Multi-task learning of time series and its application to the travel demand2017-12-21 ${\displaystyle \cong }$ |

We address the problem of modeling and prediction of a set of temporal events in the context of intelligent transportation systems. To leverage the information shared by different events, we propose a multi-task learning framework. We develop a support vector regression model for joint learning of mutually dependent time series. It is the regularization-based multi-task learning previously developed for the classification case and extended to time series. We discuss the relatedness of observed time series and first deploy the dynamic time warping distance measure to identify groups of similar series. Then we take into account both time and scale warping and propose to align multiple time series by inferring their common latent representation. We test the proposed models on the problem of travel demand prediction in Nancy (France) public transport system and analyze the benefits of multi-task learning. |

Highly comparative feature-based time-series classification2014-05-08 ${\displaystyle \cong }$ |

A highly comparative, feature-based approach to time series classification is introduced that uses an extensive database of algorithms to extract thousands of interpretable features from time series. These features are derived from across the scientific time-series analysis literature, and include summaries of time series in terms of their correlation structure, distribution, entropy, stationarity, scaling properties, and fits to a range of time-series models. After computing thousands of features for each time series in a training set, those that are most informative of the class structure are selected using greedy forward feature selection with a linear classifier. The resulting feature-based classifiers automatically learn the differences between classes using a reduced number of time-series properties, and circumvent the need to calculate distances between time series. Representing time series in this way results in orders of magnitude of dimensionality reduction, allowing the method to perform well on very large datasets containing long time series or time series of different lengths. For many of the datasets studied, classification performance exceeded that of conventional instance-based classifiers, including one nearest neighbor classifiers using Euclidean distances and dynamic time warping and, most importantly, the features selected provide an understanding of the properties of the dataset, insight that can guide further scientific investigation. |

catch22: CAnonical Time-series CHaracteristics2019-01-30 ${\displaystyle \cong }$ |

Capturing the dynamical properties of time series concisely as interpretable feature vectors can enable efficient clustering and classification for time-series applications across science and industry. Selecting an appropriate feature-based representation of time series for a given application can be achieved through systematic comparison across a comprehensive time-series feature library, such as those in the hctsa toolbox. However, this approach is computationally expensive and involves evaluating many similar features, limiting the widespread adoption of feature-based representations of time series for real-world applications. In this work, we introduce a method to infer small sets of time-series features that (i) exhibit strong classification performance across a given collection of time-series problems, and (ii) are minimally redundant. Applying our method to a set of 93 time-series classification datasets (containing over 147000 time series) and using a filtered version of the hctsa feature library (4791 features), we introduce a generically useful set of 22 CAnonical Time-series CHaracteristics, catch22. This dimensionality reduction, from 4791 to 22, is associated with an approximately 1000-fold reduction in computation time and near linear scaling with time-series length, despite an average reduction in classification accuracy of just 7%. catch22 captures a diverse and interpretable signature of time series in terms of their properties, including linear and non-linear autocorrelation, successive differences, value distributions and outliers, and fluctuation scaling properties. We provide an efficient implementation of catch22, accessible from many programming environments, that facilitates feature-based time-series analysis for scientific, industrial, financial and medical applications using a common language of interpretable time-series properties. |

Deep Transformer Models for Time Series Forecasting: The Influenza Prevalence Case2020-01-22 ${\displaystyle \cong }$ |

In this paper, we present a new approach to time series forecasting. Time series data are prevalent in many scientific and engineering disciplines. Time series forecasting is a crucial task in modeling time series data, and is an important area of machine learning. In this work we developed a novel method that employs Transformer-based machine learning models to forecast time series data. This approach works by leveraging self-attention mechanisms to learn complex patterns and dynamics from time series data. Moreover, it is a generic framework and can be applied to univariate and multivariate time series data, as well as time series embeddings. Using influenza-like illness (ILI) forecasting as a case study, we show that the forecasting results produced by our approach are favorably comparable to the state-of-the-art. |

Applying Nature-Inspired Optimization Algorithms for Selecting Important Timestamps to Reduce Time Series Dimensionality2018-12-09 ${\displaystyle \cong }$ |

