Markov model based time series similarity measuring

Similarity measure is a basic task in time series data mining and attracts much attention in the last decade. This paper considers time series similarity measure from an information theoretic perspective. Based on the function of degree of disagreement (FDOD), a new time series similarity measure method is proposed. The empirical result indicates that the method of this paper can solve the unequal time series and has less time complexity. Meanwhile, it also can measure the similarity between multivariate time series.

The similarity measure is a fundamental and key problem for time series analysis, which is widely used in classification, cluster, motif discovery and etc. Time series similarity calculation has been studied a lot and many methods have been proposed, such as Euclidean distance and elastic distance measures. However, all these methods are distance-based which get the similarity by accumulating the distances between optimal match pairs and ignore the intrinsic differences of time series. In order to solve the drawback, we discard this distance-based technique and design a Siamese Convolutional Neural Network(SCNN) to obtain the similarity of time series in this paper. Concretely, we first extract the essential features for similarity calculation by Convolutional Neural Network and then ontain the absolute difference between the essential features of time series. To conveniently train the proposed model, we make full use of the label information of datasets and construct a new binary dataset which each example contains two original time series and a binary label. In the proposed Siamese network, the parameters are shared between two branches and we take binary cross-entropy function to train our model. Experimental results on synthetic and real time series datasets show that our SCNN model is effective and achieves improved accuracy for time series classification task compared to other time series similarity calculation methods.

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.

Time series prediction has been extensively used for decision-making in many areas such as economics, engineering and medicine. And the useful data can be excavated by similarity measure of time series from a mass of historical data for predicting. The collected data from the real world is often uncertain, and the cloud model can be a good solution for the problem of uncertainty. This paper proposes a method based on the similarity degree of cloud model and combines it with back propagation network for prediction. In addition to the sequence itself, the trend of the sequence is used as another index of similarity. The neighbour set of query sequence from the training set is selected by similarity measure. Based on the neighbour set, a back propagation network is trained and used for prediction. Experimental results from the six time series show that the proposed method obtains better prediction accuracies than the comparative methods, which reveal its effectiveness.

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.

Compared with one single image, satellite image time series (SITS) can capture the dynamic changes in land cover types, thus achieving a more comprehensive and accurate land cover classification map. Due to decades of data acquisition and new high temporal resolution sensors, SITS is becoming more available. Corresponding SITS analysis techniques need to be further developed. Most satellite images are multispectral, namely, multivariate. However, multivariate time series analysis techniques are less mature compared with univariate time series. There seems to be a lack of a robust and accurate similarity measure between multivariate time series for SITS clustering. In this paper, we propose a novel method to transform multivariate SITS into univariate SITS while the useful information is kept as much as possible. And then advanced univariate time series similarity measures can be adopted to achieve SITS clustering. The proposed method is tested on Landsat-TM SITS dataset and shows a better clustering result than ordinary multivariate time series similarity measure. In addition, the overall computing time may be reduced due to dimension reduction.

Distance and similarity measures have recently been investigated in-depth within the context of hesitant fuzzy sets. By analyzing the existing studies concerning distance measures for hesitant fuzzy sets, we find that they have some limitations. To address the flaws, this study develops some novel distance measures for hesitant fuzzy sets, including the normalized Euclidean distance measure, the Hausdorff metric distance measure, the normalized generalized distance measure, and their corresponding weighted distance measures. The proposals of this study not only hold many ideal characteristics but also do not consider the lengths of hesitant fuzzy elements as well as the arrangement of their possible values. To deal with the situations where both of the universe of discourse and the weight of element are continuous, some continuous hesitant fuzzy distance measures are also investigated. Based on the relationship between distance measure and similarity measure, some novel similarity measures for hesitant fuzzy sets can be further deduced from the proposed distance measures. Finally, two numerical examples are given to demonstrate the applicability and validity of the proposed hesitant fuzzy distance measures.

