Symbolic Representation Of Time Series Research Articles

Multi-label classification with imbalanced classes by fuzzy deep neural networks

Multi-label classification is an advantageous technique for managing uncertainty in classification problems where each data instance is associated with several labels simultaneously. Such situations are frequent in real-world scenarios, where decisions rely on imprecise or noisy data and adaptable classification methods are preferred. However, the problem of class imbalance represents a common characteristic of several multi-label datasets, in which the distribution of samples and their corresponding labels is non-uniform across the data space. In this paper, we propose a multi-label classification approach utilizing fuzzy logic in order to deal with the class imbalance problem. To eliminate the need for an expert to determine the logical rules of inference, deep neural networks are adopted, which have proven to be exceptionally effective for such problems. By combining both fuzzy inference systems and deep neural networks, the strengths and weaknesses of each approach can be mitigated. As a further development, a symbolic representation of time series is put in place to reduce data dimensionality and speed up the training procedure. This allows for more flexibility in model application, in particular with respect to time constraints arising from the causality of observed time series. Tests carried out on a multi-label classification dataset related to the current and voltage profiles of several household appliances show that the proposed model outperforms four baseline models for time series classification.

SCALE-BOSS-MR: Scalable Time Series Classification Using Multiple Symbolic Representations

Time-Series-Classification (TSC) is an important machine learning task for many branches of science. Symbolic representations of time series, especially Symbolic Fourier Approximation (SFA), have been proven very effective for this task, given their abilities to reduce noise. In this paper, we improve upon SCALE-BOSS using multiple symbolic representations of time series. More specifically, the proposed SCALE-BOSS-MR incorporates into the process a variety of window sizes combined with multiple dilation parameters applied to the original and to first-order differences’ time series, with the latter modeling trend information. SCALE-BOSS-MR has been evaluated using the eight datasets with the largest training size of the UCR time series repository. The results indicate that SCALE-BOSS-MR can be instantiated to classifiers that are able to achieve state-of-the-art accuracy and can be tuned for scalability.

Association Rules Discovery of Deviant Events in Multivariate Time Series: An Analysis and Implementation of the SAX-ARM Algorithm

In this work, we propose an open-source Python implementation of the SAX-ARM algorithm introduced by Park and Jung (2019). This algorithm mines association rules efficiently among the deviant events of multivariate time series. To do so, the algorithm combines two existing methods, namely the Symbolic Aggregate approXimation (SAX) from Lin et al. (2003) - a symbolic representation of time series - and the Apriori algorithm from Agrawal et al. (1996) - a data mining method which outputs all frequent itemsets and association rules from a transactional dataset. A detailed description of the underlying principles is given along with their numerical implementation. The choice of relevant parameters is thoroughly discussed and evaluated using a public dataset on the topic of temperature and energy consumption.

МЕТОДИКА ПРЕВЕНТИВНОЙ ИДЕНТИФИКАЦИИ СОСТОЯНИЯ ОБЪЕКТОВ МОНИТОРИНГА НА ОСНОВЕ СИМВОЛЬНОГО ПРЕДСТАВЛЕНИЯ ВРЕМЕННЫХ РЯДОВ ИХ МЕТРИК

Introduction: based on the analysis of methods for estimating time series of observed parameters of devices of public information and telecommunications networks, to develop a method for preventive identification of the state of monitoring objects using a symbolic representation of time series of their metrics. Purpose: of the study is to determine the generalized universal characteristics of the time series, according to which it is possible to evaluate the variety of observed values of metrics related to a certain area of the state of the monitoring object (the class of its technical condition). Results: preventive identification of the abnormal state of the network element is carried out by identifying "forbidden" code syllables on the code word describing the observed time series of the metric. This approach to time series processing is borrowed from symbolic dynamics, which is used in bioinformatics when analyzing complex nucleotide genomic sequences. As a generalized universal characteristic of the time series, the entropy of code words is used, describing the time series encoded by the method of symbolic representation of the data of the observed metrics. An algorithm of the method of preventive identification of an abnormal situation on a time series of its parameters is developed, consisting of four stages: at the first stage, the time series is symbolically encoded according to possible parameter values; at the second, the entropy of the code word describing the time series of the observed metric is estimated; at the third, the classifier of the states of the measurement object is trained based on the entropy of shifts; at the fourth stage, the state is classified according to a test sample of measurements, in which the measured characteristic is described by its law of probability distribution of shifts. Practical relevance: when an abnormal functional state of a network element is detected, a transition to a special monitoring mode is carried out, when the frequency of polling by the monitoring server of the network element is significantly increased in order to timely take preventive control actions on the network infrastructure and prevent failure (the occurrence of an accident). Discussion: the methodology will allow to form the order of operation of the monitoring server in the future to identify the functional state of the network element and the public information and telecommunications network as a whole.

