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.

We consider the problem of object safety: how objects endowed with processing, communication, and sensing capabilities can determine their safety. We assign an agent to each object capable of looking out for its own self interests, while concurrently collaborating with its neighbors and learning/reinforcing its beliefs from them. After considering related work, we propose a general framework consisting of agents with case-bases of threat detection systems and a mechanism for sharing and confirming beliefs with other agents. While our approach is designed to be applicable to object safety domains in general, we particularly consider its application to transport chain security. We further propose a testing framework that uses real sensor data and object safety scenario simulations to evaluate our approach.

Various data mining approaches are currently being used to analyse data within different domains. Among all these approaches, clustering is one of the most-used approaches, which is typically adopted in order to group data based on their similarities. The data in various systems such as finance, healthcare, and business, are stored as time-series. Clustering such complex data can discover patterns which have valuable information. Time-series clustering is not only useful as an exploratory technique but also as a subroutine in more complex data mining algorithms. As a result, time-series clustering (as a part of temporal data mining research) has attracted increasing interest for use in various areas such as medicine, biology, finance, economics, and in the Web. Several studies which focus on time-series clustering have been conducted in said areas. Many of these studies focus on the time complexity of time-series clustering in large datasets and utilize dimensionality reduction approaches and conventional clustering algorithms to address the problem. However, as is the case in many systems, conventional clustering approaches are not practical for time-series data because they are essentially designed for static data and not for time-series data, which leads to poor clustering accuracy. Adequate clustering approaches for time-series are therefore lacking. In this thesis, the problem of the low quality in existing works is taken into account, and a new multi-step clustering model is proposed. This model facilitates the accurate clustering of time-series datasets and is designed specifically for very large time-series datasets. It overcomes the limitations of conventional clustering algorithms in dealing with time-series data. In the first step of the model, data is pre-processed, represented by symbolic aggregate approximation, and grouped approximately by a novel approach. Then, the groups are refined in the second step by using an accurate clustering method, and a representative is defined for each cluster. Finally, the representatives are merged to construct the ultimate clusters. The model is then extended as an interactive model where the results garnered by the user increase in accuracy over time. In this work, the accurate clustering based on shape similarity is performed. It is shown that clustering of time-series does not need to calculate the exact distances/similarity between all time-series in a dataset; instead, by using prototypes of similar time-series, accurate clusters can be obtained. To evaluate its accuracy, the proposed model is tested extensively by using published time-series datasets from diverse domains. This model is more accurate than any existing work and is also scalable (on large datasets) due to the use of multi-resolution of time-series in different levels of clustering. Moreover, it provides a clear understanding of the domains by its ability to generate hierarchical and arbitrary shape clusters of time-series data.

Time series discretization is a technique commonly used to tackle time series classification problems. This manuscript presents an enhanced multi-objective approach for the symbolic discretization of time series called eMODiTS. The method proposed uses a different breakpoints vector, defined per each word segment, to increase the search space of the discretization schemes. eMODiTS’ search mechanism is the well-known evolutionary multi-objective algorithm NSGA-II, which finds a set of possible solutions according to entropy, complexity, and information loss estimations. Final solutions were appraised depending on the misclassification rate computed through the decision tree classifier. The trees obtained also produce graphical and significant information from the regions, relationships, or patterns in each database. Our proposal was compared against ten state-of-the-art time symbolic discretization algorithms. The results suggest that our proposal finds a suitable discretization scheme regarding classification, dimensionality, cardinality reduction, and information loss.

Time series data is ubiquitous in financial, biomedical, and other areas. Anomaly detection in time series has been widely researched in these areas. However, most existing algorithms suffer from “curse of dimension” and may lose some information in the process of feature extraction. In this paper, we propose two new data structures named interval table (ITable) and extend interval table (EITable) for time series representation to capture more original information. We also proposed ADET: a novel A nomaly D etection algorithm based on E I T able, which only needs linear time to detect meaningful anomalies. Extensive experiments on eleven data sets of UCR Repository, MIT-BIH datasets, and the BIDMC database show that ADET has overall good performance in terms of AUC-ROC and outperforms other algorithms in time complexity.

Time series data generation is a standing problem in nearly every field, such as science, business, medicine, industry, or even entertainment. As a result, there is a growing demand for analysing this data efficiently for gauging out useful information. The time series data has intrinsic features like noise, multidimensional, and large volume. When we talk about data mining, it requires a wide spectrum searching for similar patterns, such as query by content, clustering, or classification. These data mining tasks can take great help from a good and robust time series representations. It helps in the reduction of dimensions and noise adaptation and also in achieving key aspect, effectiveness, and efficiency of data processing. This chapter aims to review the basic as well as recent approaches for representations along with dimensionality reduction for time series data.

