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.

Analysis and anomaly detection in event tensor streams consisting of timestamps and multiple attributes—such as communication logs (time, IP address, packet length)—are essential tasks in data mining. While existing tensor decomposition and anomaly detection methods provide useful insights, they face the following two limitations. (i) They cannot handle heterogeneous tensor streams, which comprises both categorical attributes (e.g., IP address) and continuous attributes (e.g., packet length). They typically require either discretizing continuous attributes or treating categorical attributes as continuous, both of which distort the underlying statistical properties of the data. Furthermore, incorrect assumptions about the distribution family of continuous attributes often degrade the model's performance. (ii) They discretize timestamps, failing to track the temporal dynamics of streams (e.g., trends, abnormal events), which makes them ineffective for detecting anomalies at the group level, referred to as ''group anomalies'' (e.g, DoS attacks). To address these challenges, we propose HeteroComp, a method for continuously summarizing heterogeneous tensor streams into ''components'' representing latent groups in each attribute and their temporal dynamics, and detecting group anomalies. Our method employs Gaussian process priors to model unknown distributions of continuous attributes, and temporal dynamics, which directly estimate probability densities from data. Extracted components give concise but effective summarization, enabling accurate group anomaly detection. Extensive experiments on real datasets demonstrate that HeteroComp outperforms the state-of-the-art algorithms for group anomaly detection accuracy, and its computational time does not depend on the data stream length.

The advent of generative AI tools has had a profound impact on societies globally, transcending geographical boundaries. Understanding these tools' global reception and utilization is crucial for service providers and policymakers in shaping future policies. Therefore, to unravel the perceptions and engagements of individuals within diverse linguistic communities with regard to generative AI tools, we extensively analyzed over 6.8 million tweets in 14 different languages. Our findings reveal a global trend in the perception of generative AI, accompanied by language-specific nuances. While sentiments toward these tools vary significantly across languages, there is a prevalent positive inclination toward Image tools and a negative one toward Chat tools. Notably, the ban of ChatGPT in Italy led to a sentiment decline and initiated discussions across languages. Furthermore, we established a taxonomy for interactions with chatbots, creating a framework for social analysis underscoring variations in generative AI usage among linguistic communities. We find that the Chinese community predominantly employs chatbots as substitutes for search, while the Italian community tends to use chatbots for tasks such as problem-solving assistance and engaging in entertainment or creative tasks. Our research provides a robust foundation for further explorations of the social dynamics surrounding generative AI tools and offers invaluable insights for decision-makers in policy, technology, and education.

Given an extensive, semi-infinite collection of multivariate coevolving data sequences (e.g., sensor/web activity streams) whose observations influence each other, how can we discover the time-changing cause-and-effect relationships in co-evolving data streams? How efficiently can we reveal dynamical patterns that allow us to forecast future values? In this paper, we present a novel streaming method, ModePlait, which is designed for modeling such causal relationships (i.e., time-evolving causality) in multivariate co-evolving data streams and forecasting their future values. The solution relies on characteristics of the causal relationships that evolve over time in accordance with the dynamic changes of exogenous variables. ModePlait has the following properties: (a) Effective: it discovers the time-evolving causality in multivariate co-evolving data streams by detecting the transitions of distinct dynamical patterns adaptively. (b) Accurate: it enables both the discovery of time-evolving causality and the forecasting of future values in a streaming fashion. (c) Scalable: our algorithm does not depend on data stream length and thus is applicable to very large sequences. Extensive experiments on both synthetic and real-world datasets demonstrate that our proposed model outperforms state-of-the-art methods in terms of discovering the time-evolving causality as well as forecasting.

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.

