Diversified Representation Approach for Time Series Using Storm

A Novel Multi-resolution Representation for Streaming Time Series

Because of high dimensionality, proven data mining and pattern recognition methods are not suitable for processing time series data. As a result, several time series representations capable of achieving significant reduction in dimensionality without losing important features have been developed. Each representation has its own advantages and disadvantages. In this paper, based on the requirements of key data mining applications, such as clustering, classification and query by content, characteristics desired in an ideal time series representation are identified. Using the identified characteristics as metrics, widely known time series representation methods are evaluated to determine the extent to which the representations satisfy the requirements.

Discovery of motifs (repeated patterns) in time series is a key factor across numerous industries and scientific fields. These and related problems have effectively been solved for offline analysis of time series; however, these approaches are computationally intensive and do not lend themselves to streaming time series, where the sampling rate imposes real-time constraints on computation and there is strong desire to locate computation as close as possible to the sensor. One promising solution is to use low-cost machine learning models to provide approximate answers to these problems. For example, prior work has trained models to predict the similarity of the most recently sampled window of data points to a representative time series used for training. This work addresses a more challenging problem: to predict not only the "strength" of the match, but also the relative location in the representative time series where the match occurs. We evaluate our approach on two different real world datasets; we demonstrate speedups as high as 40× compared to exact computations, with predictive accuracy as high as 87.9%, depending on the granularity of the prediction.

Massive bike-sharing systems (BSS) usage and performance data have been collected for years over various locations. Nevertheless, researchers encountered several challenges while dealing with massive BSS data. The challenges that could be enhanced in the previous studies are 1) reducing high dimensionality and noise of BSS time series data and 2) extracting informative usage patterns out of massive BSS data. This paper extracts patterns and reduce data dimensions of BSS usage by exploring time series representation and clustering of BSS usage data. A reduced dimension allows us to efficiently approximate the BSS usage with reasonable accuracy, which can be further used for bike usage clustering, classification and prediction. We employ a non-data adaptive representation technique -Discrete Wavelet Transform (DWT) to reduce dimensionality and filter out random errors of the raw time series. Time series are clustered using k-means based on similarities measured by Dynamic Time Warping (DTW) and prototypes computed using DTW barycenter averaging (DBA). The proposed approaches are applied on a 3-month bike usage dataset acquired on the BSS of Chicago. The analysis results show that DWT can effectively reduce dimensionality, filter out random errors and reveal the main characteristics of the raw time series. The clustering approach offers the ability to differentiate and discover bike usage patterns across different stations.

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.

In streaming time series the Clustering problem is more complex, since the dynamic nature of streaming data makes previous clustering methods inappropriate. In this paper, we propose firstly a new method to evaluate Clustering in streaming time series databases. First, we introduce a novel multi-resolution PAA (MPAA) transform to achieve our iterative clustering algorithm. The method is based on the use of a multi-resolution piecewise aggregate approximation representation, which is used to extract features of time series. Then, we propose our iterative clustering approach for streaming time series. We take advantage of the multiresolution property of MPPA and equip a stopping criteria based on Hoeffding bound in order to achieve fast response time. Our streaming time-series clustering algorithm also works by leveraging off the nearest neighbors of the incoming streaming time series datasets and fulfill incremental clustering approach. The comprehensive experiments based on several publicly available real data sets shows that significant performance improvement is achieved and produce high-quality clusters in comparison to the previous methods.KeywordsCluster AlgorithmCandidate ClusterIncremental ClusterIterative ClusterTime Series ClusterThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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.

