An analysis of time series representation methods

With the burgeoning of IoE (Internet of Everything), massive numbers of IoT devices in entensive fields are continuously producing huge number of time series, named as streaming time series (STS). The high dimensionality and dynamic uncertainty of STS lead to the main challenge on traditional time series data mining research. Accordingly, time series representation methods could not only reduce the original high dimensionality of streaming time series, but also contain the main temporal features of raw time series. More importantly, time series representation has been regarded as an necessary preprocessing tool to provide data support for the smooth progress of follow-up research. In this paper, we propose a novel online time series representation approach called continuous segmentation and diversified representation framework (CSDRF) for streaming time series, which contains two different types of time series representation results. The subsequent experiments have been conducted to demonstrate that CSDRF could not only provide the corresponding results to meet the diverse needs of different users, but also provide the corresponding qualified symbolic representation results for time series clustering.

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.

Recent advances in computing, communications, digital storage technologies, and high-throughput data-acquisition technologies, make it possible to gather and store incredible volumes of data. It creates unprecedented opportunities for large-scale knowledge discovery from huge database. Data mining (DM) technology has emerged as a means of performing this discovery. There are countless researchers working on designing efficient data mining techniques, methods, and algorithms. Many data mining methods and algorithms have been developed and applied in a lot of application fields [1]. Unfortunately, most data mining researchers pay much attention to technique problems for developing data mining models and methods, while little to basic issues of data mining [2]. In this talk, some basic issues of data mining are addressed. What is data mining? What is the product of a data mining process? What are we doing in a data mining process? What is the rule we should obey in a data mining process? Through analyzing existing data mining methods, and domain-driven (or user-driven) data mining models [3-5], we find that we should take a data mining process as a process of knowledge transformation. Based on this understanding of data mining, a conceptual data mining model of domain-oriented data-driven data mining (3DM) is proposed [2]. The relationship between traditional domain-driven (or user-driven) data mining models and our proposed 3DM model is also analyzed. Some domain-oriented data-driven data mining algorithms for mining such knowledge as default rule [6], decision tree [7], and concept lattice [8] from database are proposed. The experiment results for these algorithms are also shown to illustrate the efficiency and performance of the knowledge acquired by our 3DM data mining algorithms.

In the past decade, time series data have been generated from various fields at a rapid speed, which offers a huge opportunity for mining valuable knowledge. As a typical task of time series mining, Time Series Classification (TSC) has attracted lots of attention from both researchers and domain experts due to its broad applications ranging from human activity recognition to smart city governance. Specifically, there is an increasing requirement for performing classification tasks on diverse types of time series data in a timely manner without costly hand-crafting feature engineering. Therefore, in this paper, we propose a framework named Edge4TSC that allows time series to be processed in the edge environment, so that the classification results can be instantly returned to the end-users. Meanwhile, to get rid of the costly hand-crafting feature engineering process, deep learning techniques are applied for automatic feature extraction, which shows competitive or even superior performance compared to state-of-the-art TSC solutions. However, because time series presents complex patterns, even deep learning models are not capable of achieving satisfactory classification accuracy, which motivated us to explore new time series representation methods to help classifiers further improve the classification accuracy. In the proposed framework Edge4TSC, by building the binary distribution tree, a new time series representation method was designed for addressing the classification accuracy concern in TSC tasks. By conducting comprehensive experiments on six challenging time series datasets in the edge environment, the potential of the proposed framework for its generalization ability and classification accuracy improvement is firmly validated with a number of helpful insights.