ABBA: adaptive Brownian bridge-based symbolic aggregation of time series

A new symbolic representation of time series, called ABBA, is introduced. It is based on an adaptive polygonal chain approximation of the time series into a sequence of tuples, followed by a mean-based clustering to obtain the symbolic representation. We show that the reconstruction error of this representation can be modelled as a random walk with pinned start and end points, a so-called Brownian bridge. This insight allows us to make ABBA essentially parameter-free, except for the approximation tolerance which must be chosen. Extensive comparisons with the SAX and 1d-SAX representations are included in the form of performance profiles, showing that ABBA is often able to better preserve the essential shape information of time series compared to other approaches, in particular when time warping measures are used. Advantages and applications of ABBA are discussed, including its in-built differencing property and use for anomaly detection, and Python implementations provided.

An adaptive method for threshold of recurrence quantification analysis based on SAX

Abstract Recurrence plot (RP) is a visual tool to study complex time series. Its construction involves the threshold selection. Recurrence quantification analysis (RQA) aims at describing the complexity and structural characteristics of RP. Different thresholds produce different quantitative analysis results. In this paper, an adaptive threshold selection technique based on cumulative histogram method (CHM) is proposed. In order to overcome the large computational complexity of CHM, we introduce a symbolic representation of time series: symbolic aggregate approximation (SAX). Through experiments on simulated data and comparing the results of the original threshold selection, our modified method shows a certain application prospect. Some interesting results are found when we apply it to the financial stock markets.

Abridged Symbolic Representation of Time Series for Clustering

In recent years a couple of methods aimed at time series symbolic representation have been introduced or developed. This activity is mainly justified by practical considerations such memory savings or fast data base searching. However, some results suggest that in the subject of time series clustering symbolic representation can even upgrade the results of clustering. The article contains a proposal of a new algorithm directed at the task of time series abridged symbolic representation with the emphasis on efficient time series clustering. The idea of the proposal is based on the PAA (piecewise aggregate approximation) technique followed by segmentwise correlation analysis. The primary goal of the article is to upgrade the quality of the PAA technique with respect to possible time series clustering (its speed and quality). We also tried to answer the following questions. Is the task of time series clustering in their original form reasonable? How much memory can we save using the new algorithm? The efficiency of the new algorithm was investigated on empirical time series data sets. The results prove that the new proposal is quite effective with a very limited amount of parametric user interference needed.

Interpretable time series classification using linear models and multi-resolution multi-domain symbolic representations

