Abstract Multivariate time series classification is a crucial task in data mining, attracting growing research interest due to its broad applications. While many existing methods focus on discovering discriminative patterns in time series, real-world data does not always present such patterns, and sometimes raw numerical values can also serve as discriminative features. Additionally, the recent success of Transformer models has inspired many studies. However, when applying to time series classification, the self-attention mechanisms in Transformer models could introduce classification-irrelevant features, thereby compromising accuracy. To address these challenges, we propose a novel method, VSFormer, that incorporates both discriminative patterns (shape) and numerical information (value). In addition, we extract class-specific prior information derived from supervised information to enrich the positional encoding and provide classification-oriented self-attention learning, thereby enhancing its effectiveness. Extensive experiments on all 30 UEA archived datasets demonstrate the superior performance of our method compared to SOTA models. Through ablation studies, we demonstrate the effectiveness of the improved encoding layer and the proposed self-attention mechanism. Finally, We provide a case study on a real-world time series dataset without discriminative patterns to interpret our model.

Abstract Neural networks are widely used in machine learning and data mining. Typically, these networks need to be trained, implying the adjustment of weights (parameters) within the network based on the input data. In this work, we propose a novel approach, RandomNet, that employs untrained deep neural networks to cluster time series. RandomNet uses different sets of random weights to extract diverse representations of time series and then ensembles the clustering relationships derived from these different representations to build the final clustering results. By extracting diverse representations, our model can effectively handle time series with different characteristics. Since all parameters are randomly generated, no training is required during the process. We provide a theoretical analysis of the effectiveness of the method. To validate its performance, we conduct extensive experiments on all of the 128 datasets in the well-known UCR time series archive and perform statistical analysis of the results. These datasets have different sizes, sequence lengths, and they are from diverse fields. The experimental results show that the proposed method is competitive compared with existing state-of-the-art methods.

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.

Time series anomaly detection is an important task, with applications in a broad variety of domains. Many approaches have been proposed in recent years, but often they require that the length of the anomalies be known in advance and provided as an input parameter. This limits the practicality of the algorithms, as such information is often unknown in advance, or anomalies with different lengths might co-exist in the data. To address this limitation, previously, a linear time anomaly detection algorithm based on grammar induction has been proposed. While the algorithm can find variable-length patterns, it still requires preselecting values for at least two parameters at the discretization step. How to choose these parameter values properly is still an open problem. In this paper, we introduce a grammar-induction-based anomaly detection method utilizing ensemble learning. Instead of using a particular choice of parameter values for anomaly detection, the method generates the final result based on a set of results obtained using different parameter values. We demonstrate that the proposed ensemble approach can outperform existing grammar-induction-based approaches with different criteria for selection of parameter values. We also show that the proposed approach can achieve performance similar to that of the state-of-the-art distance-based anomaly detection algorithm.

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.

Detecting repeating patterns of different lengths in time series, also called variable-length motifs, has received a great amount of attention by researchers and practitioners. Despite the significant progress that has been made in recent single dimensional variable-length motif discovery work, detecting variable-length sub dimensional motifs -patterns that are simultaneously occurring only in a subset of dimensions in multivariate time series-remains a difficult task. The main challenge is scalability. On the one hand, the brute-force enumeration solution, which searches for motifs of all possible lengths, is very time consuming even in single dimensional time series. On the other hand, previous work show that index-based fixed-length approximate motif discovery algorithms such as random projection are not suitable for detecting variable-length motifs due to memory requirement. In this paper, we introduce an approximate variable-length subdimensional motif discovery algorithm called Collaborative HIerarchy based Motif Enumeration (CHIME) to efficiently detect variable-length subdimensional motifs given a minimum motif length in large-scale multivariate time series. We show that the memory cost of the approach is significantly smaller than that of random projection. Moreover, the speed of the proposed algorithm is significantly faster than that of the state-of-the-art algorithms. We demonstrate that CHIME can efficiently detect meaningful variable-length subdimensional motifs in large real world multivariate time series datasets.

A controlled experiment is an empirical interventional study method to evaluate the causal impact of an intervention, by identifying the dynamic feature dependency patterns in the contrast multivariate time series (CMTS) collected from the control and experimental groups. Manually labeling or interpreting the effects caused by the intervention from the CMTS data has become an infeasible task even for domain experts. Thus, it is imperative to develop an integrated technique, preferably in an unsupervised manner, that can simultaneously identify and characterize feature dynamic dependencies and their contrast patterns in CMTS, which we call the contrast dynamic feature dependency (CDFD) patterns. In this paper, we propose a generative model with partial correlation-based feature dependency regularization to help analysts understand the CMTS data by jointly 1) characterizing a set of comparable multivariate Gaussian distributions from CMTS, and 2) determining whether the intervention causes the changes between two comparable distributions. Extensive experiments demonstrate the effectiveness and scalability of the proposed method. The proposed method applied to a driving behavior application demonstrates its utility and interpretability.

