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Individual fairness guarantees are often desirable properties to have, but they become hard to formalize when the dataset contains outliers. Here, we investigate the problem of developing an individually fair $k$-means clustering algorithm…
Fairness in machine learning is crucial when individuals are subject to automated decisions made by models in high-stake domains. Organizations that employ these models may also need to satisfy regulations that promote responsible and…
We study the problem of clustering with relative constraints, where each constraint specifies relative similarities among instances. In particular, each constraint $(x_i, x_j, x_k)$ is acquired by posing a query: is instance $x_i$ more…
The area of constrained clustering has been extensively explored by researchers and used by practitioners. Constrained clustering formulations exist for popular algorithms such as k-means, mixture models, and spectral clustering but have…
The issue of fairness in machine learning models has recently attracted a lot of attention as ensuring it will ensure continued confidence of the general public in the deployment of machine learning systems. We focus on mitigating the harm…
The min-knapsack problem with compactness constraints extends the classical knapsack problem, in the case of ordered items, by introducing a restriction ensuring that they cannot be too far apart. This problem has applications in…
Finding a good clustering of vertices in a network, where vertices in the same cluster are more tightly connected than those in different clusters, is a useful, important, and well-studied task. Many clustering algorithms scale well,…
Machine learning algorithms can produce biased outcome/prediction, typically, against minorities and under-represented sub-populations. Therefore, fairness is emerging as an important requirement for the large scale application of machine…
We study coresets for clustering with capacity and fairness constraints. Our main result is a near-linear time algorithm to construct $\tilde{O}(k^2\varepsilon^{-2z-2})$-sized $\varepsilon$-coresets for capacitated $(k,z)$-clustering which…
Fairness in algorithmic decision-making is often framed in terms of individual fairness, which requires that similar individuals receive similar outcomes. A system violates individual fairness if there exists a pair of inputs differing only…
Clustering is an unsupervised machine learning methodology where unlabeled elements/objects are grouped together aiming to the construction of well-established clusters that their elements are classified according to their similarity. The…
We study the following distribution clustering problem: Given a hidden partition of $k$ distributions into two groups, such that the distributions within each group are the same, and the two distributions associated with the two clusters…
Connected clustering denotes a family of constrained clustering problems in which we are given a distance metric and an undirected connectivity graph $G$ that can be completely unrelated to the metric. The aim is to partition the $n$…
The independence clustering problem is considered in the following formulation: given a set $S$ of random variables, it is required to find the finest partitioning $\{U_1,\dots,U_k\}$ of $S$ into clusters such that the clusters…
Unsupervised learning is widely recognized as one of the most important challenges facing machine learning nowa- days. However, in spite of hundreds of papers on the topic being published every year, current theoretical understanding and…
Hierarchical clustering is a popular unsupervised data analysis method. For many real-world applications, we would like to exploit prior information about the data that imposes constraints on the clustering hierarchy, and is not captured by…
Clustering is a NP-hard problem. Thus, no optimal algorithm exists, heuristics are applied to cluster the data. Heuristics can be very resource-intensive, if not applied properly. For substantially large data sets computational efficiencies…
With rapidly increasing data, clustering algorithms are important tools for data analytics in modern research. They have been successfully applied to a wide range of domains; for instance, bioinformatics, speech recognition, and financial…
Centroid based clustering methods such as k-means, k-medoids and k-centers are heavily applied as a go-to tool in exploratory data analysis. In many cases, those methods are used to obtain representative centroids of the data manifold for…
Clustering algorithms aim to organize data into groups or clusters based on the inherent patterns and similarities within the data. They play an important role in today's life, such as in marketing and e-commerce, healthcare, data…