Abstract
Clustering, i.e., finding groups in the data, is a problem that permeates multiple fields of science and engineering. Recently, the problem of clustering with a noisy oracle has drawn attention due to various applications including crowdsourced entity resolution [33], and predicting signs of interactions in large-scale online social networks [20, 21]. Here, we consider the following fundamental model for two clusters as proposed by Mitzenmacher and Tsourakakis [28], and Mazumdar and Saha [25]; there exist n items, belonging to two unknown groups. We are allowed to query any pair of nodes whether they belong to the same cluster or not, but the answer to the query is corrupted with some probability . Let 1 > δ = 1 − 2q > 0 be the bias. In this work, we provide a polynomial time algorithm that recovers all signs correctly with high probability in the presence of noise with queries. This is the best known result for this problem for all but tiny δ, improving on the current state-of-the-art due to Mazumdar and Saha [25].
Highlights
Clustering is a central problem in data science with a rich history; hundreds of algorithms have been published on the topic
In this work we focus on clustering with a faulty oracle
Log (n) can we remove the δ 6 term from our query complexity?. Another open problem relates to the extension of our result to k clusters
Summary
Clustering is a central problem in data science with a rich history; hundreds of algorithms have been published on the topic. In this work we focus on clustering with a faulty oracle. Can we recover the clusters efficiently with high probability by performing a small number of queries?. The workers’ answers are not always reliable This can be modeled using the noisy oracle model that we study. Once deciding on whether a given pair of items refers to the same entity or not by looking at the workers’ answers, no more queries are typically performed. Our main theoretical result shows that we can recover the two clusters (R, B) with high probability in polynomial time.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