The discovery of motifs (repeated patterns) is an important task in time series data mining. The task can be formulated as finding the most similar non-overlapping pair of subsequences in a given time series. Existing exact motif discovery methods have quadratic time complexities in the length of the time series. In this work, we present an algorithm that can find the exact motif of a given time series in a linear expected time complexity. The algorithm is further modified to find all pairs of subsequences whose distances are below a given threshold value. In practice, if true motifs exist in the data or the threshold is set to a small value, the algorithms are very fast. The proof of correctness and time complexity are detailed and experiments are conducted to verify the analysis. We applied the proposed method to analyze the real-world bird sound and electrical consumption data to demonstrate its effectiveness.

Collaborative filtering techniques remain a staple in recommender systems research and applications. With the plethora of research done in recommender systems, some more recent works applied deep learning with great success. We stack a deep neural network recommender onto a shallow one for item recommendations in this work. Our experiments with popular datasets indicate that the proposed technique outperforms other state-of-the art techniques and baselines in key performance metrics.

peer reviewed

The mining of time series data has attracted much attention in the past two decades due to the ubiquity of time series in our daily lives. In particular, classification is perhaps one of the most well-studied topics for time series data. Many state-of-the-art classification techniques work by identifying and extracting patterns or characteristics from the training data, and then applying these patterns or characteristics to classify unlabeled time series. This paper presents a novel finding that sequences of values that are very different from the patterns in the labeled time series can be used as references to classify time series effectively. We propose an evolution process to generate these sequences of values, which we call separating references, from the training data. The proposed method is robust to over-fitting and is especially suitable for the situation where little labeled data is available. We demonstrate that the proposed approach is highly competitive on the well-known UCR time series classification benchmarks.

The problems of recurrent and anomalous pattern discovery in time series, e.g., motifs and discords, respectively, have received a lot of attention from researchers in the past decade. However, since the pattern search space is usually intractable, most existing detection algorithms require that the patterns have discriminative characteristics and have its length known in advance and provided as input, which is an unreasonable requirement for many real-world problems. In addition, patterns of similar structure, but of different lengths may co-exist in a time series. Addressing these issues, we have developed algorithms for variable-length time series pattern discovery that are based on symbolic discretization and grammar inference—two techniques whose combination enables the structured reduction of the search space and discovery of the candidate patterns in linear time. In this work, we present GrammarViz 3.0—a software package that provides implementations of proposed algorithms and graphical user interface for interactive variable-length time series pattern discovery. The current version of the software provides an alternative grammar inference algorithm that improves the time series motif discovery workflow, and introduces an experimental procedure for automated discretization parameter selection that builds upon the minimum cardinality maximum cover principle and aids the time series recurrent and anomalous pattern discovery.

Most trajectory data are collected with a constant sample rate (e.g. GPS data). However, the variance of velocities can be very large, which causes the non-uniformity of the sample points in trajectory dataset. That is, the trajectory dataset can be very sparse in some parts which cause most existing distance measures to get unexpected results. On the other hand, the dataset can be extremely dense in some other parts which results in unnecessarily high computational complexity. Due to the above phenomenon, choosing an appropriate sample rate becomes a difficult challenge. In order to address the dilemma, we propose a Step-Invariant Trajectory (SIT) representation that can provide a dynamic sample rate to represent any trajectories in a uniform way. The translation takes only linear time. We also propose an effective and scalable distance measure for SIT representation. We evaluate the effectiveness and efficiency of our representation along with its distance measure by performing multiple trajectory classification and clustering experiments. These results show that our distance measures on SIT representation is much more accurate and robust than other representations and distance measures on sparse trajectory datasets. Our approach can also achieve competitive accuracy compared with the state of the art model-based trajectory representations on dense datasets. However, the time required to translate the data to our representation is 2 orders of magnitude faster, on average, than translate to other model-based representations. Furthermore, our representation can also serve as a preprocessing step to provide high quality input to all trajectory learning methods.

