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The similarity measurement of time series is an important research in time series detection, which is a basic work of time series clustering, anomaly discovery, prediction and many other data mining problems. The purpose of this paper is to design a new similarity measurement algorithm to improve the performance of the original similarity measurement algorithm. The subsequence morphological information is taken into account by the proposed algorithm, and time series is represented by a pattern, so the similarity measurement algorithm is more accurate.

Following some previous researches on similarity measurement, an improved method is presented. This new method combines morphological representation and dynamic time warping (DTW) technique to measure the similarities of time series. After the segmentation of time series data into segments, three parameter values of median, point number and slope are introduced into the improved distance measurement formula. The effectiveness of the morphological weighted DTW algorithm (MW-DTW) is demonstrated by the example of momentum wheel data of an aircraft attitude control system.

The improved method is insensitive to the distortion and expansion of time axis and can be used to detect the morphological changes of time series data. Simulation results confirm that this method proposed in this paper has a high accuracy of similarity measurement.

This improved method has been used to solve the problem of similarity measurement in time series, which is widely emerged in different fields of science and engineering, such as the field of control, measurement, monitoring, process signal processing and economic analysis.

In the similarity measurement of time series, the distance between sequences is often used as the only detection index. The results of similarity measurement should not be affected by the longitudinal or transverse stretching and translation changes of the sequence, so it is necessary to incorporate the morphological changes of the sequence into similarity measurement. The MW-DTW is more suitable for the actual situation. At the same time, the MW-DTW algorithm reduces the computational complexity by transforming the computational object to subsequences.

The comparison between economic growth and the character of monetary policy is one of the most frequently studied issues in policymaking. However, the number of studies incorporating a dynamic time warping approach to analyse the similarity of macroeconomic variables is relatively small.

The study aims at assessing the mutual similarity among various variables representing the financial sector (including the monetary policy by the central bank) and the real sector (e.g. economic growth, industrial production, household consumption expenditure), as well as cross-similarity between both sectors.

The analysis is based on the dynamic time warping (DTW) method, which allows for capturing various dimensions of changes of considered variables. This method is almost non-existent in the literature to compare financial and economic time series. The application of this method constitutes the main area of value added of the research. The analysis includes five variables representing the financial sector and five from the real sector. The study covers four countries: Czechia, Hungary, Poland and Romania and the 2010–2022 period (quarterly data).

The results show that variables representing the financial sector, including those reflecting monetary policy, are weakly correlated with each other, whereas the variables representing the real economy have a solid mutual similarity. As regards individual variables, for example, GDP fluctuations show relatively substantial similarity to ROE fluctuations – especially in Czechia and Hungary. In the case of Hungary and Romania, CAR fluctuations are consistent with GDP fluctuations. In the case of Poland and Hungary, there is a relatively strong similarity between the economy's monetisation and economic growth. Comparing the individual countries, two clusters of countries can be identified. One cluster includes Poland and Czechia, while another covers Hungary and Romania.

The collaborative filtering algorithm is a classical and widely used approach in product recommendation systems. However, the existing algorithms rely mostly on common ratings of items and do not consider temporal information about items or user interests. To solve this problem, this study proposes a new user-item composite filtering (UICF) recommendation framework by leveraging temporal semantics.

The UICF framework fully utilizes the time information of item ratings for measuring the similarity of items and takes into account the short-term and long-term interest decay for computing users’ latest interest degrees. For an item to be probably recommended to a user, the interest degrees of the user on all the historically rated items are weighted by their similarities with the item to be recommended and then added up to predict the recommendation degree.

Comprehensive experiments on the MovieLens and KuaiRec datasets for user movie recommendation were conducted to evaluate the performance of the proposed UICF framework. Experimental results show that the UICF outperformed three well-known recommendation algorithms Item-Based Collaborative Filtering (IBCF), User-Based Collaborative Filtering (UBCF) and User-Popularity Composite Filtering (UPCF) in the root mean square error (RMSE), mean absolute error (MAE) and F1 metrics, especially yielding an average decrease of 11.9% in MAE.

A UICF recommendation framework is proposed that combines a time-aware item similarity model and a time-wise user interest degree model. It overcomes the limitations of common rating items and utilizes temporal information in item ratings and user interests effectively, resulting in more accurate and personalized recommendations.

