Minimizing Polarization in Noisy Leader-Follower Opinion Dynamics

The operation of creating edges has been widely applied to optimize relevant quantities of opinion dynamics. In this paper, we consider a problem of polarization optimization for the leader-follower opinion dynamics in a noisy social network with $n$ nodes and $m$ edges, where a group $Q$ of $q$ nodes are leaders, and the remaining $n-q$ nodes are followers. We adopt the popular leader-follower DeGroot model, where the opinion of every leader is identical and remains unchanged, while the opinion of every follower is subject to white noise. The polarization is defined as the steady-state variance of the deviation of each node's opinion from leaders' opinion, which equals one half of the effective resistance $\mathcal{R}_Q$ between the node group $Q$ and all other nodes. Concretely, we propose and study the problem of minimizing $\mathcal{R}_Q$ by adding $k$ new edges with each incident to a node in $Q$. We show that the objective function is monotone and supermodular. We then propose a simple greedy algorithm with an approximation factor $1-1/e$ that approximately solves the problem in $O((n-q)^3)$ time. To speed up the computation, we also provide a fast algorithm to compute (1-1/e-\eps)-approximate effective resistance $\mathcal{R}_Q$, the running time of which is \Otil (mk\eps^{-2}) for any \eps>0, where the \Otil (\cdot) notation suppresses the ${\rm poly} (\log n)$ factors. Extensive experiment results show that our second algorithm is both effective and efficient.Comment: This paper has been accepted in CIKM'23 conferenc

Updating and downdating techniques for optimizing network communicability

The total communicability of a network (or graph) is defined as the sum of the entries in the exponential of the adjacency matrix of the network, possibly normalized by the number of nodes. This quantity offers a good measure of how easily information spreads across the network, and can be useful in the design of networks having certain desirable properties. The total communicability can be computed quickly even for large networks using techniques based on the Lanczos algorithm. In this work we introduce some heuristics that can be used to add, delete, or rewire a limited number of edges in a given sparse network so that the modified network has a large total communicability. To this end, we introduce new edge centrality measures which can be used to guide in the selection of edges to be added or removed. Moreover, we show experimentally that the total communicability provides an effective and easily computable measure of how "well-connected" a sparse network is.Comment: 20 pages, 9 pages Supplementary Materia

RETAIL DATA ANALYTICS USING GRAPH DATABASE

Big data is an area focused on storing, processing and visualizing huge amount of data. Today data is growing faster than ever before. We need to find the right tools and applications and build an environment that can help us to obtain valuable insights from the data. Retail is one of the domains that collects huge amount of transaction data everyday. Retailers need to understand their customer’s purchasing pattern and behavior in order to take better business decisions. Market basket analysis is a field in data mining, that is focused on discovering patterns in retail’s transaction data. Our goal is to find tools and applications that can be used by retailers to quickly understand their data and take better business decisions. Due to the amount and complexity of data, it is not possible to do such activities manually. We witness that trends change very quickly and retailers want to be quick in adapting the change and taking actions. This needs automation of processes and using algorithms that are efficient and fast. In our work, we mine transaction data by modeling the data as graphs. We use clustering algorithms to discover communities (clusters) in the data and then use the clusters for building a recommendation system that can recommend products to customers based on their buying behavior

Transforming Graph Representations for Statistical Relational Learning

Relational data representations have become an increasingly important topic due to the recent proliferation of network datasets (e.g., social, biological, information networks) and a corresponding increase in the application of statistical relational learning (SRL) algorithms to these domains. In this article, we examine a range of representation issues for graph-based relational data. Since the choice of relational data representation for the nodes, links, and features can dramatically affect the capabilities of SRL algorithms, we survey approaches and opportunities for relational representation transformation designed to improve the performance of these algorithms. This leads us to introduce an intuitive taxonomy for data representation transformations in relational domains that incorporates link transformation and node transformation as symmetric representation tasks. In particular, the transformation tasks for both nodes and links include (i) predicting their existence, (ii) predicting their label or type, (iii) estimating their weight or importance, and (iv) systematically constructing their relevant features. We motivate our taxonomy through detailed examples and use it to survey and compare competing approaches for each of these tasks. We also discuss general conditions for transforming links, nodes, and features. Finally, we highlight challenges that remain to be addressed