Time series data account for a major part of data supply available today. Time series mining handles several tasks such as classification, clustering, query-by-content, prediction, and others. Performing data mining tasks on raw time series is inefficient as these data are high-dimensional by nature. Instead, time series are first pre-processed using several techniques before different data mining tasks can be performed on them. In general, there are two main approaches to reduce time series dimensionality, the first is what we call landmark methods. These methods are based on finding characteristic features in the target time series. The second is based on data transformations. These methods transform the time series from the original space into a reduced space, where they can be managed more efficiently. The method we present in this paper applies a third approach, as it projects a time series onto a lower-dimensional space by selecting important points in the time series. The novelty of our method is that these points are not chosen according to a geometric criterion, which is subjective in most cases, but through an optimization process. The other important characteristic of our method is that these important points are selected on a dataset-level and not on a single time series-level. The direct advantage of this strategy is that the distance defined on the low-dimensional space lower bounds the original distance applied to raw data. This enables us to apply the popular GEMINI algorithm. The promising results of our experiments on a wide variety of time series datasets, using different optimizers, and applied to the two major data mining tasks, validate our new method. |

Complexity Measures and Features for Times Series classification2020-03-04 ${\displaystyle \cong }$ |

Classification of time series is a growing problem in different disciplines due to the progressive digitalization of the world. Currently, the state of the art in time series classification is dominated by Collective of Transformation-Based Ensembles. This algorithm is composed of several classifiers of diverse nature that are combined according to their results in an internal cross validation procedure. Its high complexity prevents it from being applied to large datasets. One Nearest Neighbours with Dynamic Time Warping remains the base classifier in any time series classification problem, for its simplicity and good results. Despite their good performance, they share a weakness, which is that they are not interpretable. In the field of time series classification, there is a tradeoff between accuracy and interpretability. In this work, we propose a set of characteristics capable of extracting information of the structure of the time series in order to face time series classification problems. The use of these characteristics allows the use of traditional classification algorithms in time series problems. The experimental results demonstrate a statistically significant improvement in the accuracy of the results obtained by our proposal with respect to the original time series. Apart from the improvement in accuracy, our proposal is able to offer interpretable results based on the set of characteristics proposed. |

Improving the Accuracy of Global Forecasting Models using Time Series Data Augmentation2020-08-06 ${\displaystyle \cong }$ |

Forecasting models that are trained across sets of many time series, known as Global Forecasting Models (GFM), have shown recently promising results in forecasting competitions and real-world applications, outperforming many state-of-the-art univariate forecasting techniques. In most cases, GFMs are implemented using deep neural networks, and in particular Recurrent Neural Networks (RNN), which require a sufficient amount of time series to estimate their numerous model parameters. However, many time series databases have only a limited number of time series. In this study, we propose a novel, data augmentation based forecasting framework that is capable of improving the baseline accuracy of the GFM models in less data-abundant settings. We use three time series augmentation techniques: GRATIS, moving block bootstrap (MBB), and dynamic time warping barycentric averaging (DBA) to synthetically generate a collection of time series. The knowledge acquired from these augmented time series is then transferred to the original dataset using two different approaches: the pooled approach and the transfer learning approach. When building GFMs, in the pooled approach, we train a model on the augmented time series alongside the original time series dataset, whereas in the transfer learning approach, we adapt a pre-trained model to the new dataset. In our evaluation on competition and real-world time series datasets, our proposed variants can significantly improve the baseline accuracy of GFM models and outperform state-of-the-art univariate forecasting methods. |

Multi-Faceted Representation Learning with Hybrid Architecture for Time Series Classification2020-12-21 ${\displaystyle \cong }$ |

Time series classification problems exist in many fields and have been explored for a couple of decades. However, they still remain challenging, and their solutions need to be further improved for real-world applications in terms of both accuracy and efficiency. In this paper, we propose a hybrid neural architecture, called Self-Attentive Recurrent Convolutional Networks (SARCoN), to learn multi-faceted representations for univariate time series. SARCoN is the synthesis of long short-term memory networks with self-attentive mechanisms and Fully Convolutional Networks, which work in parallel to learn the representations of univariate time series from different perspectives. The component modules of the proposed architecture are trained jointly in an end-to-end manner and they classify the input time series in a cooperative way. Due to its domain-agnostic nature, SARCoN is able to generalize a diversity of domain tasks. Our experimental results show that, compared to the state-of-the-art approaches for time series classification, the proposed architecture can achieve remarkable improvements for a set of univariate time series benchmarks from the UCR repository. Moreover, the self-attention and the global average pooling in the proposed architecture enable visible interpretability by facilitating the identification of the contribution regions of the original time series. An overall analysis confirms that multi-faceted representations of time series aid in capturing deep temporal corrections within complex time series, which is essential for the improvement of time series classification performance. Our work provides a novel angle that deepens the understanding of time series classification, qualifying our proposed model as an ideal choice for real-world applications. |

