Fair Clustering with Multiple Colors

Böhm, Matteo; Fazzone, Adriano; Leonardi, Stefano; Schwiegelshohn, Chris

doi:10.48550/arxiv.2002.07892

Cited by 7 publications

(15 citation statements)

References 16 publications

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“…Simultaneously, the running complexity is linear in the number of clusters and near-linear in the number of data points. Böhm et al (2020) propose an (α+2)-approximate algorithm for fair clustering using minimum costperfect matching algorithm. While the approach works with a multi-valued protected attribute, it has O(n 3 ) time complexity and is not scalable.…”

Section: Related Workmentioning

confidence: 99%

Efficient Algorithms For Fair Clustering with a New Fairness Notion

Gupta¹,

Ghalme²,

Krishnan³

et al. 2021

Preprint

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We revisit the problem of fair clustering, first introduced by Chierichetti et al. (2017) , that requires each protected attribute to have approximately equal representation in every cluster; i.e., a Balance property. Existing solutions to fair clustering are either not scalable or do not achieve an optimal trade-off between clustering objective and fairness. In this paper, we propose a new notion of fairness, which we call τ -ratio fairness, that strictly generalizes the Balance property and enables a finegrained efficiency vs. fairness trade-off. Furthermore, we show that simple greedy round-robin based algorithms achieve this trade-off efficiently. Under a more general setting of multi-valued protected attributes, we rigorously analyze the theoretical properties of the our algorithms. Our experimental results suggest that the proposed solution outperforms all the state-of-the-art algorithms and works exceptionally well even for a large number of clusters.

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Section: Related Workmentioning

confidence: 99%

Efficient Algorithms For Fair Clustering with a New Fairness Notion

Gupta¹,

Ghalme²,

Krishnan³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Moreover, due to the inherent exponential dependency on d of the coreset size, the running time of the algorithm in [57] still depends exponentially on d (see Table 3). Böhm et al [17] considered (1, k)-fair clustering with multiple colors. They designed near-linear time constant-approximation algorithms in this restricted setting.…”

Section: Comparison With Related Workmentioning

confidence: 99%

“…Clustering with fairness constraints or fair clustering was introduced by Chierichetti et al [29] in a seminal work. The notion became widely popular within a short period triggering a large body of new work [78,13,15,57,8,17,28,3,67]. The idea of fair clustering is to enforce additional (fairness) constraints to remove the inherent bias or discrimination from vanilla (unconstrained) clustering.…”

Section: Introductionmentioning

confidence: 99%

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On Coresets for Fair Clustering in Metric and Euclidean Spaces and Their Applications

Bandyapadhyay,

Fomin,

Simonov

2020

Preprint

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Fair clustering is a constrained variant of clustering where the goal is to partition a set of colored points, such that the fraction of points of any color in every cluster is more or less equal to the fraction of points of this color in the dataset. This variant was recently introduced by Chierichetti et al. [NeurIPS, 2017] in a seminal work and became widely popular in the clustering literature. In this paper, we propose a new construction of coresets for fair clustering based on random sampling. The new construction allows us to obtain the first coreset for fair clustering in general metric spaces. For Euclidean spaces, we obtain the first coreset whose size does not depend exponentially on the dimension. Our coreset results solve open questions proposed by Schmidt et al. [WAOA, 2019] and Huang et al. [NeurIPS, 2019].The new coreset construction helps to design several new approximation and streaming algorithms. In particular, we obtain the first true constant-approximation algorithm for metric fair clustering, whose running time is fixed-parameter tractable (FPT). In the Euclidean case, we derive the first (1+ )-approximation algorithm for fair clustering whose time complexity is near-linear and does not depend exponentially on the dimension of the space. Besides, our coreset construction scheme is fairly general and gives rise to coresets for a wide range of constrained clustering problems. This leads to improved constant-approximations for these problems in general metrics and near-linear time (1 + )-approximations in the Euclidean metric.

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“…This notion was previously studied for (1) k-center Schmidt, 2018, Bercea et al, 2019] and (2) k-clustering with ℓ p -objective on balanced instances (instances with f j = 1 for all j and f = ℓ) [Böhm et al, 2020]. In all these special cases of exact fairness, the fair clustering problem admits a constant factor approximation.…”

Section: Introductionmentioning

confidence: 99%

Fair Representation Clustering with Several Protected Classes

Dai¹,

Makarychev²,

Vakilian³

2022

Preprint

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We study the problem of fair k-median where each cluster is required to have a fair representation of individuals from different groups. In the fair representation k-median problem, we are given a set of points X in a metric space. Each point x ∈ X belongs to one of ℓ groups. Further, we are given fair representation parameters αj and βj for each group j ∈ [ℓ]. We say that a k-clustering C1, • • • , C k fairly represents all groups if the number of points from group j in cluster Ci is between αj |Ci| and βj |Ci| for every j ∈ [ℓ] and i ∈ [k]. The goal is to find a set C of k centers and an assignment φ : X → C such that the clustering defined by (C, φ) fairly represents all groups and minimizes the ℓ1-objectiveWe present an O(log k)-approximation algorithm that runs in time n O(ℓ) . Note that the known algorithms for the problem either (i) violate the fairness constraints by an additive term or (ii) run in time that is exponential in both k and ℓ. We also consider an important special case of the problem where αj = βj = f j f and fj , f ∈ N for all j ∈ [ℓ]. For this special case, we present an O(log k)-approximation algorithm that runs in (kf ) O(ℓ) log n + poly(n) time.

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Fair Clustering with Multiple Colors

Cited by 7 publications

References 16 publications

Efficient Algorithms For Fair Clustering with a New Fairness Notion

Efficient Algorithms For Fair Clustering with a New Fairness Notion

On Coresets for Fair Clustering in Metric and Euclidean Spaces and Their Applications

Fair Representation Clustering with Several Protected Classes

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