasets demonstrate that COMPCUBE consistently outperforms the best state-of- the-art methods in terms of both accuracy and execution speed.

Given a large collection of co-evolving online activities, such as searches for the keywords "Xbox", "PlayStation" and "Wii", how can we find patterns and rules? Are these keywords related? If so, are they competing against each other? Can we forecast the volume of user activity for the coming month? We conjecture that online activities compete for user attention in the same way that species in an ecosystem compete for food. We present ECOWEB, (i.e., Ecosystem on the Web), which is an intuitive model designed as a non-linear dynamical system for mining large-scale co-evolving online activities. Our second contribution is a novel, parameter-free, and scalable fitting algorithm, ECOWEB-FIT, that estimates the parameters of ECOWEB. Extensive experiments on real data show that ECOWEB is effective, in that it can capture long-range dynamics and meaningful patterns such as seasonalities, and practical, in that it can provide accurate long-range forecasts. ECOWEB consistently outperforms existing methods in terms of both accuracy and execution speed.

Given a large collection of co-evolving multiple time-series, which contains an unknown number of patterns of different durations, how can we efficiently and effectively find typical patterns and the points of variation? How can we statistically summarize all the sequences, and achieve a meaningful segmentation? In this paper we present AutoPlait, a fully automatic mining algorithm for co-evolving time sequences. Our method has the following properties: (a) effectiveness: it operates on large collections of time-series, and finds similar segment groups that agree with human intuition; (b) scalability: it is linear with the input size, and thus scales up very well; and (c) AutoPlait is parameter-free, and requires no user intervention, no prior training, and no parameter tuning. Extensive experiments on 67GB of real datasets demonstrate that AutoPlait does indeed detect meaningful patterns correctly, and it outperforms state-of-the-art competitors as regards accuracy and speed: AutoPlait achieves near-perfect, over 95% precision and recall, and it is up to 472 times faster than its competitors.

Given huge collections of time-evolving events such as web-click logs, which consist of multiple attributes (e.g., URL, userID, times- tamp), how do we find patterns and trends? How do we go about capturing daily patterns and forecasting future events? We need two properties: (a) effectiveness, that is, the patterns should help us understand the data, discover groups, and enable forecasting, and (b) scalability, that is, the method should be linear with the data size. We introduce TriMine, which performs three-way mining for all three attributes, namely, URLs, users, and time. Specifically TriMine discovers hidden topics, groups of URLs, and groups of users, simultaneously. Thanks to its concise but effective summarization, it makes it possible to accomplish the most challenging and important task, namely, to forecast future events. Extensive experiments on real datasets demonstrate that TriMine discovers meaningful topics and makes long-range forecasts, which are notoriously difficult to achieve. In fact, TriMine consistently outperforms the best state-of-the-art existing methods in terms of accuracy and execution speed (up to 74x faster).