A Combinatorial Necessary and Sufficient Condition for Cluster Consensus

In this technical note, cluster consensus of discrete-time linear multi-agent systems is investigated. A set of stochastic matrices $\mathcal{P}$ is said to be a cluster consensus set if the system achieves cluster consensus for any initial state and any sequence of matrices taken from $\mathcal{P}$. By introducing a cluster ergodicity coefficient, we present an equivalence relation between a range of characterization of cluster consensus set under some mild conditions including the widely adopted inter-cluster common influence. We obtain a combinatorial necessary and sufficient condition for a compact set $\mathcal{P}$ to be a cluster consensus set. This combinatorial condition is an extension of the avoiding set condition for global consensus, and can be easily checked by an elementary routine. As a byproduct, our result unveils that the cluster-spanning trees condition is not only sufficient but necessary in some sense for cluster consensus problems.Comment: 6 page

Name Disambiguation from link data in a collaboration graph using temporal and topological features

In a social community, multiple persons may share the same name, phone number or some other identifying attributes. This, along with other phenomena, such as name abbreviation, name misspelling, and human error leads to erroneous aggregation of records of multiple persons under a single reference. Such mistakes affect the performance of document retrieval, web search, database integration, and more importantly, improper attribution of credit (or blame). The task of entity disambiguation partitions the records belonging to multiple persons with the objective that each decomposed partition is composed of records of a unique person. Existing solutions to this task use either biographical attributes, or auxiliary features that are collected from external sources, such as Wikipedia. However, for many scenarios, such auxiliary features are not available, or they are costly to obtain. Besides, the attempt of collecting biographical or external data sustains the risk of privacy violation. In this work, we propose a method for solving entity disambiguation task from link information obtained from a collaboration network. Our method is non-intrusive of privacy as it uses only the time-stamped graph topology of an anonymized network. Experimental results on two real-life academic collaboration networks show that the proposed method has satisfactory performance.Comment: The short version of this paper has been accepted to ASONAM 201