The Normalized Mutual Information (NMI) metric is widely utilized in the evaluation of clustering and community detection algorithms. This study explores the performance of NMI, specifically examining its performance in relation to the quantity of communities, and uncovers a significant drawback associated with the metric's behavior as the number of communities increases. Our findings reveal a pronounced bias in the NMI as the number of communities escalates. While previous studies have noted this biased behavior, they have not provided a formal proof and have not addressed the causation of this problem, leaving a gap in the existing literature. In this study, we fill this gap by employing a mathematical approach to formally demonstrate why NMI exhibits biased behavior, thereby establishing its unsuitability as a metric for evaluating clustering and community detection algorithms. Crucially, our study exposes the vulnerability of entropy-based metrics that employ logarithmic functions to similar bias.

Echo chambers, a recent phenomenon in the realm of social networks, have garnered significant attention from researchers due to their profound implications. Their role in propagating information, reinforcing beliefs and opinions, and potentially fostering inequality within networks and societies underscores the critical need for comprehensive understanding. Despite the lack of a clear definition, existing research has primarily concentrated on five aspects of echo chambers: their attributes, underlying mechanisms, modeling, detection, and mitigation strategies. The main objectives of this systematic review are to identify terminology, examine the effects of echo chambers, analyze approaches to echo chamber mechanisms, assess modeling and detection techniques, and evaluate metrics used to specify echo chambers in online social networks. By doing so, this article aims to illuminate the strengths and weaknesses of current approaches. To conduct this study, a systematic review was conducted of studies published from 2013 to October 2022, peer-reviewed in five prestigious publishers, including ACM Digital Library, IEEE Xplore, Science Direct, Springer, and Nature. The methodology of this systematic review was guided by the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) statement. Ultimately, 28 studies were selected for the final review. The findings of this study highlight several main limitations. Firstly, there is a lack of an accurate definition for echo chambers. Secondly, there is a lack of a solid approach to address the components of echo chambers. Thirdly, there is a controversial issue regarding the effect of echo chambers. Lastly, the measures used mostly did not adequately specify echo chambers.

Sentiment analysis has become a focal point of interdisciplinary research, prompting the use of diverse methodologies and the continual emergence of programming language packages. Notably, Python and R have introduced comprehensive packages in this realm. In this study, we analyze established packages in these languages, focusing on accuracy while also considering time complexity. Across experiments conducted on seven distinct datasets, a crucial revelation surfaces: the accuracy of these packages significantly varies depending on the dataset used. Among these, the ’sentimentr’ package consistently performs well across diverse datasets. Generally, Python libraries showcase superior processing speed. However, it’s essential to note that while these packages adeptly classify sentences as positive or negative, capturing sentiment intensity proves challenging. Our findings highlight a prevalent trend of overfitting, where these packages excel on familiar datasets but struggle when faced with unfamiliar ones.

Purpose: Users are the key players in an online social network (OSN), so the behavior of the OSN is strongly related to their behavior. User weight refers to the influence of the users on the OSN. The purpose of this paper is to propose a method to identify the user weight based on a new metric for defining the time intervals. Design/methodology/approach: The behavior of an OSN changes over time, thus the user weight in the OSN is different in each time frame. Therefore, a good metric for estimating the user weight in an OSN depends on the accuracy of the metric used to define the time interval. New metric for defining the time intervals is based on the standard deviation and identifies that the user weight is based on a simple exponential smoothing model. Findings: The results show that the proposed method covers the maximum behavioral changes of the OSN and is able to identify the influential users in the OSN more accurately than existing methods. Research limitations/implications: In event detection, when a terrorist attack occurs as an event, knowing the influential users help us to know the leader of the attack. Knowing the influential user in each time interval based on this study can help us to detect communities which formed around these people. Finally, in marketing, this issue helps us to have a targeted advertising. Practical implications: User effect is a significant issue in many OSN domain problems, such as community detection, event detection and recommender systems. Originality/value: Previous studies do not give priority to the recent time intervals in identifying the relative importance of users. Thus, defining a metric to compute a time interval that covers the maximum changes in the network is a major shortcoming of earlier studies. Some experiments were conducted on six different data sets to test the performance of the proposed model in terms of the computed time intervals and user weights.

Long Short-Term Memory (LSTM) is widely used in time-series analysis and prediction. Combining LSTM with mathematical transformer models such as Fourier and Wavelet or with statistical methods like Lomb-Scargle, Harmonic Regression, and Seasonal-Trend decomposition can effectively capture time-series behavior and enhance the efficiency and accuracy of prediction models. However, this approach heavily relies on the characteristics of the data. Depending on whether the time series data is periodic, chaotic, or quasi-periodic, the selection of appropriate tools varies—an issue often overlooked in current research that combines LSTM with mathematical transformers or statistical methods. In this study, we aim to demonstrate that using nonlinear dynamic systems techniques, which can capture the characteristics of time series data, leads to the selection of the best transformer. Moreover, this approach explains why LSTM and its combination models may not always perform well. This insight is vital for designing new models based on the dynamic behavior of data. Our experimental findings on two real-world datasets indicate that a combination of LSTM with transformers or decomposition tools does not perform well on highly sensitive and chaotic time series. In other words, we present a model that explains the inefficiencies of LSTM-based models in certain scenarios.

The distance between users has an effect on the formation of social network ties, but it is not the only or even the main factor. Knowing all the features that influence such ties is very important for many related domains such as location-based recommender systems and community and event detection systems for online social networks (OSNs). In recent years, researchers have analyzed the role of user geo-location in OSNs. Researchers have also attempted to determine the probability of friendships being established based on distance, where friendship is not only a function of distance. However, some important features of OSNs remain unknown. In order to comprehensively understand the OSN phenomenon, we also need to analyze users’ attributes. Basically, an OSN functions according to four main user properties: user geo-location, user weight, number of user interactions, and user lifespan. The research presented here sought to determine whether the user mobility pattern can be used to predict users’ interaction behavior. It also investigated whether, in addition to distance, the number of friends (known as user weight) interferes in social network tie formation. To this end, we analyzed the above-stated features in three large-scale OSNs. We found that regardless of a high degree freedom in user mobility, the fraction of the number of outside activities over the inside activity is a significant fraction that helps us to address the user interaction behavior. To the best of our knowledge, research has not been conducted elsewhere on this issue. We also present a high-resolution formula in order to improve the friendship probability function.