Time series data generation has exploded in almost every domain such as in business, industry, or medicine. The demand for analyzing efficiently the huge amount of this information necessitates the application of a representation on the purpose of reducing the intrinsically high dimensionality of time series. In this paper we introduce DPAA, a new representation that can be considered as a variation of Piecewise Aggregate Approximation (PAA). DPAA segments a time series into a series of equal length sections and the corresponding mean and standard deviation are recorded for each one of them. The difference with PAA is that DPAA takes into consideration not only the central tendency but also the dispersion present in each section. We evaluate our representation by applying 1-NN classification on 20 widely utilized datasets in the literature. Experimental results indicate that the proposed representation performs better than other commonly applied representations in the majority of the datasets.

This paper presents the most up-to-date methods for the task of designing a system to accurately classify abnormal events, or faults, in a complex tribological mechanism, using elemental analysis of lubrication oil as an indicator of engine condition. The discussion combines perspectives from numerous fault diagnosis applications, both online and offline, to focus upon the task of offline event detection and diagnosis of datasets from elemental analysis, and although this does not suffer from complexity issues as in real-time processing, it introduces a number of other problems such as sparsity and selecting an accurate knowledge representation as well as reasoning under uncertainty and ignorance. The role of confounding variables is significant in sparse datasets, and as such this paper demonstrates an alternative perspective on both eliminating to an extent the effect of confounding variables and inferring unseen variables from measured variables. There has been little review work on this subject, and as a result this paper helps to join disparate research from a number of different domains to achieve some unification of alternative perspectives. This paper concludes by providing a case study to identify the methods that can be utilized in combination.

This paper presents a novel method for financial time series representation. The method can generate accurate and effective representation and segmentation in different resolutions and get better experimental results on real stock data.

This paper introduces a novel method of predicting future concentrations of elements in lubrication oil, for the aim of identifying possible anomalies in continued operation aboard a large marine vessel. The research carried out is supported by a discussion of previous work in the field of fault detection in tribological mechanisms, although with a focus upon two stroke marine diesel engines. The approach taken implements an n-dimensional Markov chain model with a singular weighted connection between layers. The approach leverages the computational simplicity of the Markov chain and combines this with a weighted decision calculated from the correlational coefficients between variables, with the notable assumption that interconnectivity between elements is not constant. The approach is compared to an established method, which is the Kalman filter, with promising results for future work and extension of the method to include expert knowledge in the decision making process.

There is a widespread belief that certain patterns of stock prices over time portend specific future types of movement of those prices. We consider various criteria for identifying these types of patterns, and briefly look at some historical price data. We then look at various specific types of breakout movements, and discuss ways to determine bags of patterns that may tend to precede these breakouts.

The classification accuracy of time series is highly dependent on the quality of used features. In this study, features of new type, called SAX (Symbolic Aggregate approXimation) similarity features, are presented. SAX similarity features are a combination of the traditional statistical number-based and the template-based classification. SAX similarity features are obtained from the data of the time window by first transforming the time series into a discrete presentation using SAX. Then the similarity between this SAX presentation and predefined SAX templates are calculated, and these similarity values are considered as SAX similarity features. The functioning of these features was tested using five different activity data sets collected using wearable inertial sensors and five different classifiers. The results show that the recognition rates calculated using SAX similarity features together with traditional features are much better than those obtained employing traditional features only. In 20 tested cases out of 23, the improvement is statistically significant according to the paired t-test.

The challenges in efficient data representation and similarity measures on massive amounts of time series have enormous impact on many applications. This paper addresses an improvement on Symbolic Aggregate approXimation (SAX), is one of the efficient representations for time series mining. Because SAX represents its symbols by the average (mean) value of a segment with the assumption of Gaussian distribution, it is insufficient to serve the entire deterministic information and causes sometimes incorrect results in time series classification. In this work, SAX representation and distance measure is improved with the addition of another moment of the prior distribution, standard deviation; SAX_SD is proposed. We provide comprehensive analysis for the proposed SAX_SD and confirm both the highest classification accuracy and the highest dimensionality reduction ratio on University of California, Riverside (UCR) datasets in comparison to state of the art methods such as SAX, Extended SAX (ESAX) and SAX Trend Distance (SAX_TD).

The Symbolic Aggregate Approximation (iSAX) is widely used in time series data mining. Its popularity arises from the fact that it largely reduces time series size, it is symbolic, allows lower bounding and is space efficient. However, it requires setting two parameters: the symbolic length and alphabet size, which limits the applicability of the technique. The optimal parameter values are highly application dependent. Typically, they are either set to a fixed value or experimentally probed for the best configuration. In this work we propose an approach to automatically estimate iSAX’s parameters. The approach – AutoiSAX – not only discovers the best parameter setting for each time series in the database, but also finds the alphabet size for each iSAX symbol within the same word. It is based on simple and intuitive ideas from time series complexity and statistics. The technique can be smoothly embedded in existing data mining tasks as an efficient sub-routine. We analyze its impact in visualization interpretability, classification accuracy and motif mining. Our contribution aims to make iSAX a more general approach as it evolves towards a parameter-free method.