Integrated Time Series Summarization and Prediction Algorithm and its Application to COVID-19 Data Mining2020-05-01 ${\displaystyle \cong }$ |

This paper proposes a simple method to extract from a set of multiple related time series a compressed representation for each time series based on statistics for the entire set of all time series. This is achieved by a hierarchical algorithm that first generates an alphabet of shapelets based on the segmentation of centroids for clustered data, before labels of these shapelets are assigned to the segmentation of each single time series via nearest neighbor search using unconstrained dynamic time warping as distance measure to deal with non-uniform time series lenghts. Thereby, a sequence of labels is assigned for each time series. Completion of the last label sequence permits prediction of individual time series. Proposed method is evaluated on two global COVID-19 datasets, first, for the number of daily net cases (daily new infections minus daily recoveries), and, second, for the number of daily deaths attributed to COVID-19 as of April 27, 2020. The first dataset involves 249 time series for different countries, each of length 96. The second dataset involves 264 time series, each of length 96. Based on detected anomalies in available data a decentralized exit strategy from lockdowns is advocated. |

Automatic time-series phenotyping using massive feature extraction2016-12-15 ${\displaystyle \cong }$ |

Across a far-reaching diversity of scientific and industrial applications, a general key problem involves relating the structure of time-series data to a meaningful outcome, such as detecting anomalous events from sensor recordings, or diagnosing patients from physiological time-series measurements like heart rate or brain activity. Currently, researchers must devote considerable effort manually devising, or searching for, properties of their time series that are suitable for the particular analysis problem at hand. Addressing this non-systematic and time-consuming procedure, here we introduce a new tool, hctsa, that selects interpretable and useful properties of time series automatically, by comparing implementations over 7700 time-series features drawn from diverse scientific literatures. Using two exemplar biological applications, we show how hctsa allows researchers to leverage decades of time-series research to quantify and understand informative structure in their time-series data. |

Multivariate Time-series Anomaly Detection via Graph Attention Network2020-09-04 ${\displaystyle \cong }$ |

Anomaly detection on multivariate time-series is of great importance in both data mining research and industrial applications. Recent approaches have achieved significant progress in this topic, but there is remaining limitations. One major limitation is that they do not capture the relationships between different time-series explicitly, resulting in inevitable false alarms. In this paper, we propose a novel self-supervised framework for multivariate time-series anomaly detection to address this issue. Our framework considers each univariate time-series as an individual feature and includes two graph attention layers in parallel to learn the complex dependencies of multivariate time-series in both temporal and feature dimensions. In addition, our approach jointly optimizes a forecasting-based model and are construction-based model, obtaining better time-series representations through a combination of single-timestamp prediction and reconstruction of the entire time-series. We demonstrate the efficacy of our model through extensive experiments. The proposed method outperforms other state-of-the-art models on three real-world datasets. Further analysis shows that our method has good interpretability and is useful for anomaly diagnosis. |

Temporal Attribute Prediction via Joint Modeling of Multi-Relational Structure Evolution2020-07-13 ${\displaystyle \cong }$ |

Time series prediction is an important problem in machine learning. Previous methods for time series prediction did not involve additional information. With a lot of dynamic knowledge graphs available, we can use this additional information to predict the time series better. Recently, there has been a focus on the application of deep representation learning on dynamic graphs. These methods predict the structure of the graph by reasoning over the interactions in the graph at previous time steps. In this paper, we propose a new framework to incorporate the information from dynamic knowledge graphs for time series prediction. We show that if the information contained in the graph and the time series data are closely related, then this inter-dependence can be used to predict the time series with improved accuracy. Our framework, DArtNet, learns a static embedding for every node in the graph as well as a dynamic embedding which is dependent on the dynamic attribute value (time-series). Then it captures the information from the neighborhood by taking a relation specific mean and encodes the history information using RNN. We jointly train the model link prediction and attribute prediction. We evaluate our method on five specially curated datasets for this problem and show a consistent improvement in time series prediction results. We release the data and code of model DArtNet for future research at https://github.com/INK-USC/DArtNet . |