Repeating patterns as symbols for long time series representation

A large part of the information emitted by contemporary technological devices comes in the form of time series. The massive commercialization of these kinds of devices has made the study of time series feature extraction techniques acquire a vital relevance in last years. Two main things are essential when applying feature extraction techniques to time series: to reduce the dimensionality so it occupies the least amount of storage memory possible, and to make features that contain the relevant information regarding the nature of the data set and the goals to be achieved. For this purpose, we propose in this work a brand new technique called the State Changes Representation for Time Series (SCRTS), which relies on the relevant data associated with the conditional probabilities of the time series (also known in the literature as Markov model’s features), and the distribution of its values. This method is length-independent, which means that we can apply it to time series of different dimensions obtaining the same number of features for each one. Also, it provides a visual representation of the input data, so it is possible to interpret what makes a certain time series different from the other. After explaining how it works, we apply it to 3 different wearable accelerometer data sets. This algorithm reduces the original dimension of the time series considerably (in the best case from 5499 values to 31), having a good performance in the classification results (in the best chance with an accuracy of 98%).

Rare earth elements price forecasting by means of transgenic time series developed with ARIMA models

This article has been retracted from publication in the Taylor & Francis journal, Acta Agriculturae Scandinavica, Section B — Soil & Plant Science. Following publication, concerns were raised by multiple third-parties around the content of the special issue and the decision-making process. Following an investigation by the Taylor & Francis Publishing Ethics & Integrity team in full cooperation with the Editor-in-Chief, it was confirmed that this article included in Special Issue titled “ Envisage Computer Modelling and Statistics for Agriculture”, guest edited by Gunasekaran Manogaran was not peer-reviewed appropriately, in line with the Journal's peer review standards and policy. As the stringency of the peer review process is core to the integrity of the publication process, the Editor and Publisher have decided to retract all of the articles within the above-named Special Issue. The journal has not confirmed if the authors were aware of this compromised peer review process. The journal is committed to correcting the scientific record and will fully cooperate with any institutional investigations into this matter. The authors have been informed of this decision. We have been informed in our decision-making by our policy on publishing ethics and integrity and the COPE guidelines.

This study is concerned with a fundamental issue of time series representation for modeling and prediction with Fuzzy Cognitive Maps. We introduce two distinct time series representation schemes for Fuzzy Cognitive Map design. First method is based on time series amplitude, amplitude change, and change of amplitude change (dynamics perspective). Second scheme is based on three consecutive historical observations: present value, past value and before past value (history perspective). Introduced procedures are experimentally verified and compared on several synthetic and real-world time series of various characteristics. The history-oriented time series representation turned out to be more advantageous. Quality of FCM-based time series models and one-step-ahead predictions were measured in terms of Mean Squared Error. We have shown that models designed with history-oriented time series representation generally require less FCM nodes to be of comparable quality as models built on dynamics-oriented time series representation. As a result, with the history-oriented time series representation scheme we are able to construct simpler and therefore better models.

Time series classification is one of the most active research topics in time series data mining, because it covers a broad range of applications in many different domains. Representation for time series is a technique that converts time series to feature vectors representing the characteristics of time series. The performance of classifying time series depends on this representation. Chaotic time series analyses have been well-studied. Moreover, recurrence plotting underlying chaos theory is one of the most robust representation for time series. In this study, we propose a new time series representation utilising the recurrence plot technique. Moving average convergence divergence (MACD) histogram is the acceleration of time that can represent local-variation in time series. Therefore, a recurrence plot that is made from MACD histogram, which is called a MACD-histogram-based recurrence plot (MHRP), can handle time series very well. Recurrence plots are referred to as grey-scale images and we utilise stacked auto-encoders as a classifier for MHRPs. To evaluate the performance of the proposed classifier, experiments using the UCR time series classification archive was conducted. The experimental results showed that the proposed classifier outperforms other methods.

The article will present the methodology for holistic time series analysis, based on time series transformation model REFII (REFII is an acronym for Raise-Equal-Fall and the model version is II or 2) Patel et al. (Mining motifs in massive time series databases, 2002) [1], Perng and Parker (SQL/LPP: a time series extension of SQL based on limited patience patterns, 1999) [2], Popivanov and Miller (Similarity search over time series data using wavelets, 2002) [3]. The main purpose of REFII model is to automate time series analysis through a unique transformation model of time series. The advantage of this approach to a time series analysis is the linkage of different methods for time series analysis linking traditional data mining tools in time series, and constructing new algorithms for analyzing time series. REFII model is not a closed system, which means that there is a finite set of methods. This is primarily a model used for transformation of values of time series, which prepares data used by different sets of methods based on the same model of transformation in the domain of problem space. REFII model gives a new approach in time series analysis based on a unique model of transformation, which is a base for all kind of time series analyses. In combination with elements of other methods, such as self-organizing maps or frequent-pattern trees, REFII models can make new hybrid methods for efficient time temporal data mining. Similar principle of hybridization could be used as a tool for time series temporal pattern recognition. The article describes real case study illustrating practical application of described methodology.