Multivariate time series data often have a very high dimensionality. Classifying such high dimensional data poses a challenge because a vast number of features can be extracted. Furthermore, the meaning of the normally intuitive term similar needs to be precisely defined. Representing the time series data effectively is an essential task for decision-making activities such as prediction, clustering and classification. In this paper we propose a feature-based classification approach to classify real-world multivariate time series generated by drilling rig sensors in the oil and gas industry. Our approach encompasses two main phases: representation and classification. For the representation phase, we propose a novel representation of time series which combines trend-based and value-based approximations (we abbreviate it as TVA). It produces a compact representation of the time series which consists of symbolic strings that represent the trends and the values of each variable in the series. The TVA representation improves both the accuracy and the running time of the classification process by extracting a set of informative features suitable for common classifiers. For the classification phase, we propose a memory-based classifier which takes into account the antecedent results of the classification process. The inputs of the proposed classifier are the TVA features computed from the current segment, as well as the predicted class of the previous segment. Our experimental results on real-world multivariate time series show that our approach enables highly accurate and fast classification of multivariate time series.

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.

The Internet of things (IoT) technologies plays a key role in the Fourth Industrial Revolution (Industry 4.0). It means the digitisation of the industry and its services to improve the productiveness. To achieve the necessary information throughout the different processes, useful data streams are obtained to provide the Artificial Intelligence and Big data algorithms. However, strategic decision-making based on these algorithms may not be successful if they have been developed based on inadequate low-quality data. This research work proposes a set of metrics to measure Data Quality (DQ) in streaming time series and implements and validates a set of techniques and tools that allow monitoring and improving the quality of the information. These techniques allow the early detection of problems that arise in relation to the quality of the data collected; and, in addition, they provide some mechanisms to solve these problems. Later, also as part of the work, a use case related to industrial field is presented, where these techniques and tools have been deployed into the data management, monitoring and data analysis platform. This integration provides additional functionality to the platform, a Decision Support System (DSS) named <i>DQ-REMAIN</i> (<i>Data Quality REport MAnagement and ImprovemeNt</i>), to decision-making regarding the quality of data obtained from streaming time series.

Similarity search in streaming time series is a crucial subroutine of a number of real-time applications dealing with time-series streams. In finding subsequences of time-series streams that match with patterns under Dynamic Time Warping (DTW), data normalization plays a very important role and should not be ignored. SPRING proposed by Sakurai et al. conducts the similarity search by mitigating the time and space complexity of DTW. Unfortunately, SPRING produces inaccurate results since no data normalization is taken into account before the DTW calculation. In this paper, we improve the SPRING method to deal with similarity search for prespecified patterns in streaming time series under DTW by applying incremental min-max normalization before the DTW calculation. For every pattern, our proposed method uses a monitoring window anchored at the entry of one streaming time series to keep track of min-max coefficients, and then the DTW distance between the normalized subsequence and the normalized pattern is incrementally computed. The experimental results reveal that our proposed method obtains best-so-far values better than those of another state-of-the-art method and the wall-clock time of the proposed method is acceptable.

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 abundance of data and importance of knowledge extraction to foresee the future has made time dependent data analysis an inevitable and challenging task in all areas of science and engineering. High dimensionality and the presence of noise in the non-linear time-series data makes it difficult for the existing clustering algorithms to produce efficient results. Hence, two approaches for time series representation (TSR) techniques by name hybrid dimensionality reduction (HDR) and extended hybrid dimensionality reduction (EHDR) and high low non-overlapping (HLN) clustering algorithm that produces efficient results by controlling noise and reducing the dimensionality optimally are proposed. A comparison of the experimental results on intraday non-linear stock data sets to predict the similarity in their intraday behaviour using K-means clustering algorithm with MINDIST as distance measure using symbolic aggregate approximation (SAX) and HLN using HDR and EHDR has proved that EHDR and HDR TSRs outperforms the other models.