The time series classification literature has expanded rapidly over the last decade, with many new classification approaches published each year. Prior research has mostly focused on improving the accuracy and efficiency of classifiers, with interpretability being somewhat neglected. This aspect of classifiers has become critical for many application domains and the introduction of the EU GDPR legislation in 2018 is likely to further emphasize the importance of interpretable learning algorithms. Currently, state-of-the-art classification accuracy is achieved with very complex models based on large ensembles (COTE) or deep neural networks (FCN). These approaches are not efficient with regard to either time or space, are difficult to interpret and cannot be applied to variable-length time series, requiring pre-processing of the original series to a set fixed-length. In this paper we propose new time series classification algorithms to address these gaps. Our approach is based on symbolic representations of time series, efficient sequence mining algorithms and linear classification models. Our linear models are as accurate as deep learning models but are more efficient regarding running time and memory, can work with variable-length time series and can be interpreted by highlighting the discriminative symbolic features on the original time series. We advance the state-of-the-art in time series classification by proposing new algorithms built using the following three key ideas: (1) Multiple resolutions of symbolic representations: we combine symbolic representations obtained using different parameters, rather than one fixed representation (e.g., multiple SAX representations); (2) Multiple domain representations: we combine symbolic representations in time (e.g., SAX) and frequency (e.g., SFA) domains, to be more robust across problem types; (3) Efficient navigation in a huge symbolic-words space: we extend a symbolic sequence classifier (SEQL) to work with multiple symbolic representations and use its greedy feature selection strategy to effectively filter the best features for each representation. We show that our multi-resolution multi-domain linear classifier (mtSS-SEQL+LR) achieves a similar accuracy to the state-of-the-art COTE ensemble, and to recent deep learning methods (FCN, ResNet), but uses a fraction of the time and memory required by either COTE or deep models. To further analyse the interpretability of our classifier, we present a case study on a human motion dataset collected by the authors. We discuss the accuracy, efficiency and interpretability of our proposed algorithms and release all the results, source code and data to encourage reproducibility.

Discovery of Corrosion Patterns using Symbolic Time Series Representation and N-gram Model

There are many factors that can contribute to corrosion in the pipeline. Therefore, it is important for decision makers to analyze and identify the main factor of corrosion in order to take appropriate actions. The factor of corrosion can be analyzed using data mining based on historical datasets collected from monitoring sensors. The purpose of this study is to analyze the trends of corroding agents for pipeline corrosion based on symbolic representation of time series corrosion dataset using Symbolic Aggregation Approximation (SAX). The paper presents the analysis and evaluation of the patterns using N-gram model. Text mining using N-gram model is proposed to mine trend changes from corrosion time series dataset that are transformed as symbolic representation. N-gram was applied for the analysis in order to find significant symbolic patterns that are represented as text. Pattern analysis is performed and the results are discussed according to each environmental factor of pipeline corrosion.

Repeating patterns as symbols for long time series representation

A symbolic time series representation using repeating shapes as symbols is proposed.Lower bounding similarity measure properties evaluated on URC datasets.Electricity consumption dataset used to evaluate on very long, seasonal time series.Reconstruction error and dimensionality reduction ability comparable to PAA. Over the past years, many representations for time series were proposed with the main purpose of dimensionality reduction and as a support for various algorithms in the domain of time series data processing. However, most of the transformation algorithms are not directly applicable on streams of data but only on static collections of the data as they are iterative in their nature. In this work we propose a symbolic representation of time series along with a method for transformation of time series data into the proposed representation. As one of the basic requirements for applicable representation is the distance measure which would accurately reflect the true shape of the data, we propose a distance measure operating on the proposed representation and lower bounding the Euclidean distance on the original data. We evaluate properties of the proposed representation and the distance measure on the UCR collection of datasets. As we focus on stream data processing, we evaluate the properties and limitations of the proposed representation on very long time series from the domain of electricity consumption monitoring, simulating the processing of potentially unbound data stream.

Symbolic representation based on trend features for knowledge discovery in long time series

The symbolic representation of time series has attracted much research interest recently. The high dimensionality typical of the data is challenging, especially as the time series becomes longer. The wide distribution of sensors collecting more and more data exacerbates the problem. Representing a time series effectively is an essential task for decision-making activities such as classification, prediction, and knowledge discovery. In this paper, we propose a new symbolic representation method for long time series based on trend features, called trend feature symbolic approximation (TFSA). The method uses a two-step mechanism to segment long time series rapidly. Unlike some previous symbolic methods, it focuses on retaining most of the trend features and patterns of the original series. A time series is represented by trend symbols, which are also suitable for use in knowledge discovery, such as association rules mining. TFSA provides the lower bounding guarantee. Experimental results show that, compared with some previous methods, it not only has better segmentation efficiency and classification accuracy, but also is applicable for use in knowledge discovery from time series.

