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ABSTRACT In this short note, we address the identifiability issues inherent in the degree‐corrected stochastic block model (DCSBM). We provide a rigorous proof demonstrating that the parameters of the DCSBM are identifiable up to a scaling factor and a permutation of the community labels, under a mild condition. 

Bipartite graphs are ubiquitous across various scientific and engineering fields. Simultaneously grouping the two types of nodes in a bipartite graph via biclustering represents a fundamental challenge in network analysis for such graphs. The latent block model (LBM) is a commonly used model-based tool for biclustering. However, the effectiveness of the LBM is often limited by the influence of row and column sums in the data matrix. To address this limitation, we introduce the degree-corrected latent block model (DC-LBM), which accounts for the varying degrees in row and column clusters, significantly enhancing performance on real-world data sets and simulated data. We develop an efficient variational expectation-maximization algorithm by creating closed-form solutions for parameter estimates in the M steps. Furthermore, we prove the label consistency and the rate of convergence of the variational estimator under the DC-LBM, allowing the expected graph density to approach zero as long as the average expected degrees of rows and columns approach infinity when the size of the graph increases. 

Many patients with mental disorders take dietary supplement, but their use patterns remain unclear. In this study, we developed a method to detect signals of associations between dietary supplement intake and mental disorder in Twitter data. We developed an annotated dataset and trained a convolutional neural network classifier that can identify language use pattern of dietary supplement intake with an F1-score of 0.899, a precision of 0.900, and a recall of 0.900. Using the classifier, we discovered that melatonin and vitamin D were the most commonly used supplements among Twitter users who self-diagnosed mental disorders. Sentiment analysis using Linguistic Inquiry and Word Count has shown that among Twitter users who posted mental disorder self-diagnosis, users who indicated supplement intake are more active and express more negative emotions and fewer positive emotions than those who have not mentioned supplement intake. 

Social media embed rich but noisy signals of physical locations of their users. Accurately inferring a user's location can significantly improve the user's experience on the social media and enable the development of new location-based applications. This paper proposes a novel community-based approach for predicting the location of a user by using communities in the egonet of the user. We further propose both geographical proximity and structural proximity metrics to profile communities in the ego-net of a user, and then evaluate the effectiveness of each individual metric on real social media data. We discover that geographical proximity metrics, such as average/median haversine distance and community closeness, are strong indicators of a good community for geotagging. In addition, structural proximity metric conductance performs comparable to geographical proximity metrics while triangle participation ratio and internal density are weak location indicators. To the best of our knowledge, this is the first effort to infer the physical location of a user from the perspective of latent communities in the user's ego-net.