Near-Optimal Comparison Based Clustering

• URL: http://arxiv.org/abs/2010.03918v2
• Date: Fri, 9 Oct 2020 12:51:45 GMT
• Title: Near-Optimal Comparison Based Clustering
• Authors: Micha\"el Perrot and Pascal Mattia Esser and Debarghya Ghoshdastidar
• Abstract summary: We show that our method can recover a planted clustering using a near-optimal number of comparisons. We empirically validate our theoretical findings and demonstrate the good behaviour of our method on real data.
• Score: 7.930242839366938
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The goal of clustering is to group similar objects into meaningful partitions. This process is well understood when an explicit similarity measure between the objects is given. However, far less is known when this information is not readily available and, instead, one only observes ordinal comparisons such as "object i is more similar to j than to k." In this paper, we tackle this problem using a two-step procedure: we estimate a pairwise similarity matrix from the comparisons before using a clustering method based on semi-definite programming (SDP). We theoretically show that our approach can exactly recover a planted clustering using a near-optimal number of passive comparisons. We empirically validate our theoretical findings and demonstrate the good behaviour of our method on real data.

Related papers

• Cluster-Aware Similarity Diffusion for Instance Retrieval [64.40171728912702]
  Diffusion-based re-ranking is a common method used for retrieving instances by performing similarity propagation in a nearest neighbor graph. We propose a novel Cluster-Aware Similarity (CAS) diffusion for instance retrieval.
  arXiv  Detail & Related papers  (2024-06-04T14:19:50Z)
• Linear time Evidence Accumulation Clustering with KMeans [0.0]
  This work describes a trick which mimic the behavior of average linkage clustering. We found a way of computing efficiently the density of a partitioning, reducing the cost from a quadratic to linear complexity. The k-means results are comparable to the best state of the art in terms of NMI while keeping the computational cost low.
  arXiv  Detail & Related papers  (2023-11-15T14:12:59Z)
• Rethinking k-means from manifold learning perspective [122.38667613245151]
  We present a new clustering algorithm which directly detects clusters of data without mean estimation. Specifically, we construct distance matrix between data points by Butterworth filter. To well exploit the complementary information embedded in different views, we leverage the tensor Schatten p-norm regularization.
  arXiv  Detail & Related papers  (2023-05-12T03:01:41Z)
• A Revenue Function for Comparison-Based Hierarchical Clustering [5.683072566711975]
  We propose a new revenue function that allows one to measure the goodness of dendrograms using only comparisons. We show that this function is closely related to Dasgupta's cost for hierarchical clustering that uses pairwise similarities. On the theoretical side, we use the proposed revenue function to resolve the open problem of whether one can approximately recover a latent hierarchy using few triplet comparisons.
  arXiv  Detail & Related papers  (2022-11-29T18:40:02Z)
• A sampling-based approach for efficient clustering in large datasets [0.8952229340927184]
  We propose a simple and efficient clustering method for high-dimensional data with a large number of clusters. Our contribution is substantially more efficient than k-means as it does not require an all to all comparison of data points and clusters.
  arXiv  Detail & Related papers  (2021-12-29T19:15:20Z)
• Shift of Pairwise Similarities for Data Clustering [7.462336024223667]
  We consider the case where the regularization term is the sum of the squared size of the clusters, and then generalize it to adaptive regularization of the pairwise similarities. This leads to shifting (adaptively) the pairwise similarities which might make some of them negative. We then propose an efficient local search optimization algorithm with fast theoretical convergence rate to solve the new clustering problem.
  arXiv  Detail & Related papers  (2021-10-25T16:55:07Z)
• Scalable Hierarchical Agglomerative Clustering [65.66407726145619]
  Existing scalable hierarchical clustering methods sacrifice quality for speed. We present a scalable, agglomerative method for hierarchical clustering that does not sacrifice quality and scales to billions of data points.
  arXiv  Detail & Related papers  (2020-10-22T15:58:35Z)
• Contrastive Clustering [57.71729650297379]
  We propose Contrastive Clustering (CC) which explicitly performs the instance- and cluster-level contrastive learning. In particular, CC achieves an NMI of 0.705 (0.431) on the CIFAR-10 (CIFAR-100) dataset, which is an up to 19% (39%) performance improvement compared with the best baseline.
  arXiv  Detail & Related papers  (2020-09-21T08:54:40Z)
• LSD-C: Linearly Separable Deep Clusters [145.89790963544314]
  We present LSD-C, a novel method to identify clusters in an unlabeled dataset. Our method draws inspiration from recent semi-supervised learning practice and proposes to combine our clustering algorithm with self-supervised pretraining and strong data augmentation. We show that our approach significantly outperforms competitors on popular public image benchmarks including CIFAR 10/100, STL 10 and MNIST, as well as the document classification dataset Reuters 10K.
  arXiv  Detail & Related papers  (2020-06-17T17:58:10Z)
• Point-Set Kernel Clustering [11.093960688450602]
  This paper introduces a new similarity measure called point-set kernel which computes the similarity between an object and a set of objects. We show that the new clustering procedure is both effective and efficient that enables it to deal with large scale datasets.
  arXiv  Detail & Related papers  (2020-02-14T00:00:03Z)
• Clustering Binary Data by Application of Combinatorial Optimization Heuristics [52.77024349608834]
  We study clustering methods for binary data, first defining aggregation criteria that measure the compactness of clusters. Five new and original methods are introduced, using neighborhoods and population behavior optimization metaheuristics. From a set of 16 data tables generated by a quasi-Monte Carlo experiment, a comparison is performed for one of the aggregations using L1 dissimilarity, with hierarchical clustering, and a version of k-means: partitioning around medoids or PAM.
  arXiv  Detail & Related papers  (2020-01-06T23:33:31Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.