Repeating patterns as symbols for long time series representation

With the availability of large geospatial datasets, the study of collective human mobility spatiotemporal patterns provides a new way to explore urban spatial environments from the perspective of residents. In this paper, we constructed a classification model for mobility patterns that is suitable for taxi OD (Origin-Destination) point data, and it is comprised of three parts. First, a new aggregate unit, which uses a road intersection as the constraint condition, is designed for the analysis of the taxi OD point data. Second, the time series similarity measurement is improved by adding a normalization procedure and time windows to address the particular characteristics of the taxi time series data. Finally, the DBSCAN algorithm is used to classify the time series into different mobility patterns based on a proximity index that is calculated using the improved similarity measurement. In addition, we used the random forest algorithm to establish a correlation model between the mobility patterns and the regional functional characteristics. Based on the taxi OD point data from Nanjing, we delimited seven mobility patterns and illustrated that the regional functions have obvious driving effects on these mobility patterns. These findings are applicable to urban planning, traffic management and planning, and land use analyses in the future.

Aiming at the defect of visibility graph, this paper first proposes the definition of fuzzy visibility graph, then gives a new similarity measure of time series induced from the similarity of fuzzy visibility graphs. Based on the proposed definition and similarity measure, a novel time series forecasting method is established. To demonstrate the performance of the proposed method, experiments are carried out on Alabama enrollment, stock price index and Shanghai Pudong Development Bank’s closing price. The results show that the proposed method improves the accuracy of prediction.

Distance and similarity measures are fundamentally important in a variety of scientific fields such as clustering analysis, pattern recognition and decision making, etc. In this paper, by analyzing the existing distance and similarity measures between hesitant fuzzy sets, we show that they are not reasonable in some situations. To this end, we propose a novel concept of hesitancy index of hesitant fuzzy set to measure the hesitancy degree among the possible values in each hesitant fuzzy element of the hesitant fuzzy set. By taking their hesitancy indices into account, new methods for measuring the distances between hesitant fuzzy sets are proposed and their properties are discussed. According to the relationship between the distance measure and the similarity measure, two novel similarity measures for hesitant fuzzy sets are further developed. Afterwards, we propound a novel hesitant fuzzy clustering algorithm on the basis of the novel similarity measures for classifying objects with hesitant fuzzy sets. At length, a real-life example is given to illustrate the detailed implementation process of the proposed clustering approach, and a comparative study on the same example is conducted.

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.

An effective similarity measure approach on specific data sets is becoming the focus in time series data mining. To solve the problem that financial time series are lacking dynamic information of trend after they are deal with dimension reduction with SAX, in this work we propose a novel similarity measure function, Composite-Distance-Function which joins point-distance advantages and trend-distance advantages together. Through the experiments of SAX with different distance function, we prove that Composite-Distance-Function is a useful function which provides new ideas to reveal the interdependence between the financial data and helps to solve the problem of time series similarity.

Dynamic Time Warping (DTW) is a well-known similarity measure for time series. The standard dynamic programming approach to compute the DTW distance of two length-n time series, however, requires O(n^2) time, which is often too slow for real-world applications. Therefore, many heuristics have been proposed to speed up the DTW computation. These are often based on lower bounding techniques, approximating the DTW distance, or considering special input data such as binary or piecewise constant time series. In this paper, we present a first exact algorithm to compute the DTW distance of two run-length encoded time series whose running time only depends on the encoding lengths of the inputs. The worst-case running time is cubic in the encoding length. In experiments we show that our algorithm is indeed fast for time series with short encoding lengths.

The novel Time Series Data Mining (TSDM) framework is applied to analyzing financial time series. The TSDM framework adapts and innovates data mining concepts to analyzing time series data. In particular, it creates a set of methods that reveal hidden temporal patterns that are characteristic and predictive of time series events. This contrasts with other time series analysis techniques, which typically characterize and predict all observations. The TSDM framework and concepts are reviewed, and the applicable TSDM method is discussed. Finally, the TSDM method is applied to time series generated by a basket of financial securities. The results show that statistically significant temporal patterns that are both characteristic and predictive of events in financial time series can be identified.