Marine buoys aid in the battle against Illegal, Unreported and Unregulated (IUU) fishing by detecting fishing vessels in their vicinity. Marine buoys, however, may be disrupted by natural causes and buoy vandalism. In this paper, we formulate marine buoy placement as a clustering problem, and propose dropout k-means an…
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28 results for “k-median”
We study the sample-based k-median clustering objective under a sequential setting without substitutions. In this setting, an i.i.d. sequence of examples is observed. An example can be selected as a center only immediately after it is observed, and it cannot be substituted later. The goal is to select a set of centers …
Clustering is a fundamental problem in unsupervised learning, and has been studied widely both as a problem of learning mixture models and as an optimization problem. In this paper, we study clustering with respect the emph{k-median} objective function, a natural formulation of clustering in which we attempt to minimiz…
Replicable clustering algorithms for k-medians, k-means, and k-centers are proposed.
problem Designing clustering algorithms that produce the same partition on repeated runs under the same distribution.
method Utilizing approximation routines for combinatorial clustering problems in a black-box manner.
result Replicable algorithms for statistical -medians, -means, and -centers with specified approximation and sample complexities.
-Median Clustering via Metric Embedding: Towards Better Initialization with Differential Privacycs.DS
New method for better initial centers in clustering with improved accuracy and privacy.
problem Improving the quality of clustering centers in metric spaces.
method HST initialization based on metric embedding tree structure, combined with efficient search algorithm and DP extension.
result HST initialization produces better initial centers than -median++ with comparable efficiency and improved privacy.
Algorithm provides fair clustering guarantees for k-means and k-median.
problem Ensuring fair clustering guarantees for every point in a dataset.
method Local search algorithm for -median and -means, with individual fairness as a key metric.
result Achieves fair clustering with a constant factor approximation of the optimal solution.
A Constant Approximation Algorithm for Sequential Random-Order No-Substitution k-Median Clusteringcs.LG
New algorithm for clustering data streams with no substitutions.
problem Clustering sequential data with no point substitution.
method Careful risk estimation, linear bin division, multiscale center selection.
result First constant approximation algorithm for random-order k-median clustering.
Improves clustering interpretability with decision trees.
problem Hard-to-explain cluster assignments in clustering algorithms.
method Decision tree-based clustering with -means and -medians objectives.
result An efficient algorithm producing explainable clusters with provable guarantees.
This paper provides new algorithms for distributed clustering for two popular center-based objectives, k-median and k-means. These algorithms have provable guarantees and improve communication complexity over existing approaches. Following a classic approach in clustering by \cite{har2004coresets}, we reduce the proble…
Efficiently private clustering algorithms with tight approximation ratios.
problem Differentially private clustering of various types.
method Efficient algorithms achieving tight approximation ratios for clustering problems.
result Achieves approximation ratios similar to non-private algorithms with small additive errors.
The paper tackles fair correlation clustering with new algorithms and analysis.
problem Fair variants of correlation clustering under various constraints.
method Introducing a novel combinatorial optimization problem for fairlet decomposition.
result Approximation algorithms for fair correlation clustering under multiple fairness constraints.
In a recent work, [19] studied the following "fair" variants of classical clustering problems such as -means and -median: given a set of data points in and a binary type associated to each data point, the goal is to cluster the points while ensuring that the proportion of each type in each clus…
Clustering with fast algorithms large samples of high dimensional data is an important challenge in computational statistics. Borrowing ideas from MacQueen (1967) who introduced a sequential version of the -means algorithm, a new class of recursive stochastic gradient algorithms designed for the -medians loss cri…
We study exact recovery conditions for convex relaxations of point cloud clustering problems, focusing on two of the most common optimization problems for unsupervised clustering: -means and -median clustering. Motivations for focusing on convex relaxations are: (a) they come with a certificate of optimality, and…
We analyze the performance of spectral clustering for community extraction in stochastic block models. We show that, under mild conditions, spectral clustering applied to the adjacency matrix of the network can consistently recover hidden communities even when the order of the maximum expected degree is as small as $\l…
Fair clustering under the disparate impact doctrine requires that population of each protected group should be approximately equal in every cluster. Previous work investigated a difficult-to-scale pre-processing step for -center and -median style algorithms for the special case of this problem when the number of …
Community detection is a fundamental problem in network analysis which is made more challenging by overlaps between communities which often occur in practice. Here we propose a general, flexible, and interpretable generative model for overlapping communities, which can be thought of as a generalization of the degree-co…
We study the -median clustering problem for high-dimensional polygonal curves with finite but unbounded number of vertices. We tackle the computational issue that arises from the high number of dimensions by defining a Johnson-Lindenstrauss projection for polygonal curves. We analyze the resulting error in terms of …
We study the question of fair clustering under the {\em disparate impact} doctrine, where each protected class must have approximately equal representation in every cluster. We formulate the fair clustering problem under both the -center and the -median objectives, and show that even with two protected classes th…
We design a new algorithm for the Euclidean -means problem that operates in the local model of differential privacy. Unlike in the non-private literature, differentially private algorithms for the -means objective incur both additive and multiplicative errors. Our algorithm significantly reduces the additive erro…
Quantum algorithms reduce clustering input size, achieving near-linear approximation.
problem Efficiently clustering large datasets in quantum computing.
method Quantum coresets for -clustering with sublinear query complexity.
result Achieves near-linear approximation for -clustering with coresets.
The stochastic block model (SBM) is a popular framework for studying community detection in networks. This model is limited by the assumption that all nodes in the same community are statistically equivalent and have equal expected degrees. The degree-corrected stochastic block model (DCSBM) is a natural extension of S…
Fair HAC algorithms ensure clustering fairness across protected groups.
problem Ensuring clustering fairness in HAC algorithms when datasets contain biases.
method Proposes fair algorithms for HAC that enforce fairness constraints regardless of distance linkage criteria.
result Our fair HAC algorithms find fairer clusterings compared to vanilla HAC and other fair clustering approaches.
Improved approximation for socially fair clustering with -objective.
problem Finding a set of centers minimizing the maximum distance to all points in each group.
method Introduced a strengthened LP relaxation with an integrality gap of .
result Improved approximation algorithm with -approximation.
Fair Wasserstein Coresetsstat.ML
FWC creates fair synthetic samples for machine learning tasks.
problem Addressing biases in machine learning models for fair decision-making.
method FWC uses an efficient majority minimization algorithm to minimize Wasserstein distance while enforcing demographic parity.
result FWC achieves a competitive fairness-utility tradeoff and reduces biases in predictions from large language models.
The paper introduces group-representative clustering to ensure fair representation of different groups in clusters.
problem Ensuring fair representation of different groups in clusters.
method Developed a new clustering approach called group-representative clustering, which parallels fairness notions in classification.
result Presented approximation algorithms for group representative -median clustering and evaluated on real-world data.
We introduce an evolutionary algorithm called recombinator--means for optimizing the highly non-convex kmeans problem. Its defining feature is that its crossover step involves all the members of the current generation, stochastically recombining them with a repurposed variant of the -means++ seeding algorithm. Th…
New method preserves distances in time series data.
problem Preserving distances in time series data under interpolation.
method Developed lines-preserving terminal embeddings.
result First dimension-free coresets for Fréchet distance clustering.