Recently, we have been inundated with dynamic, time-evolving activity data streams generated by various individual IoT/sensor devices (e.g., healthcare devices and factory equipment).What would be the ideal mechanism for adaptively summarizing and modeling individual and local activities directly on small IoT devices with limited computing resources?In this paper, we present MicroAdapt, which comprises scalable and effective algorithms for modeling and forecasting time-evolving data streams.Our proposed method has the following advantages: (a) Adaptivity: it continuously monitors the latest time-series patterns in data streams, recognizes any sudden changes, updates model parameters, and enables realtime, long-range forecasting; (b) Any-time processing: it operates on a large collection of data streams, requiring a constant time (i.e., 𝑂 (1)) for model updates and future predictions, at any point in time; (c) Lightweight computing: it does not require high-performance computing machines equipped with powerful GPUs, such as those used in deep learning, and can run on lightweight computers or even "edge" computing devices, such as Raspberry Pi.Intuitively, our method is inspired by the concept of an evolutionary adaptation mechanism of microorganisms, and thus it enables adaptive, any-time, lightweight model estimation and summarization of nonstationary data streams whose time-series patterns are constantly changing over time.We conduct extensive experiments on real datasets and demonstrate that MicroAdapt effectively captures important time-series patterns in the data streams, makes long-range forecasts, and consistently outperforms the existing state-of-the-art methods (e.g., TSMixer) as regards accuracy and execution speed.MicroAdapt improves accuracy by about 60% for MSE and 30% for MAE, while reducing computation time by up to six orders of magnitude (more than 100,000 times).We also applied our analytics to experiments implemented on Raspberry Pi with real IoT data streams, thus demonstrating the practicality and effectiveness of our approach.In fact, our proposed method required less than 1.95GB of memory and consumed less than 1.69W of power.

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.

While end-to-end multi-channel electroencephalography (EEG) learning approaches have shown significant promise, their applicability is often constrained in neurological diagnostics, such as intracranial EEG resources. When provided with a single-channel EEG, how can we learn representations that are robust to multi-channels and scalable across varied tasks, such as seizure prediction? In this paper, we present SplitSEE, a structurally splittable framework designed for effective temporal-frequency representation learning in single-channel EEG. The key concept of SplitSEE is a self-supervised framework incorporating a deep clustering task. Given an EEG, we argue that the time and frequency domains are two distinct perspectives, and hence, learned representations should share the same cluster assignment. To this end, we first propose two domain-specific modules that independently learn domain-specific representation and address the temporal-frequency tradeoff issue in conventional spectrogram-based methods. Then, we introduce a novel clustering loss to measure the information similarity. This encourages representations from both domains to coherently describe the same input by assigning them a consistent cluster. SplitSEE leverages a pretraining-to-fine-tuning framework within a splittable architecture and has following properties: (a) Effectiveness: it learns representations solely from single-channel EEG but has even outperformed multi-channel baselines. (b) Robustness: it shows the capacity to adapt across different channels with low performance variance. Superior performance is also achieved with our collected clinical dataset. (c) Scalability: With just one fine-tuning epoch, SplitSEE achieves high and stable performance using partial model layers.

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.

The Transformer model has shown leading performance in time series forecasting. Nevertheless, in some complex scenarios, it tends to learn low-frequency features in the data and overlook high-frequency features, showing a frequency bias. This bias prevents the model from accurately capturing important high-frequency data features. In this paper, we undertake empirical analyses to understand this bias and discover that frequency bias results from the model disproportionately focusing on frequency features with higher energy. Based on our analysis, we formulate this bias and propose Fredformer, a Transformer-based framework designed to mitigate frequency bias by learning features equally across different frequency bands. This approach prevents the model from overlooking lower amplitude features important for accurate forecasting. Extensive experiments show the effectiveness of our proposed approach, which can outperform other baselines in different real-world time-series datasets. Furthermore, we introduce a lightweight variant of the Fredformer with an attention matrix approximation, which achieves comparable performance but with much fewer parameters and lower computation costs. The code is available at: https://github.com/chenzRG/Fredformer

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.

Social media has been a paramount arena for election campaigns for political actors. While many studies have been paying attention to the political campaigns related to partisanship, politicians also can conduct different campaigns according to their chances of winning. Leading candidates, for example, do not behave the same as fringe candidates in their elections, and vice versa. We, however, know little about this difference in social media political campaign strategies according to their odds in elections. We tackle this problem by analyzing candidates' tweets in terms of users, topics, and sentiment of replies. Our study finds that, as their chances of winning increase, candidates narrow the targets they communicate with, from people in general to the electrical districts and specific persons (verified accounts or accounts with many followers). Our study brings new insights into the candidates' campaign strategies through the analysis based on the novel perspective of the candidate's electoral situation.

