New RunLLM response generated: >>>*# Question* Hello Bohdan, I hope you had a pleasant weekend. I'm sorry to hear about the anticipated power outage in your area; I hope it is resolved promptly. Regarding our meeting, I understand the need to reschedule and am available to extend it by one day. Please let me know the new proposed time, and I'll do my best to accommodate it. Thank you for sharing your progress on understanding the NoNClus algorithm. It appears you're exploring methods to express the matrix H by applying a softmax function to the distance between Ui and Vj, and normalizing it. While this approach is valid and commonly used, I want to ensure that the interpretation of H aligns with the algorithm's objectives. In the NoNClus algorithm, H represents the similarity between different networks (Ai) clustered using matrix factorization. Specifically, hij denotes the similarity between network Ai and cluster j, capturing how well Ai aligns with the common structure represented by cluster j. This interpretation is crucial for the algorithm's performance, as it ensures that networks are grouped based on structural similarities. To deepen your understanding, you might find it helpful to review this paper: Ni, J., Tong, H., Fan, W., Zhang, X.: Flexible and robust multi-network clustering. In: Proceedings of the 21th ACM SIGKDD international conference on knowledge discovery and data mining. pp. 835–844 (2015) I believe there’s a key aspect of the objective function that still needs clarification. The term h represents the similarity between different networks Ai , and it's clustered using matrix factorization in the first part of the objective function. This means that we can't derive H based on the distance between Ui and Vj, because Ui is the factor for network Ai, while Vj is the common factor for all networks within cluster j . The second term of the objective function is there to ensure that networks in the same cluster have a shared structure, reinforcing the assumption of similarity. This is why the NoNClus algorithm requires a deeper understanding, especially in terms of how hij relates to the rest of the objective function. Instead of providing H , we need to learn and optimize for it. To summarize: if we measure the similarity between all networks Ai for (i =1,,g) or between their factors Ui​ , we will form a similarity matrix G (a super network representing similarity among the subnetworks). When we factor G using non-negative symmetric matrix factorization, we obtain H, which has g rows (number of networks) and k columns (number of clusters in the super network). Let’s touch base once your situation improves and discuss further. Best, Nouf # Answer