The purpose of this paper is to propose a new methodology that handles the issue of the dynamic behavior of customers over time.

A new methodology is presented based on time series clustering to extract dominant behavioral patterns of customers over time. This methodology is implemented using bank customers’ transactions data which are in the form of time series data. The data include the recency (R), frequency (F) and monetary (M) attributes of businesses that are using the point-of-sale (POS) data of a bank. This data were obtained from the data analysis department of the bank.

After carrying out an empirical study on the acquired transaction data of 2,531 business customers that are using POS devices of the bank, the dominant trends of behavior are discovered using the proposed methodology. The obtained trends were analyzed from the marketing viewpoint. Based on the analysis of the monetary attribute, customers were divided into four main segments, including high-value growing customers, middle-value growing customers, prone to churn and churners. For each resulted group of customers with a distinctive trend, effective and practical marketing recommendations were devised to improve the bank relationship with that group. The prone-to-churn segment contains most of the customers; therefore, the bank should conduct interesting promotions to retain this segment.

The discovered trends of customer behavior and proposed marketing recommendations can be helpful for banks in devising segment-specific marketing strategies as they illustrate the dynamic behavior of customers over time. The obtained trends are visualized so that they can be easily interpreted and used by banks. This paper contributes to the literature on customer relationship management (CRM) as the proposed methodology can be effectively applied to different businesses to reveal trends in customer behavior.

In the current business condition, customer behavior is changing continually over time and customers are churning due to the reduced switching costs. Therefore, choosing an effective customer segmentation methodology which can consider the dynamic behaviors of customers is essential for every business. This paper proposes a new methodology to capture customer dynamic behavior using time series clustering on time-ordered data. This is an improvement over previous studies, in which static segmentation approaches have often been adopted. To the best of the authors’ knowledge, this is the first study that combines the recency, frequency, and monetary model and time series clustering to reveal trends in customer behavior.

This study aims to construct a sentiment series generation method for danmu comments based on deep learning, and explore the features of sentiment series after clustering.

This study consisted of two main parts: danmu comment sentiment series generation and clustering. In the first part, the authors proposed a sentiment classification model based on BERT fine-tuning to quantify danmu comment sentiment polarity. To smooth the sentiment series, they used methods, such as comprehensive weights. In the second part, the shaped-based distance (SBD)-K-shape method was used to cluster the actual collected data.

The filtered sentiment series or curves of the microfilms on the Bilibili website could be divided into four major categories. There is an apparently stable time interval for the first three types of sentiment curves, while the fourth type of sentiment curve shows a clear trend of fluctuation in general. In addition, it was found that “disputed points” or “highlights” are likely to appear at the beginning and the climax of films, resulting in significant changes in the sentiment curves. The clustering results show a significant difference in user participation, with the second type prevailing over others.

Their sentiment classification model based on BERT fine-tuning outperformed the traditional sentiment lexicon method, which provides a reference for using deep learning as well as transfer learning for danmu comment sentiment analysis. The BERT fine-tuning–SBD-K-shape algorithm can weaken the effect of non-regular noise and temporal phase shift of danmu text.

The purpose of this paper is to overcome the shortcomings of existing multivariate grey incidence models that cannot analyze the similarity of behavior matrixes.

First, the feasibility of using gradient to measure the similarity of continuous functions is analyzed theoretically and intuitively. Then, a grey incidence degree is constructed for multivariable continuous functions. The model employs the gradient to measure the local similarity, as incidence coefficient function, of two functions, and combines local similarity into global similarity, as grey incidence degree by double integral. Third, the gradient incidence degree model for behavior matrix is proposed by discretizing the continuous models. Furthermore, the properties and satisfaction of grey incidence atom of the proposed model are research, respectively. Finally, a financial case is studied to examine the validity of the model.

The proposed model satisfies properties of invariance under mean value transformation, multiple transformation and linear transformation, which proves it is a model constructed from similarity perspective. Meanwhile, the case study shows that proposed model performs effectively.

The method proposed in the paper could be used in financial multivariable time series clustering, personalized recommendation in e-commerce, etc., when the behavior matrixes need to be analyzed from trend similarity perspective.

It will promote the accuracy of multivariate grey incidence model.