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.

In this paper, we describe a method for detecting partial discharge (PD) in underground transmission lines from time series data. In general, PD is a discharge phenomenon that occurs when electric fields concentrate on voids or protrusions at the insulator interface of underground transmission lines. The accurate detection of PD and classification of its patterns play an important role in the diagnosis of underground transmission line deterioration. In this paper, we propose a method for using time series PD data to form a basis matrix that represents discharge patterns and a coefficient matrix that represents the contribution of each basis pattern over time by applying nonnegative matrix factorization. The proposed method (a) does not require a large amount of data, (b) works without any supervised information, and (c) can track new patterns of PD data by adding bases. Experiments using real data confirmed that PD patterns could be separated as a basis matrix. In addition, it was suggested that PD data could be extracted even for unknown time series, and new PD patterns could be extracted by re-learning.

Large quantifies of online user activity data, such as weekly web search volumes, which co-evolve with the mutual influence of several queries and locations, serve as an important social sensor. It is an important task to accurately forecast the future activity by discovering latent interactions from such data, i.e., the ecosystems between each query and the flow of influences between each area. However, this is a difficult problem in terms of data quantity and complex patterns covering the dynamics. To tackle the problem, we propose FluxCube, which is an effective mining method that forecasts large collections of co-evolving online user activity and provides good interpretability. Our model is the expansion of a combination of two mathematical models: a reaction-diffusion system provides a framework for modeling the flow of influences between local area groups and an ecological system models the latent interactions between each query. Also, by leveraging the concept of physics-informed neural networks, FluxCube achieves high interpretability obtained from the parameters and high forecasting performance, together. Extensive experiments on real datasets showed that FluxCube outperforms comparable models in terms of the forecasting accuracy, and each component in FluxCube contributes to the enhanced performance. We then show some case studies that FluxCube can extract useful latent interactions between queries and area groups.

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.

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.

The recent explosion in the adoption of search engines and new media such as blogs and Twitter have facilitated the faster propagation of news and rumors. How quickly does a piece of news spread over these media? How does its popularity diminish over time? Does the rising and falling pattern follow a simple universal law? In this article, we propose SpikeM, a concise yet flexible analytical model of the rise and fall patterns of information diffusion. Our model has the following advantages. First, unification power: it explains earlier empirical observations and generalizes theoretical models including the SI and SIR models. We provide the threshold of the take-off versus die-out conditions for SpikeM and discuss the generality of our model by applying it to an arbitrary graph topology. Second, practicality: it matches the observed behavior of diverse sets of real data. Third, parsimony: it requires only a handful of parameters. Fourth, usefulness: it makes it possible to perform analytic tasks such as forecasting, spotting anomalies, and interpretation by reverse engineering the system parameters of interest (quality of news, number of interested bloggers, etc.). We also introduce an efficient and effective algorithm for the real-time monitoring of information diffusion, namely SpikeStream, which identifies multiple diffusion patterns in a large collection of online event streams. Extensive experiments on real datasets demonstrate that SpikeM accurately and succinctly describes all patterns of the rise and fall spikes in social networks.

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 time series, such as web-click logs, electric medical records and motion capture sensors, how can we efficiently and effectively find typical patterns? How can we statistically summarize all the sequences, and achieve a meaningful segmentation? What are the major tools for forecasting and outlier detection? Time-series data analysis is becoming of increasingly high importance, thanks to the decreasing cost of hardware and the increasing on-line processing capability.

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 huge stream of multiple co-evolving sequences, such as motion capture and web-click logs, how can we find meaningful patterns and spot anomalies? Our aim is to monitor data streams statistically, and find sub sequences that have the characteristics of a given hidden Markov model (HMM). For example, consider an online web-click stream, where massive amounts of access logs of millions of users are continuously generated every second. So how can we find meaningful building blocks and typical access patterns such as weekday/weekend patterns, and also, detect anomalies and intrusions? In this paper, we propose Stream Scan, a fast and exact algorithm for monitoring multiple co-evolving data streams. Our method has the following advantages: (a) it is effective, leading to novel discoveries and surprising outliers, (b) it is exact, and we theoretically prove that Stream Scan guarantees the exactness of the output, (c) it is fast, and requires O (1) time and space per time-tick. Our experiments on 67GB of real data illustrate that Stream Scan does indeed detect the qualifying subsequence patterns correctly and that it can offer great improvements in speed (up to 479,000 times) over its competitors.