Detecting repeated variable-length patterns, also called variable-length motifs, has received a great amount of attention in recent years. Current state-of-the-art algorithm utilizes fixed-length motif discovery algorithm as a subroutine to enumerate variable-length motifs. As a result, it may take hours or days to execute when enumeration range is large. In this work, we introduce an approximate algorithm called HierarchIcal based Motif Enumeration (HIME) to detect variable-length motifs with a large enumeration range in million-scale time series. We show in the experiments that the scalability of the proposed algorithm is significantly better than that of the state-of-the-art algorithm. Moreover, the motif length range detected by HIME is considerably larger than previous sequence-matching based approximate variable-length motif discovery approach. We demonstrate that HIME can efficiently detect meaningful variable-length motifs in long, real world time series.

In recent years, finding repetitive similar patterns in time series has become a popular problem. These patterns are called time series motifs. Recent studies show that using grammar compression algorithms to find repeating patterns from the symbolized time series holds promise in discovering approximate motifs with variable length. However, grammar compression algorithms are traditionally designed for string compression. Therefore, existing work on grammar induction has not fully utilized much available information that can be used to enhance the performance of the algorithms. In this work, an iterative framework based on grammar induction is proposed. In each iteration, a revision operator called Noise Reduction Operator is applied to revise the symbolized time series string based on the rules returned from a base grammar induction algorithm. In our experiments, we show that the proposed work can find motifs of the same quality, with much faster running time compared to the state-of-the-art variable-length exact motif discovery algorithm in real world time series data.

Time series classification has attracted much attention due to the ubiquity of time series. With the advance of technologies, the volume of available time series data becomes huge and the content is changing rapidly. This requires time series data mining methods to have low computational complexities. In this paper, we propose a parameter-free time series classification method that has a linear time complexity. The approach is evaluated on all the 85 datasets in the well-known UCR time series classification archive. The results show that the new method achieves better overall classification accuracy performance than the widely used benchmark, i.e. 1-nearest neighbor with dynamic time warping, while consuming orders of magnitude less running time. The proposed method is also applied on a large real-world bird sounds dataset to verify its effectiveness.

The recommendation challenge can be posed as the problem of predicting either item ratings or item rankings. The latter approach has proven more effective. Pairwise learning-to-rank techniques have been relatively successful. Hence, they are popularly used for learning recommender model parameters such as those in collaborative filtering (CF) models. The model parameters are learned by optimizing close smooth approximations of the non-smooth information retrieval (IR) metrics such as Mean Area Under ROC curve (AUC).

The problem of anomaly detection in time series has received a lot of attention in the past two decades. However, existing techniques cannot locate where the anomalies are within anomalous time series, or they require users to provide the length of potential anomalies. To address these limitations, we propose a self-learning online anomaly detection algorithm that automatically identifies anomalous time series, as well as the exact locations where the anomalies occur in the detected time series. We evaluate our approach on several real datasets, including two CPU manufacturing data from Intel. We demonstrate that our approach can successfully detect the correct anomalies without requiring any prior knowledge about the data.

Time series classication is an important problem that has received a great amount of attention by researchers and practitioners in the past two decades. In this work, we propose a novel algorithm for time series classication based on the discovery of class-specic representative patterns. We dene representative patterns of a class as a set of subsequences that has the greatest discriminative power to distinguish one class of time series from another. Our approach rests upon two techniques with linear complexity: symbolic discretization of time series, which generalizes the structural patterns, and grammatical inference, which automatically nds recurrent correlated patterns of variable length, producing an initial pool of common patterns shared by many instances in a class. From this pool of candidate patterns, our algorithm selects the most representative patterns that capture the class specicities, and that can be used to eectively discriminate between time series classes. Through an exhaustive experimental evaluation we show that our algorithm is competitive in accuracy and speed with the stateof-the-art classication techniques on the UCR time series repository, robust on shifted data, and demonstrates excellent performance on real-world noisy medical time series.

Spatial trajectory analysis is crucial to uncovering insights into the motives and nature of human behavior. In this work, we study the problem of discovering motifs in trajectories based on symbolically transformed representations and context free grammars. We propose a fast and robust grammar induction algorithm called mSEQUITUR to infer a grammar rule set from a trajectory for motif generation. Second, we designed the Symbolic Trajectory Analysis and VIsualization System (STAVIS), the first of its kind trajectory analytical system that applies grammar inference to derive trajectory signatures and enable mining tasks on the signatures. Third, an empirical evaluation is performed to demonstrate the efficiency and effectiveness of mSEQUITUR for generating trajectory signatures and discovering motifs.