Telecommunications fraud, a new type of crime, is showing a rising trend in recent years. However, research from data mining perspectives to detect such frauds is scarce, especially with the behavioral sequences considered. Though the call detail records (CDRs) in telecommunication is generally a snapshot, the history of a caller/callee can be treated as sequences. Indeed, the historical calling sequences can better indicate the fraudulent behaviors. Thus, clustering the time sequences provides a new way to identify fraudulent groups, and therefore the problem of clustering the multidimensional sequences has to be addressed. To that end, in this paper, a combinatorial clustering method for sequential data is presented to identify fraudulent groups and reveal the underlying behavioral patterns. Specifically, the historical CDR data is divided into multiple sequences with the time interval of an hour. Then, several key features are chosen, and K-means in combination with Dynamic Time Warping (DTW) is performed on the time series data with each individual feature. Finally, the individual feature clustering results are ensembled into the final result. Experiments on real world data set demonstrate the effectiveness of the method.

Symbolic Aggregate approximation (SAX) is a classical symbolic approach in many time series data mining applications. However, SAX only reflects the segment mean value feature and misses important information in a segment, namely the trend of the value change in the segment. Such a miss may cause a wrong classification in some cases, since the SAX representation cannot distinguish different time series with similar average values but different trends. In this paper, we present Trend Feature Symbolic Aggregate approximation (TFSAX) to solve this problem. First, we utilize Piecewise Aggregate Approximation (PAA) approach to reduce dimensionality and discretize the mean value of each segment by SAX. Second, extract trend feature in each segment by using trend distance factor and trend shape factor. Then, design multi-resolution symbolic mapping rules to discretize trend information into symbols. We also propose a modified distance measure by integrating the SAX distance with a weighted trend distance. We show that our distance measure has a tighter lower bound to the Euclidean distance than that of the original SAX. The experimental results on diverse time series data sets demonstrate that our proposed representation significantly outperforms the original SAX representation and an improved SAX representation for classification.

Symbolic Aggregate approximation (SAX) is a classical symbolic approach in many time series data mining applications. However, SAX only reflects the segment mean value feature and misses important information in a segment, namely the trend of the value change in the segment. Such a miss may cause a wrong classification in some cases, since the SAX representation cannot distinguish different time series with similar average values but different trends. In this paper, we present Trend Feature Symbolic Aggregate approximation (TFSAX) to solve this problem. First, we utilize Piecewise Aggregate Approximation (PAA) approach to reduce dimensionality and discretize the mean value of each segment by SAX. Second, extract trend feature in each segment by using trend distance factor and trend shape factor. Then, design multi-resolution symbolic mapping rules to discretize trend information into symbols. We also propose a modified distance measure by integrating the SAX distance with a weighted trend distance. We show that our distance measure has a tighter lower bound to the Euclidean distance than that of the original SAX. The experimental results on diverse time series data sets demonstrate that our proposed representation significantly outperforms the original SAX representation and an improved SAX representation for classification.

Symbolic Aggregate Approximation (SAX) is a popular method in many time series data mining applications, but its representation of time series is incomplete because it doesn’t take the trend feature of time series segment into consideration. In this paper, an improved SAX for time series based on trend feature (TRSAX) is proposed to solve this problem. Specifically, we firstly extract trend features of equal-sized time series segments by two sine functions to quantitatively measure different trends. Then, we define our TRSAX distance by integrating a weighted trend distance into the original SAX distance. To show the effectiveness and efficiency, TRSAX is compared with other traditional methods Euclidean distance (ED), dynamic time warping (DTW), SAX and extended SAX (ESAX) on diverse time series data sets. The experimental results show that compared with ED, DTW, SAX, and ESAX, our method TRSAX has a better performance.

Selecting the portfolio of huge stocks is the main issue for investors to reduce a risk investment. This problem could be solved by employing a clustering as a data mining task. The technique groups together the stocks with less distance. A method to measure those dissimilarities is crucial to produce a good clustering quality. This paper is to confirm the improved distance method, dynamic time warping (DTW), stated as powerful compared to the classical way, Euclidean. Then, hierarchical clustering (HC) was used to examine the sequences from two sources of the dataset. It includes 25 stocks indexed by Indonesia Sharia Stock Index (ISSI) and 30 stocks indexed by the Jakarta Islamic Index (JII) during the year 2000-2020. The effectiveness of the distance method in clustering was evaluated by calculating the Silhouette index and running time. According to the value of the average Silhouette index, DTW-based HC gave a higher output which was not significantly different from Euclidean-based HC. In the other hand, the type of dataset contributes significantly. The Silhouette Index for JII dataset (homogeneous) is better than that for ISSI (heterogeneous). Therefore, it prefers to use similarity method with faster processing time to cluster the data if its quality is merely similar to any similarity methods.

SAX Symbolic Aggregate approXimation is one of the main symbolization techniques for time series. A well-known limitation of SAX is that trends are not taken into account in the symbolization. This paper proposes 1d-SAX a method to represent a time series as a sequence of symbols that each contain information about the average and the trend of the series on a segment. We compare the efficiency of SAX and 1d-SAX in terms of goodness-of-fit, retrieval and classification performance for querying a time series database with an asymmetric scheme. The results show that 1d-SAX improves performance using equal quantity of information, especially when the compression rate increases.