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Query Complexity of Clustering with Side Information
Suppose, we are given a set of n elements to be clustered into k (unknow...
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Clustering with Noisy Queries
In this paper, we initiate a rigorous theoretical study of clustering wi...
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Correlation Clustering with Adaptive Similarity Queries
We investigate learning algorithms that use similarity queries to approx...
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A numerical measure of the instability of Mapper-type algorithms
Mapper is an unsupervised machine learning algorithm generalising the no...
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Penalized k-means algorithms for finding the correct number of clusters in a dataset
In many applications we want to find the number of clusters in a dataset...
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Efficient Algorithms for Generating Provably Near-Optimal Cluster Descriptors for Explainability
Improving the explainability of the results from machine learning method...
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Semisupervised Clustering by Queries and Locally Encodable Source Coding
Source coding is the canonical problem of data compression in informatio...
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Same-Cluster Querying for Overlapping Clusters
Overlapping clusters are common in models of many practical data-segmentation applications. Suppose we are given n elements to be clustered into k possibly overlapping clusters, and an oracle that can interactively answer queries of the form "do elements u and v belong to the same cluster?" The goal is to recover the clusters with minimum number of such queries. This problem has been of recent interest for the case of disjoint clusters. In this paper, we look at the more practical scenario of overlapping clusters, and provide upper bounds (with algorithms) on the sufficient number of queries. We provide algorithmic results under both arbitrary (worst-case) and statistical modeling assumptions. Our algorithms are parameter free, efficient, and work in the presence of random noise. We also derive information-theoretic lower bounds on the number of queries needed, proving that our algorithms are order optimal. Finally, we test our algorithms over both synthetic and real-world data, showing their practicality and effectiveness.
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