Adaptive Piecewise Approximation Based on Weighted Average Approach for Symbolic Time Series Representation

The process of time series representation has become a significant research problem. It is a challenging task to effectively manage and analyze large volumes of data with high dimensionality. Many high-level representations of time series have been proposed for mining tasks. The selection of effective and scalable method for the appropriate representation of data is another challenge. Piecewise Aggregate Approximation (PAA) method is applied in an effective similarity search of time series to minimize dimensionality by the mean values of equal-sized frames. PAA focus on mean value takes into consideration exclusively the central tendency and not the dispersion present in each segment, which may contribute to some important patterns being missed in some time series data sets and may not yield good tightness of the lower bound. We propose a method based on PAA called Time-weighted Average for Symbolic Aggregate Approximation (TWA_SAX) and compare its performance with the current methods. TWA_SAX enables raw data to be specifically compared to the minimized representation and ensures reduced limits to Euclidean distance. TWA_SAX is utilized to generate faster, more precise algorithms for similarity searches and improves the preciseness of the representation of time series data through enabling better tightness of the lower limit.

A Novel Symbolic Representation Based on Fast Segmentation

Symbolic representation of time series has recently attracted a lot of research interest. This is a difficult problem because of the high dimensionality of the data, particularly when the length of the time series becomes longer. In this paper, we introduce a new symbolic representation based on fast segmentation, called the trend feature symbols approximation (TFSA). The experimental results show that compared to some method, the segmentation efficiency of TFSA is improved.

Information directionality in coupled time series using transcripts

In ordinal symbolic dynamics, transcripts describe the algebraic relationship between ordinal patterns. Using the concept of transcript, we exploit the mathematical structure of the group of permutations to derive properties and relations among information measures of the symbolic representations of time series. These theoretical results are then applied for the assessment of coupling directionality in dynamical systems, where suitable coupling directionality measures are introduced depending only on transcripts. These measures improve the reliability of the information flow estimates and reduce to well-established coupling directionality quantifiers when some general conditions are satisfied. Furthermore, by generalizing the definition of transcript to ordinal patterns of different lengths, several of the commonly used information directionality measures can be encompassed within the same framework.

Granulation-based symbolic representation of time series and semi-supervised classification

We present a semi-supervised time series classification method based on co-training which uses the hidden Markov model (HMM) and one nearest neighbor (1-NN) as two learners. For modeling time series effectively, the symbolization of time series is required and a new granulation-based symbolic representation method is proposed in this paper. First, a granule for each segment of time series is constructed, and then the segments are clustered by spectral clustering applied to the formed similarity matrix. Using four time series datasets from UCR Time Series Data Mining Archive, the experimental results show that proposed symbolic representation works successfully for HMM. Compared with the supervised method, the semi-supervised method can construct accurate classifiers with very little labeled data available.

Experiencing SAX: a novel symbolic representation of time series

Many high level representations of time series have been proposed for data mining, including Fourier transforms, wavelets, eigenwaves, piecewise polynomial models, etc. Many researchers have also considered symbolic representations of time series, noting that such representations would potentiality allow researchers to avail of the wealth of data structures and algorithms from the text processing and bioinformatics communities. While many symbolic representations of time series have been introduced over the past decades, they all suffer from two fatal flaws. First, the dimensionality of the symbolic representation is the same as the original data, and virtually all data mining algorithms scale poorly with dimensionality. Second, although distance measures can be defined on the symbolic approaches, these distance measures have little correlation with distance measures defined on the original time series. In this work we formulate a new symbolic representation of time series. Our representation is unique in that it allows dimensionality/numerosity reduction, and it also allows distance measures to be defined on the symbolic approach that lower bound corresponding distance measures defined on the original series. As we shall demonstrate, this latter feature is particularly exciting because it allows one to run certain data mining algorithms on the efficiently manipulated symbolic representation, while producing identical results to the algorithms that operate on the original data. In particular, we will demonstrate the utility of our representation on various data mining tasks of clustering, classification, query by content, anomaly detection, motif discovery, and visualization.