Hybrid moments of the Riemann zeta-function

The "hybrid" moments $$\int_T^{2T}|\zeta(1/2+it)|^k{(\int_{t-G}^{t+G}|\zeta(1/2+ix)|^\ell dx)}^m dt$$ of the Riemann zeta-function $\zeta(s)$ on the critical line $\Re s = 1/2$ are studied. The expected upper bound for the above expression is $O_\epsilon(T^{1+\epsilon}G^m)$. This is shown to be true for certain specific values of the natural numbers $k,\ell,m$, and the explicitly determined range of $G = G(T;k,\ell,m)$. The application to a mean square bound for the Mellin transform function of $|\zeta(1/2+ix)|^4$ is given.Comment: 27 page

Intent-Aware Contextual Recommendation System

Recommender systems take inputs from user history, use an internal ranking algorithm to generate results and possibly optimize this ranking based on feedback. However, often the recommender system is unaware of the actual intent of the user and simply provides recommendations dynamically without properly understanding the thought process of the user. An intelligent recommender system is not only useful for the user but also for businesses which want to learn the tendencies of their users. Finding out tendencies or intents of a user is a difficult problem to solve. Keeping this in mind, we sought out to create an intelligent system which will keep track of the user's activity on a web-application as well as determine the intent of the user in each session. We devised a way to encode the user's activity through the sessions. Then, we have represented the information seen by the user in a high dimensional format which is reduced to lower dimensions using tensor factorization techniques. The aspect of intent awareness (or scoring) is dealt with at this stage. Finally, combining the user activity data with the contextual information gives the recommendation score. The final recommendations are then ranked using filtering and collaborative recommendation techniques to show the top-k recommendations to the user. A provision for feedback is also envisioned in the current system which informs the model to update the various weights in the recommender system. Our overall model aims to combine both frequency-based and context-based recommendation systems and quantify the intent of a user to provide better recommendations. We ran experiments on real-world timestamped user activity data, in the setting of recommending reports to the users of a business analytics tool and the results are better than the baselines. We also tuned certain aspects of our model to arrive at optimized results.Comment: Presented at the 5th International Workshop on Data Science and Big Data Analytics (DSBDA), 17th IEEE International Conference on Data Mining (ICDM) 2017; 8 pages; 4 figures; Due to the limitation "The abstract field cannot be longer than 1,920 characters," the abstract appearing here is slightly shorter than the one in the PDF fil

PersonaSAGE: A Multi-Persona Graph Neural Network

Graph Neural Networks (GNNs) have become increasingly important in recent years due to their state-of-the-art performance on many important downstream applications. Existing GNNs have mostly focused on learning a single node representation, despite that a node often exhibits polysemous behavior in different contexts. In this work, we develop a persona-based graph neural network framework called PersonaSAGE that learns multiple persona-based embeddings for each node in the graph. Such disentangled representations are more interpretable and useful than a single embedding. Furthermore, PersonaSAGE learns the appropriate set of persona embeddings for each node in the graph, and every node can have a different number of assigned persona embeddings. The framework is flexible enough and the general design helps in the wide applicability of the learned embeddings to suit the domain. We utilize publicly available benchmark datasets to evaluate our approach and against a variety of baselines. The experiments demonstrate the effectiveness of PersonaSAGE for a variety of important tasks including link prediction where we achieve an average gain of 15% while remaining competitive for node classification. Finally, we also demonstrate the utility of PersonaSAGE with a case study for personalized recommendation of different entity types in a data management platform.Comment: 10 pages, 6 figures, 7 table

CGC: Contrastive Graph Clustering for Community Detection and Tracking

Given entities and their interactions in the web data, which may have occurred at different time, how can we find communities of entities and track their evolution? In this paper, we approach this important task from graph clustering perspective. Recently, state-of-the-art clustering performance in various domains has been achieved by deep clustering methods. Especially, deep graph clustering (DGC) methods have successfully extended deep clustering to graph-structured data by learning node representations and cluster assignments in a joint optimization framework. Despite some differences in modeling choices (e.g., encoder architectures), existing DGC methods are mainly based on autoencoders and use the same clustering objective with relatively minor adaptations. Also, while many real-world graphs are dynamic, previous DGC methods considered only static graphs. In this work, we develop CGC, a novel end-to-end framework for graph clustering, which fundamentally differs from existing methods. CGC learns node embeddings and cluster assignments in a contrastive graph learning framework, where positive and negative samples are carefully selected in a multi-level scheme such that they reflect hierarchical community structures and network homophily. Also, we extend CGC for time-evolving data, where temporal graph clustering is performed in an incremental learning fashion, with the ability to detect change points. Extensive evaluation on real-world graphs demonstrates that the proposed CGC consistently outperforms existing methods.Comment: TheWebConf 2022 Research Trac