Given a large collection of epidemiological data consisting of the count of d contagious diseases for l locations of duration n, how can we find patterns, rules and outliers? For example, the Project Tycho provides open access to the count infections for U.S. states from 1888 to 2013, for 56 contagious diseases (e.g., measles, influenza), which include missing values, possible recording errors, sudden spikes (or dives) of infections, etc. So how can we find a combined model, for all these diseases, locations, and time-ticks? In this paper, we present FUNNEL, a unifying analytical model for large scale epidemiological data, as well as a novel fitting algorithm, FUNNELFIT, which solves the above problem. Our method has the following properties: (a) Sense-making: it detects important patterns of epidemics, such as periodicities, the appearance of vaccines, external shock events, and more; (b) Parameter-free: our modeling framework frees the user from providing parameter values; (c) Scalable: FUNNELFIT is carefully designed to be linear on the input size; (d) General: our model is general and practical, which can be applied to various types of epidemics, including computer-virus propagation, as well as human diseases. Extensive experiments on real data demonstrate that FUNNELFIT does indeed discover important properties of epidemics: (P1) disease seasonality, e.g., influenza spikes in January, Lyme disease spikes in July and the absence of yearly periodicity for gonorrhea; (P2) disease reduction effect, e.g., the appearance of vaccines; (P3) local/state-level sensitivity, e.g., many measles cases in NY; (P4) external shock events, e.g., historical flu pandemics; (P5) detect incongruous values, i.e., data reporting errors.

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).

The recent explosion in the adoption of search engines and new media such as blogs and Twitter have facilitated faster propagation of news and rumors. How quickly does a piece of news spread over these media? How does its popularity diminish over time? Does the rising and falling pattern follow a simple universal law?

Given a large stream of users clicking on web sites, how can we find trends, patterns and anomalies? We have developed a novel method, WindMine, and its fine-tuning sibling, WindMine-part, to find patterns and anomalies in such datasets. Our approach has the following advantages: (a) it is effective in discovering meaningful “building blocks” and patterns such as the lunch-break trend and anomalies, (b) it automatically determines suitable window sizes, and (c) it is fast, with its wall clock time linear on the duration of sequences. Moreover, it can be made sub-quadratic on the number of sequences (WindMine-part), with little loss of accuracy. We examine the effectiveness and scalability by performing experiments on 67 GB of real data (one billion clicks for 30 days). Our proposed WindMine does produce concise, informative and interesting patterns. We also show that WindMine-part can be easily implemented in a parallel or distributed setting, and that, even in a single-machine setting, it can be an order of magnitude faster (up to 70 times) than the plain version.

Distribution data naturally arise in countless domains, such as meteorology, biology, geology, industry and economics. However, relatively little attention has been paid to data mining for large distribution sets. Given n distributions of multiple categories and a query distribution Q, we want to find similar clouds (i.e., distributions), to discover patterns, rules and outlier clouds. For example, consider the numerical case of sales of items, where, for each item sold, we record the unit price and quantity; then, each customer is represented as a distribution of 2d points (one for each item he/she bought). We want to find similar users, e.g., for market segmentation, anomaly/fraud detection. We propose to address this problem and present D-search, which includes fast and effective algorithms for similarity search in large distribution datasets. Our main contributions are (1) approximate KL divergence, which can speed up cloud-similarity computations, (2) multi-step sequential scan, which efficiently prunes a significant number of search candidates and leads to a direct reduction in the search cost. We also introduce an extended version of D-search: (3) time-series distribution mining, which finds similar subsequences in time-series distribution datasets. Extensive experiments on real multi-dimensional datasets show that our solution achieves up to 2,300 faster wall-clock time over the naive implementation while it does not sacrifice accuracy.