The problem of time series motif discovery has received a lot of attention from researchers in the past decade. Most existing work on finding time series motifs require that the length of the motifs be known in advance. However, such information is not always available. In addition, motifs of different lengths may co-exist in a time series dataset. In this work, we develop a motif visualization system based on grammar induction. We demonstrate that grammar induction in time series can effectively identify repeated patterns without prior knowledge of their lengths. The motifs discovered by the visualization system are variable-lengths in two ways. Not only can the inter-motif subsequences have variable lengths, the intra-motif subsequences also are not restricted to have identical length—a unique property that is desirable, but has not been seen in the literature.

Reverse nearest neighbor queries are useful in identifying objects that are of significant influence or importance. Existing methods either rely on pre-computation of nearest neighbor distances, do not scale well with high dimensionality, or do not produce exact solutions. In this work we motivate and investigate the problem of reverse nearest neighbor search on high dimensional, multimedia data. We propose exact and approximate algorithms that do not require pre-computation of nearest neighbor distances, and can potentially prune off most of the search space. We demonstrate the utility of reverse nearest neighbor search by showing how it can help improve the classification accuracy.

In this work, we introduce the new problem of finding time series discords. Time series discords are subsequences of a longer time series that are maximally different to all the rest of the time series subsequences. They thus capture the sense of the most unusual subsequence within a time series. Time series discords have many uses for data mining, including improving the quality of clustering, data cleaning, summarization, and anomaly detection. Discords are particularly attractive as anomaly detectors because they only require one intuitive parameter (the length of the subsequence) unlike most anomaly detection algorithms that typically require many parameters. We evaluate our work with a comprehensive set of experiments. In particular, we demonstrate the utility of discords with objective experiments on domains as diverse as Space Shuttle telemetry monitoring, medicine, surveillance, and industry, and we demonstrate the effectiveness of our discord discovery algorithm with more than one million experiments, on 82 different datasets from diverse domains.

Moments before the launch of every space vehicle, engineering discipline specialists must make a critical go/no-go decision. The cost of a false positive, allowing a launch in spite of a fault, or a false negative, stopping a potentially successful launch, can be measured in the tens of millions of dollars, not including the cost in morale and other more intangible detriments. The Aerospace Corporation is responsible for providing engineering assessments critical to the go/no-go decision for every Department of Defense space vehicle. These assessments are made by constantly monitoring streaming telemetry data in the hours before launch. We will introduce VizTree, a novel time-series visualization tool to aid the Aerospace analysts who must make these engineering assessments. VizTree was developed at the University of California, Riverside and is unique in that the same tool is used for mining archival data and monitoring incoming live telemetry. The use of a single tool for both aspects of the task allows a natural and intuitive transfer of mined knowledge to the monitoring task. Our visualization approach works by transforming the time series into a symbolic representation, and encoding the data in a modified suffix tree in which the frequency and other properties of patterns are mapped onto colors and other visual properties. We demonstrate the utility of our system by comparing it with state-of-the-art batch algorithms on several real and synthetic datasets.

Time series data is perhaps the most frequently encountered type of data examined by the data mining community. Clustering is perhaps the most frequently used data mining algorithm, being useful in it's own right as an exploratory technique, and also as a subroutine in more complex data mining algorithms such as rule discovery, indexing, summarization, anomaly detection, and classification. Given these two facts, it is hardly surprising that time series clustering has attracted much attention. The data to be clustered can be in one of two formats: many individual time series, or a single time series, from which individual time series are extracted with a sliding window. Given the recent explosion of interest in streaming data and online algorithms, the latter case has received much attention. We make an amazing claim. Clustering of streaming time series is completely meaningless. More concretely, clusters extracted from streaming time series are forced to obey a certain constraint that is pathologically unlikely to be satisfied by any dataset, and because of this, the clusters extracted by any clustering algorithm are essentially random. While this constraint can be intuitively demonstrated with a simple illustration and is simple to prove, it has never appeared in the literature. We can justify calling our claim surprising, since it invalidates the contribution of dozens of previously published papers. We will justify our claim with a theorem, illustrative examples, and a comprehensive set of experiments on reimplementations of previous work.

The problem of efficiently locating previously known patterns in a time series database (i.e., query by content) has received much attention and may now largely be regarded as a solved problem. However, from a knowledge discovery viewpoint, a more interesting problem is the enumeration of previously unknown, frequently occurring patterns. We call such patterns "motifs", because of their close analogy to their discrete counterparts in computation biology. An efficient motif discovery algorithm for time series would be useful as a tool for summarizing and visualizing massive time series databases. In addition it could be used as a subroutine in various other data mining tasks, including the discovery of association rules, clustering and classification. In this paper we carefully motivate, then introduce, a nontrivial definition of time series motifs. We propose an efficient algorithm to discover them, and we demonstrate the utility and efficiency of our approach on several real world datasets.