A Stochastic Alternating Balance k-Means Algorithm for Fair Clustering

In the application of data clustering to human-centric decision-making systems, such as loan applications and advertisement recommendations, the clustering outcome might discriminate against people across different demographic groups, leading to unfairness. A natural conflict occurs between the cost of clustering (in terms of distance to cluster centers) and the balance representation of all demographic groups across the clusters, leading to a bi-objective optimization problem that is nonconvex and nonsmooth. To determine the complete trade-off between these two competing goals, we design a novel stochastic alternating balance fair k-means (SAfairKM) algorithm, which consists of alternating classical mini-batch k-means updates and group swap updates. The number of k-means updates and the number of swap updates essentially parameterize the weight put on optimizing each objective function. Our numerical experiments show that the proposed SAfairKM algorithm is robust and computationally efficient in constructing well-spread and high-quality Pareto fronts both on synthetic and real datasets. Moreover, we propose a novel companion algorithm, the stochastic alternating bi-objective gradient descent (SA2GD) algorithm, which can handle a smooth version of the considered bi-objective fair k-means problem, more amenable for analysis. A sublinear convergence rate of O(1/T ) is established under strong convexity for the determination of a stationary point of a weighted sum of the two functions parameterized by the number of steps or updates on each function.

[1]  Christian Sohler,et al.  Fair Coresets and Streaming Algorithms for Fair k-Means Clustering , 2018, ArXiv.

[2]  Sara Ahmadian,et al.  Clustering without Over-Representation , 2019, KDD.

[3]  Michael Carl Tschantz,et al.  Automated Experiments on Ad Privacy Settings: A Tale of Opacity, Choice, and Discrimination , 2014, ArXiv.

[4]  Jorge Nocedal,et al.  Optimization Methods for Large-Scale Machine Learning , 2016, SIAM Rev..

[5]  S. P. Lloyd,et al.  Least squares quantization in PCM , 1982, IEEE Trans. Inf. Theory.

[6]  Yoshua Bengio,et al.  Convergence Properties of the K-Means Algorithms , 1994, NIPS.

[7]  Toniann Pitassi,et al.  Fairness through awareness , 2011, ITCS '12.

[8]  Jianhong Wu,et al.  Data clustering - theory, algorithms, and applications , 2007 .

[9]  Pavel Berkhin,et al.  A Survey of Clustering Data Mining Techniques , 2006, Grouping Multidimensional Data.

[10]  Krzysztof Onak,et al.  Scalable Fair Clustering , 2019, ICML.

[11]  Eric Granger,et al.  Clustering with Fairness Constraints: A Flexible and Scalable Approach , 2019, ArXiv.

[12]  Toon Calders,et al.  Building Classifiers with Independency Constraints , 2009, 2009 IEEE International Conference on Data Mining Workshops.

[13]  Santosh Vempala,et al.  Socially Fair k-Means Clustering , 2020, FAccT.

[14]  Deeparnab Chakrabarty,et al.  Fair Algorithms for Clustering , 2019, NeurIPS.

[15]  Pranjal Awasthi,et al.  A Notion of Individual Fairness for Clustering , 2020, ArXiv.

[16]  Nisheeth K. Vishnoi,et al.  Coresets for Clustering with Fairness Constraints , 2019, NeurIPS.

[17]  Paulo Cortez,et al.  A data-driven approach to predict the success of bank telemarketing , 2014, Decis. Support Syst..

[18]  Silvio Lattanzi,et al.  Fair Clustering Through Fairlets , 2018, NIPS.

[19]  Kamesh Munagala,et al.  Proportionally Fair Clustering , 2019, ICML.

[20]  Pranjal Awasthi,et al.  Guarantees for Spectral Clustering with Fairness Constraints , 2019, ICML.

[21]  Shokri Z. Selim,et al.  K-Means-Type Algorithms: A Generalized Convergence Theorem and Characterization of Local Optimality , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[22]  Nathan Srebro,et al.  Equality of Opportunity in Supervised Learning , 2016, NIPS.

[23]  Savitha Sam Abraham,et al.  Fairness in Clustering with Multiple Sensitive Attributes , 2019, EDBT.

[24]  Melanie Schmidt,et al.  Privacy preserving clustering with constraints , 2018, ICALP.

[25]  Pranjal Awasthi,et al.  Fair k-Center Clustering for Data Summarization , 2019, ICML.

[26]  Ron Kohavi,et al.  Scaling Up the Accuracy of Naive-Bayes Classifiers: A Decision-Tree Hybrid , 1996, KDD.

[27]  Sepideh Mahabadi,et al.  (Individual) Fairness for k-Clustering , 2020, ICML.

[28]  David M. Mount,et al.  A local search approximation algorithm for k-means clustering , 2002, SCG '02.

[29]  T. L. Saaty,et al.  The computational algorithm for the parametric objective function , 1955 .

[30]  Aditya Bhaskara,et al.  Fair Clustering via Equitable Group Representations , 2021, FAccT.

[31]  Andrew D. Selbst,et al.  Big Data's Disparate Impact , 2016 .