GRATIS: GeneRAting TIme Series with diverse and controllable characteristics2020-01-07 ${\displaystyle \cong }$ |

The explosion of time series data in recent years has brought a flourish of new time series analysis methods, for forecasting, clustering, classification and other tasks. The evaluation of these new methods requires either collecting or simulating a diverse set of time series benchmarking data to enable reliable comparisons against alternative approaches. We propose GeneRAting TIme Series with diverse and controllable characteristics, named GRATIS, with the use of mixture autoregressive (MAR) models. We simulate sets of time series using MAR models and investigate the diversity and coverage of the generated time series in a time series feature space. By tuning the parameters of the MAR models, GRATIS is also able to efficiently generate new time series with controllable features. In general, as a costless surrogate to the traditional data collection approach, GRATIS can be used as an evaluation tool for tasks such as time series forecasting and classification. We illustrate the usefulness of our time series generation process through a time series forecasting application. |

Time Series Clustering via Community Detection in Networks2015-08-19 ${\displaystyle \cong }$ |

In this paper, we propose a technique for time series clustering using community detection in complex networks. Firstly, we present a method to transform a set of time series into a network using different distance functions, where each time series is represented by a vertex and the most similar ones are connected. Then, we apply community detection algorithms to identify groups of strongly connected vertices (called a community) and, consequently, identify time series clusters. Still in this paper, we make a comprehensive analysis on the influence of various combinations of time series distance functions, network generation methods and community detection techniques on clustering results. Experimental study shows that the proposed network-based approach achieves better results than various classic or up-to-date clustering techniques under consideration. Statistical tests confirm that the proposed method outperforms some classic clustering algorithms, such as $k$-medoids, diana, median-linkage and centroid-linkage in various data sets. Interestingly, the proposed method can effectively detect shape patterns presented in time series due to the topological structure of the underlying network constructed in the clustering process. At the same time, other techniques fail to identify such patterns. Moreover, the proposed method is robust enough to group time series presenting similar pattern but with time shifts and/or amplitude variations. In summary, the main point of the proposed method is the transformation of time series from time-space domain to topological domain. Therefore, we hope that our approach contributes not only for time series clustering, but also for general time series analysis tasks. |

Trainable Time Warping: Aligning Time-Series in the Continuous-Time Domain2019-03-21 ${\displaystyle \cong }$ |

DTW calculates the similarity or alignment between two signals, subject to temporal warping. However, its computational complexity grows exponentially with the number of time-series. Although there have been algorithms developed that are linear in the number of time-series, they are generally quadratic in time-series length. The exception is generalized time warping (GTW), which has linear computational cost. Yet, it can only identify simple time warping functions. There is a need for a new fast, high-quality multisequence alignment algorithm. We introduce trainable time warping (TTW), whose complexity is linear in both the number and the length of time-series. TTW performs alignment in the continuous-time domain using a sinc convolutional kernel and a gradient-based optimization technique. We compare TTW and GTW on 85 UCR datasets in time-series averaging and classification. TTW outperforms GTW on 67.1% of the datasets for the averaging tasks, and 61.2% of the datasets for the classification tasks. |

Prediction of hierarchical time series using structured regularization and its application to artificial neural networks2020-07-29 ${\displaystyle \cong }$ |

This paper discusses the prediction of hierarchical time series, where each upper-level time series is calculated by summing appropriate lower-level time series. Forecasts for such hierarchical time series should be coherent, meaning that the forecast for an upper-level time series equals the sum of forecasts for corresponding lower-level time series. Previous methods for making coherent forecasts consist of two phases: first computing base (incoherent) forecasts and then reconciling those forecasts based on their inherent hierarchical structure. With the aim of improving time series predictions, we propose a structured regularization method for completing both phases simultaneously. The proposed method is based on a prediction model for bottom-level time series and uses a structured regularization term to incorporate upper-level forecasts into the prediction model. We also develop a backpropagation algorithm specialized for application of our method to artificial neural networks for time series prediction. Experimental results using synthetic and real-world datasets demonstrate the superiority of our method in terms of prediction accuracy and computational efficiency. |

Free congruence: an exploration of expanded similarity measures for time series data2021-01-17 ${\displaystyle \cong }$ |

