Corpus ID: 10680176

Local correlation clustering

  title={Local correlation clustering},
  author={Francesco Bonchi and David Garc{\'i}a-Soriano and Konstantin Kutzkov},
Correlation clustering is perhaps the most natural formulation of clustering. Given $n$ objects and a pairwise similarity measure, the goal is to cluster the objects so that, to the best possible extent, similar objects are put in the same cluster and dissimilar objects are put in different clusters. Despite its theoretical appeal, the practical relevance of correlation clustering still remains largely unexplored, mainly due to the fact that correlation clustering requires the $\Theta(n^2… Expand
Query-Efficient Correlation Clustering
This paper devise a correlation clustering algorithm that, given a budget of Q queries, attains a solution whose expected number of disagreements is at most , where is the optimal cost for the instance. Expand
Correlation Clustering with Adaptive Similarity Queries
This work investigates correlation clustering as an active learning problem: each similarity score can be learned by making a query, and the goal is to minimise both the disagreements and the total number of queries. Expand
Regular Partitions and Their Use in Structural Pattern Recognition
This thesis introduces a framework to summarize large graphs based on Szemeredi's Regularity Remma (RL), which roughly states that any sufficiently large graph can almost entirely be partitioned into a bounded number of random-like bipartite graphs. Expand
Revealing structure in large graphs: Szemerédi's regularity lemma and its use in pattern recognition
An overview of the regularity lemma and its algorithmic aspects is provided, and its relevance in the context of pattern recognition research is discussed. Expand
Graph summarization with quality guarantees
This work develops the first polynomial-time approximation algorithms to compute the best possible summary of a certain size under both measures of the original graph. Expand
Graph Summarization with Quality Guarantees
This paper develops the first polynomial-time approximation algorithm to compute the best possible summary of a given size of a graph. Expand


Correlation clustering with a fixed number of clusters
This paper focuses on the situation when the number of clusters is stipulated to be a small constant k, and finds that for every k, there is a polynomial time approximation scheme for both maximizing agreements and minimizing disagreements. Expand
Correlation Clustering
This formulation is motivated from a document clustering problem in which one has a pairwise similarity function f learned from past data, and the goal is to partition the current set of documents in a way that correlates with f as much as possible; it can also be viewed as a kind of “agnostic learning” problem. Expand
A discriminative framework for clustering via similarity functions
A theoretical framework that can be viewed as an analog of the PAC learning model for clustering, where the object of study is a class of (concept, similarity function) pairs, or equivalently, a property the similarity function should satisfy with respect to the ground truth clustering is developed. Expand
Correlation Clustering Revisited: The "True" Cost of Error Minimization Problems
This work argues that it is more reasonable to measure the output clustering's accuracy against the unknown underlying true clustering, and presents a novel method for continuously morphing a general (non-metric) function into a pseudometric. Expand
Correlation clustering in general weighted graphs
An O(log n)-approximation algorithm is given for the general case based on a linear-programming rounding and the "region-growing" technique for Kr, r-minor-free graphs and it is proved that this linear program has a gap of Ω( log n), and therefore the approximation is tight under this approach. Expand
Clustering with qualitative information
A factor 4 approximation for minimization on complete graphs, and a factor O(logn) approximation for general graphs are demonstrated, and the APX-hardness of minimization of complete graphs is proved. Expand
Higher-Order Correlation Clustering for Image Segmentation
Experimental results on various datasets show that the proposed higher-order correlation clustering outperforms other state-of-the-art image segmentation algorithms. Expand
A Local Clustering Algorithm for Massive Graphs and Its Application to Nearly Linear Time Graph Partitioning
This work presents a local clustering algorithm, a useful primitive for handling massive graphs, such as social networks and web-graphs, that finds a good cluster---a subset of vertices whose internal connections are significantly richer than its external connections---near a given vertex. Expand
Correlation Clustering: maximizing agreements via semidefinite programming
  • C. Swamy
  • Mathematics, Computer Science
  • SODA '04
  • 2004
This work gives a 0.7666-approximation algorithm for maximizing agreements on any graph even when the edges have non-negative weights (along with labels) and they want to maximize the weight of agreements. Expand
Small Space Representations for Metric Min-sum k-Clustering and Their Applications
The first efficient construction of a coreset for min-sum k-clustering in metric spaces is shown, and the concept of α-preserving metric embeddings is introduced, which is to find a metric embedding into a (structurally simpler) metric space that approximates the original metric up to a factor of α. Expand