[1] A recent article by Rosenlof and Reid [2008] (hereinafter referred to as RR08) examines the relationship in the tropics between long-term cooling in the stratosphere and warming of the sea surface, with special emphasis in the western Pacific. In the stratosphere, radiosonde observations seem to show that most of the cooling took place since the mid-1990s, apparently coincident to a considerable extent with an increase in the rate of warming of sea surface temperatures (SSTs). A link was proposed by RR08 whereby the increase in SSTs leads to enhanced convection, which is responsible, dynamically, for cooling in the stratosphere. [2] The stratospheric analyses of RR08 rely considerably on tropical radiosonde observations, particularly those from several island stations in the western tropical Pacific. There is extensive evidence that the long-term variation in worldwide radiosonde temperatures is affected critically by inhomogeneities introduced through changes in instruments and measurement practices [e.g., Gaffen, 1994; Gaffen et al., 2000; Lanzante et al . , 2003a, 2003b; Climate Change Science Program (CCSP), 2006], a fact which is acknowledged by RR08. However, they minimize the importance of any such inhomogeneities in the six stations located in the ‘‘warm pool’’ region which they employ [RR08, paragraph 10]: ‘‘However, for our analysis, and in particular for changes noted post-1990, these discontinuities are not sufficient to preclude the use of these stations.’’ The purpose of this comment is to demonstrate that in fact such discontinuities are present, post-1990, and critically affect the evaluation of stratospheric temperatures made by RR08. [3] In their Figures 2, 3, and 5, RR08 display temperature time series for several levels in the lower stratosphere for the four stations located in the heart of the western Pacific warm pool. They note that while most of the earlier part of the records show little long-term trend, a pronounced cooling is seen for about the last 10 years of the record ( 1995–2005). Furthermore, they note an abrupt rise in temperature in early 1999 that lasts for about 2 years. As further evidence to bolster their findings, they note [RR08, paragraph 12] the similarity of the time series from the different stations: ‘‘. . . the overall similarity of the time series in Figure 2 shows that the assumption of homogeneity over the warm pool region is reasonable.’’ Unfortunately, there is considerable evidence to dispute the veracity of these claims. [4] The apparent substantial cooling during the final 10 years of the record can be explained largely by a change in radiosonde instrument type, specifically the transition from Viz to Vaisala, hereafter referred to as the VVT. Abrupt cooling upon introduction of Vaisala radiosondes was noted by Parker et al. [1997] for stations in Australia and New Zealand in the mid to late 1980s, and for U.S. controlled tropical Pacific stations beginning in 1995 [Stendel et al., 2000]. More generally, there has been a systematic worldwide change to Vaisala radiosondes since the 1980s with an expected artificial cooling, especially in the stratosphere [Lanzante et al., 2003a; Christy et al., 2003; CCSP, 2006] (see also Integrated Global Radiosonde Archive (IGRA) station history metadata available at http:// www1.ncdc.noaa.gov/pub/data/igra/igra-metadata.txt). [5] The IGRA metadata indicate that the VVT occurs in November or December 1995 for five of the six stations shown in Figure 1 of RR08 (Lihue, Truk, Koror, Yap, and Pago Pago). The literature cited above suggests that the major part of the drop in stratospheric temperature after 1995 (as seen quite clearly in Figure 5 of RR08) is almost certainly artificial. To further illustrate this point, Figure 1a shows several time series of stratospheric temperatures at Koror. The thick black curve is based on the IGRA data [Durre et al., 2006], which were used by RR08. Note that the IGRA data, although of very high quality (i.e., they have been carefully checked for consistency in time and in the vertical, random errors and outliers, as well as duplicate soundings, etc.), have not been adjusted to account for artificial inhomogeneities. A number of teams have produced adjusted radiosonde temperature time series, each using a different homogenization method. Also shown in Figure 1a are corresponding adjusted time series (HadAT2) [Thorne et al., 2005], RATPAC [Free et al., 2005], IUK [Sherwood et al., 2008], RAOBCORE 1.4 [Haimberger et al., 2008], and RICH [Haimberger et al., 2008] produced by these teams. In comparing the IGRA with the various adjusted time series in Figure 1a it is seen that the adjusted versions all show much less long-term cooling, as indicated by the accompanying trend lines. A closer look at Figure 1a reveals that most of the difference is attributable to the transition across 1995. The adjusted time series shows a JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 114, D12104, doi:10.1029/2008JD010542, 2009 Click Here for Full Article

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