Time series (TS) data are ubiquitous across various application areas, rendering time series forecasting (TSF) a fundamental task. With the astounding advances in large language models (LLMs), a variety of methods have been developed to adapt LLMs for time series forecasting. Despite unlocking the potential of LLMs in comprehending TS data, existing methods are inherently constrained by their shallow integration of TS information, wherein LLMs typically access TS representations at shallow layers, primarily at the input layer. This causes the influence of TS representations to progressively fade in deeper layers and eventually leads to ineffective adaptation between textual embeddings and TS representations. In this paper, we propose the Multi-layer Steerable Embedding Fusion (MSEF), a novel framework that enables LLMs to directly access time series patterns at all depths, thereby mitigating the progressive loss of TS information in deeper layers. Specifically, MSEF leverages off-the-shelf time series foundation models to extract semantically rich embeddings, which are fused with intermediate text representations across LLM layers via layer-specific steering vectors. These steering vectors are designed to continuously optimize the alignment between time series and textual modalities and facilitate a layer-specific adaptation mechanism that ensures efficient few-shot learning capabilities. Experimental results on seven benchmarks demonstrate significant performance improvements by MSEF compared with baselines, with an average reduction of 31.8% in terms of MSE. The code is available at https://github.com/One1sAll/MSEF.

The high dimension of multivariate time series (MTS) is one of the major factors that impact on the efficiency and effectiveness of data mining. It has two kinds of dimensions, time-based dimensionality, and variable-based dimensionality. They often cause most of the algorithms and techniques applied to the field of MTS data mining to be a failure. In view of the importance of the correlation between any two variables in an MTS, the covariances between any two variables are applied to analyze the extraction of the features for every MTS. In this way, a covariance sequence can be constructed to represent the characteristic of the MTS. Furthermore, an excellent method of dimensionality reduction, principal component analysis (PCA), is used to extract the features of the covariance sequences that derived from an MTS dataset. Thus Euclidean distance is suitable to measure the similarity between the features fast. The experimental results demonstrate that the proposed method not only can handle multivariate time series with different lengths but also is more efficient and effective than the existing methods for the MTS data mining.

Data mining (knowledge discovery in data base) is comparatively new interdisciplinary field developed by joint efforts of mathematicians, statisticians, computer scientists and engineers. There are twelve important ingredients of this field along with their applications in real world problems. In this chapter, we have reviewed application of wavelet methods to data mining, particularly denoising, dimension reduction, similarity search, feature extraction and prediction. Meteorological data of Saudi Arabia and Stock market data of India are considered for illustration.

The previous decade has brought a remarkable increase of the interest in applications that deal with querying and mining of time series data. Many of the research efforts in this context have focused on introducing new representation methods for dimensionality reduction or novel similarity measures for the underlying data. In the vast majority of cases, each individual work introducing a particular method has made specific claims and, aside from the occasional theoretical justifications, provided quantitative experimental observations. However, for the most part, the comparative aspects of these experiments were too narrowly focused on demonstrating the benefits of the proposed methods over some of the previously introduced ones. In order to provide a comprehensive validation, we conducted an extensive experimental study re-implementing eight different time series representations and nine similarity measures and their variants, and testing their effectiveness on 38 time series data sets from a wide variety of application domains. In this article, we give an overview of these different techniques and present our comparative experimental findings regarding their effectiveness. In addition to providing a unified validation of some of the existing achievements, our experiments also indicate that, in some cases, certain claims in the literature may be unduly optimistic.