Time series similarity measures are highly relevant in a wide range of emerging applications including training machine learning models, classification, and predictive modeling. Standard similarity measures for time series most often involve point-to-point distance measures including Euclidean distance and Dynamic Time Warping. Such similarity measures fundamentally require the fluctuation of values in the time series being compared to follow a corresponding order or cadence for similarity to be established. This paper is spurred by the exploration of a broader definition of similarity, namely one that takes into account the sheer numerical resemblance between sets of statistical properties for time series segments irrespectively of value labeling. Further, the presence of common pattern components between time series segments was examined even if they occur in a permuted order, which would not necessarily satisfy the criteria of more conventional point-to-point distance measures. Results were compared with those of Dynamic Time Warping on the same data for context. Surprisingly, the test for the numerical resemblance between sets of statistical properties established a stronger resemblance for pairings of decline years with greater statistical significance than Dynamic Time Warping on the particular data and sample size used. |

Extreme-SAX: Extreme Points Based Symbolic Representation for Time Series Classification2020-10-01 ${\displaystyle \cong }$ |

Time series classification is an important problem in data mining with several applications in different domains. Because time series data are usually high dimensional, dimensionality reduction techniques have been proposed as an efficient approach to lower their dimensionality. One of the most popular dimensionality reduction techniques of time series data is the Symbolic Aggregate Approximation (SAX), which is inspired by algorithms from text mining and bioinformatics. SAX is simple and efficient because it uses precomputed distances. The disadvantage of SAX is its inability to accurately represent important points in the time series. In this paper we present Extreme-SAX (E-SAX), which uses only the extreme points of each segment to represent the time series. E-SAX has exactly the same simplicity and efficiency of the original SAX, yet it gives better results in time series classification than the original SAX, as we show in extensive experiments on a variety of time series datasets. |

Graph Deep Factors for Forecasting2020-10-14 ${\displaystyle \cong }$ |

Deep probabilistic forecasting techniques have recently been proposed for modeling large collections of time-series. However, these techniques explicitly assume either complete independence (local model) or complete dependence (global model) between time-series in the collection. This corresponds to the two extreme cases where every time-series is disconnected from every other time-series in the collection or likewise, that every time-series is related to every other time-series resulting in a completely connected graph. In this work, we propose a deep hybrid probabilistic graph-based forecasting framework called Graph Deep Factors (GraphDF) that goes beyond these two extremes by allowing nodes and their time-series to be connected to others in an arbitrary fashion. GraphDF is a hybrid forecasting framework that consists of a relational global and relational local model. In particular, we propose a relational global model that learns complex non-linear time-series patterns globally using the structure of the graph to improve both forecasting accuracy and computational efficiency. Similarly, instead of modeling every time-series independently, we learn a relational local model that not only considers its individual time-series but also the time-series of nodes that are connected in the graph. The experiments demonstrate the effectiveness of the proposed deep hybrid graph-based forecasting model compared to the state-of-the-art methods in terms of its forecasting accuracy, runtime, and scalability. Our case study reveals that GraphDF can successfully generate cloud usage forecasts and opportunistically schedule workloads to increase cloud cluster utilization by 47.5% on average. |

Meta-Learning for Koopman Spectral Analysis with Short Time-series2021-02-09 ${\displaystyle \cong }$ |

Koopman spectral analysis has attracted attention for nonlinear dynamical systems since we can analyze nonlinear dynamics with a linear regime by embedding data into a Koopman space by a nonlinear function. For the analysis, we need to find appropriate embedding functions. Although several neural network-based methods have been proposed for learning embedding functions, existing methods require long time-series for training neural networks. This limitation prohibits performing Koopman spectral analysis in applications where only short time-series are available. In this paper, we propose a meta-learning method for estimating embedding functions from unseen short time-series by exploiting knowledge learned from related but different time-series. With the proposed method, a representation of a given short time-series is obtained by a bidirectional LSTM for extracting its properties. The embedding function of the short time-series is modeled by a neural network that depends on the time-series representation. By sharing the LSTM and neural networks across multiple time-series, we can learn common knowledge from different time-series while modeling time-series-specific embedding functions with the time-series representation. Our model is trained such that the expected test prediction error is minimized with the episodic training framework. We experimentally demonstrate that the proposed method achieves better performance in terms of eigenvalue estimation and future prediction than existing methods. |