Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The stochastic block model is a classical cluster-exhibiting random graph model that has been widely studied in statistics, physics, and computer science. In its simplest form, the model is a random graph with two equal-sized clusters, with intracluster edge probability    $p$   , and intercluster edge probability    $q$   .  focus on the sparse case, i.e.,    $p, q = O(1/n)$   , which is practically more relevant and also mathematically more challenging. A conjecture of Decelle, Krzakala, Moore, and Zdeborova, based on ideas from statistical physics, predicted a specific threshold for clustering. The negative direction of the conjecture was proved by Mossel, Neeman, and Sly (2012), and more recently, the positive direction was independently proved by Massoulie and Mossel, Neeman, and Sly. In many real network clustering problems, nodes contain information as ll.  study the interplay beten node and network information in clustering by studying a labeled block model, where in addition to the edge information, the true cluster labels of a small fraction of the nodes are revealed. In the case of two clusters,  show that below the threshold, a small amount of node information does not affect recovery. On the other hand,  show that for any small amount of information, efficient local clustering is achievable as long as the number of clusters is sufficiently large (as a function of the amount of revealed information).
['Varun Kanade', 'Elchanan Mossel', 'Tselil Schramm']
I am writing a research paper on a idea Global and Local Information in Clustering Labeled Block Models
[{"from": "human", "value": "I am writing a research paper on a idea Global and Local Information in Clustering Labeled Block Models"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The stochastic block model is a classical cluster-exhibiting random graph model that has been widely studied in statistics, physics, and computer science. In its simplest form, the model is a random graph with two equal-sized clusters, with intracluster edge probability    $p$   , and intercluster edge probability    $q$   .  focus on the sparse case, i.e.,    $p, q = O(1/n)$   , which is practically more relevant and also mathematically more challenging. A conjecture of Decelle, Krzakala, Moore, and Zdeborova, based on ideas from statistical physics, predicted a specific threshold for clustering. The negative direction of the conjecture was proved by Mossel, Neeman, and Sly (2012), and more recently, the positive direction was independently proved by Massoulie and Mossel, Neeman, and Sly. In many real network clustering problems, nodes contain information as ll.  study the interplay beten node and network information in clustering by studying a labeled block model, where in addition to the edge information, the true cluster labels of a small fraction of the nodes are revealed. In the case of two clusters,  show that below the threshold, a small amount of node information does not affect recovery. On the other hand,  show that for any small amount of information, efficient local clustering is achievable as long as the number of clusters is sufficiently large (as a function of the amount of revealed information)."}]