Related papers: Individual Preference Stability for Clustering
Clustering is a fundamental data mining tool that aims to divide data into groups of similar items. Generally, intuition about clustering reflects the ideal case -- exact data sets endowed with flawless dissimilarity between individual…
The objective of clustering is to discover natural groups in datasets and to identify geometrical structures which might reside there, without assuming any prior knowledge on the characteristics of the data. The problem can be seen as…
Clustering with most objective functions is NP-Hard, even to approximate well in the worst case. Recently, there has been work on exploring different notions of stability which lend structure to the problem. The notion of stability,…
We study stable matching problems with locality of information and control. In our model, each agent is a node in a fixed network and strives to be matched to another agent. An agent has a complete preference list over all other agents it…
A cluster id assignment scheme labels each cluster of a clustering with a distinct id. The goal of id assignment is semantic id stability, which means that, whenever possible, a cluster for the same underlying concept as that of a…
Consensus clustering seeks to combine multiple clusterings of the same dataset, potentially derived by considering various non-sensitive attributes by different agents in a multi-agent environment, into a single partitioning that best…
We give a local search based algorithm for $k$-median and $k$-means (and more generally for any $k$-clustering with $\ell_p$ norm cost function) from the perspective of individual fairness. More precisely, for a point $x$ in a point set $P$…
Clustering methods must be tailored to the dataset it operates on, as there is no objective or universal definition of ``cluster,'' but nevertheless arbitrariness in the clustering method must be minimized. This paper develops a…
Cluster synchronization is a phenomenon in which a network self-organizes into a pattern of synchronized sets. It has been shown that diverse patterns of stable cluster synchronization can be captured by symmetries of the network. Here we…
Given the widespread popularity of spectral clustering (SC) for partitioning graph data, we study a version of constrained SC in which we try to incorporate the fairness notion proposed by Chierichetti et al. (2017). According to this…
We study the canonical fair clustering problem where each cluster is constrained to have close to population-level representation of each group. Despite significant attention, the salient issue of having incomplete knowledge about the group…
Determining the number of clusters present in a dataset is an important problem in cluster analysis. Conventional clustering techniques generally assume this parameter to be provided up front. %user supplied. %Recently, robustness of any…
The problem of clustering is considered, for the case when each data point is a sample generated by a stationary ergodic process. We propose a very natural asymptotic notion of consistency, and show that simple consistent algorithms exist,…
The problem of clustering is considered, for the case when each data point is a sample generated by a stationary ergodic process. We propose a very natural asymptotic notion of consistency, and show that simple consistent algorithms exist,…
Spectral clustering is popular among practitioners and theoreticians alike. While performance guarantees for spectral clustering are well understood, recent studies have focused on enforcing ``fairness'' in clusters, requiring them to be…
We introduce a generalized version of the famous Stable Marriage problem, now based on multi-modal preference lists. The central twist herein is to allow each agent to rank its potentially matching counterparts based on more than one…
We consider the problem of center-based clustering in low-dimensional Euclidean spaces under the perturbation stability assumption. An instance is $\alpha$-stable if the underlying optimal clustering continues to remain optimal even when…
The separability of clusters is one of the most desired properties in clustering. There is a wide range of settings in which different clusterings of the same data set appear. We are interested in applications where there is a need for an…
In this paper, we consider a matroid generalization of the stable matching problem. In particular, we consider the setting where preferences may contain ties. For this generalization, we propose a polynomial-time algorithm for the problem…
Internal measures that are used to assess the quality of a clustering usually take into account intra-group and/or inter-group criteria. There are many papers in the literature that propose algorithms with provable approximation guarantees…