Within smart homes, ambient sensors are used to monitor interactions between users and the home environment. The data produced from the sensors are used as the basis for the inference of the users' behaviour information. Partitioning sensor data in response to individual instances of activity is critical for a smart home to be fully functional and to fulfil its roles, such as correctly measuring health status and detecting emergency situations. The purpose of this study is to propose a similarity‐based segmentation approach applied on time series sensor data in an effort to detect and recognise activities within a smart home.

The paper explores methods for analysing time‐related sensor activation events in an effort to undercover hidden activity events through the use of generic sensor modelling of activity based upon the general knowledge of the activities. Two similarity measures are proposed to compare a time series based sensor sequence and a generic sensor model of an activity. In addition, a framework is developed for automatically analysing sensor streams.

The results from evaluation of the proposed methodology on a publicly accessible reference dataset show that the proposed methods can detect and recognise multi‐category activities with satisfying accuracy, in addition to the capability of detecting interleaved activities.

The concepts introduced in this paper will improve automatic detection and recognition of daily living activities from timely ordered sensor events based on domain knowledge of the activities.

The traditional grey relational models directly describe the behavioural characteristics of the systems based on the sample point connections. Few grey relational models can measure the dynamic periodic fluctuation rules of the objects, and most of these models do not have affinities, which results in instabilities of the relational results because of sequence translation. The paper aims to discuss these issues.

Fourier transform functions are used to fit the system behaviour curves, redefine the area difference between the curves and construct a grey relational model based on discrete Fourier transform (DFTGRA).

To verify its validity, feasibility and superiority, DFTGRA is applied to research on the correlation between macroeconomic growth and marine economic growth in China coastal areas. It is proved that DFTGRA has the superior properties of affinity, symmetry, uniqueness, etc., and wide applicability.

DFTGRA can not only be applied to equidistant and equal time sequences but also be adopted for non-equidistant and unequal time sequences. DFTGRA can measure both the global relational degree and the dynamic correlation of the variable cyclical fluctuation between sequences.

The common methods for clustering time series are the use of specific distance criteria or the use of standard clustering algorithms. Ensemble clustering is one of the common techniques used in data mining to increase the accuracy of clustering. In this study, based on segmentation, selecting the best segments, and using ensemble clustering for selected segments, a multistep approach has been developed for the whole clustering of time series data.

First, this approach divides the time series dataset into equal segments. In the next step, using one or more internal clustering criteria, the best segments are selected, and then the selected segments are combined for final clustering. By using a loop and how to select the best segments for the final clustering (using one criterion or several criteria simultaneously), two algorithms have been developed in different settings. A logarithmic relationship limits the number of segments created in the loop.

According to Rand's external criteria and statistical tests, at first, the best setting of the two developed algorithms has been selected. Then this setting has been compared to different algorithms in the literature on clustering accuracy and execution time. The obtained results indicate more accuracy and less execution time for the proposed approach.

This paper proposed a fast and accurate approach for time series clustering in three main steps. This is the first work that uses a combination of segmentation and ensemble clustering. More accuracy and less execution time are the remarkable achievements of this study.

Wiki is a new form of information production and organization, which has become one of the most important knowledge resources. In recent years, with the increase of users in wikis, “free rider problem” has been serious. In order to motivate editors to contribute more to a wiki system, it is important to fully understand their contribution behavior. The purpose of this paper is to explore the law of dynamic contribution behavior of editors in wikis.

After developing a dynamic model of contribution behavior, the authors employed both the metrological and clustering methods to process the time series data. The experimental data were collected from Baidu Baike, a renowned Chinese wiki system similar to Wikipedia.

There are four categories of editors: “testers,” “dropouts,” “delayers” and “stickers.” Testers, who contribute the least content and stop contributing rapidly after editing a few articles. After editing a large amount of content, dropouts stop contributing completely. Delayers are the editors who do not stop contributing during the observation time, but they may stop contributing in the near future. Stickers, who keep contributing and edit the most content, are the core editors. In addition, there are significant time-of-day and holiday effects on the number of editors’ contributions.

By using the method of time series analysis, some new characteristics of editors and editor types were found. Compared with the former studies, this research also had a larger sample. Therefore, the results are more scientific and representative and can help managers to better optimize the wiki systems and formulate incentive strategies for editors.