# Clustering with Noisy Queries

@article{Mazumdar2017ClusteringWN, title={Clustering with Noisy Queries}, author={Arya Mazumdar and Barna Saha}, journal={ArXiv}, year={2017}, volume={abs/1706.07510} }

In this paper, we initiate a rigorous theoretical study of clustering with noisy queries (or a faulty oracle). Given a set of $n$ elements, our goal is to recover the true clustering by asking minimum number of pairwise queries to an oracle. Oracle can answer queries of the form : "do elements $u$ and $v$ belong to the same cluster?" -- the queries can be asked interactively (adaptive queries), or non-adaptively up-front, but its answer can be erroneous with probability $p$. In this paper, we…

## 65 Citations

### Query Complexity of Clustering with Side Information

- Computer ScienceNIPS
- 2017

The dramatic power of side information aka similarity matrix on reducing the query complexity of clustering is shown, and intriguing connection to popular community detection models such as the {\em stochastic block model}, significantly generalizes them, and opens up many venues for interesting future research.

### Top-m Clustering with a Noisy Oracle

- Computer Science2019 National Conference on Communications (NCC)
- 2019

The goal is to identify the top-m clusters in terms of size, using the noisy answers from the oracle, and provides an upper bound which is a function of the number of recovered clusters $m$ and the sizes of the top clusters.

### Same-Cluster Querying for Overlapping Clusters

- Computer ScienceNeurIPS
- 2019

This paper provides upper bounds (with algorithms) on the sufficient number of queries on the more practical scenario of overlapping clusters, and provides algorithmic results under both arbitrary (worst-case) and statistical modeling assumptions.

### Optimal Clustering with Noisy Queries via Multi-Armed Bandit

- Computer ScienceICML
- 2022

An interesting connection between the problem and multi-armed bandit might provide useful insights for other similar problems, and a new polynomial time algorithm with O ( n ( k +log n ) δ 2 + poly( k, 1 δ , log n )) queries is proposed.

### Correlation Clustering with Same-Cluster Queries Bounded by Optimal Cost

- Computer ScienceESA
- 2019

This paper presents an efficient algorithm that recovers an exact optimal clustering using at most $2C_{OPT} $ queries and an efficient algorithms that outputs a $2-approximation using at least two queries, both of which are efficient against several known correlation clustering algorithms.

### 81 : 2 Same-Cluster Queries Bounded by Optimal Cost Funding

- Computer Science
- 2019

This paper presents two efficient algorithms for correlation clustering whose error and query bounds are parameterized by COPT rather than by the number of clusters, and shows that under a plausible complexity assumption, there does not exist any polynomial time algorithm that has an approximation ratio better than 1 + α for an absolute constant α > 0 with o(COPT ) queries.

### Clustering with a faulty oracle

- Computer Science, MathematicsWWW
- 2020

This work provides a polynomial time algorithm that recovers all signs correctly with high probability in the presence of noise with queries, improving on the current state-of-the-art due to Mazumdar and Saha.

### Towards a Query-Optimal and Time-Efficient Algorithm for Clustering with a Faulty Oracle

- Computer ScienceCOLT
- 2021

A time-efficient algorithm is provided with nearly-optimal query complexity for all constant k and any δ in the regime when information-theoretic recovery is possible and is built on a connection to the stochastic block model.

### On Margin-Based Cluster Recovery with Oracle Queries

- Computer Science, MathematicsNeurIPS
- 2021

We study an active cluster recovery problem where, given a set of n points and an oracle answering queries like “are these two points in the same cluster?”, the task is to recover exactly all…

### Optimal Clustering in Stable Instances Using Combinations of Exact and Noisy Ordinal Queries

- Computer ScienceAlgorithms
- 2021

This work studies clustering algorithms which operates with ordinal or comparison-based queries (operations) and provides several variants of these algorithms using ordinal operations and, in particular, non-trivial trade-offs between the number of high-cost and low-cost operations that are used.

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