Related papers: The Mean Partition Theorem of Consensus Clustering

Cluster analysis has attracted more and more attention in the field of machine learning and data mining. Numerous clustering algorithms have been proposed and are being developed due to diverse theories and various requirements of emerging…

We continue the investigation of problems concerning correlation clustering or clustering with qualitative information, which is a clustering formulation that has been studied recently. The basic setup here is that we are given as input a…

Clustering is an effective technique in data mining to generate groups that are the matter of interest. Among various clustering approaches, the family of k-means algorithms and min-cut algorithms gain most popularity due to their…

Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…

We study the problem of finding low-cost Fair Clusterings in data where each data point may belong to many protected groups. Our work significantly generalizes the seminal work of Chierichetti et.al. (NIPS 2017) as follows. - We allow the…

The Kemeny aggregation problem consists of computing the consensus rankings of an election with respect to the well-known Kemeny-Young voting method. These consensus rankings satisfy various fundamental properties and are the geometric…

Set partitioning is a key component of many algorithms in machine learning, signal processing, and communications. In general, the problem of finding a partition that minimizes a given impurity (loss function) is NP-hard. As such, there…

Clustering algorithms are widely utilized for many modern data science applications. This motivates the need to make outputs of clustering algorithms fair. Traditionally, new fair algorithmic variants to clustering algorithms are developed…

The well known maximum-entropy principle due to Jaynes, which states that given mean parameters, the maximum entropy distribution matching them is in an exponential family, has been very popular in machine learning due to its "Occam's…

A measure of distance between two clusterings has important applications, including clustering validation and ensemble clustering. Generally, such distance measure provides navigation through the space of possible clusterings. Mostly used…

We present a stochastic version of the mean-shift clustering algorithm. In this stochastic version a randomly chosen sequence of data points move according to partial gradient ascent steps of the objective function. Theoretical results…

$K$-means clustering is one of the most widely-used partitioning algorithm in cluster analysis due to its simplicity and computational efficiency. However, $K$-means does not provide an appropriate clustering result when applying to data…

We establish Multilayer Correlation Clustering, a novel generalization of Correlation Clustering to the multilayer setting. In this model, we are given a series of inputs of Correlation Clustering (called layers) over the common set $V$ of…

We present a clustering method and provide a theoretical analysis and an explanation to a phenomenon encountered in the applied statistical literature since the 1990's. This phenomenon is the natural adaptability of the order when using a…

Many clustering problems in computer vision and other contexts are also classification problems, where each cluster shares a meaningful label. Subspace clustering algorithms in particular are often applied to problems that fit this…

We consider a large class of random geometric graphs constructed from samples $\mathcal{X}_n = \{X_1,X_2,\ldots,X_n\}$ of independent, identically distributed observations of an underlying probability measure $\nu$ on a bounded domain…

We consider the problem of estimating the missing mass, partition function or evidence and its probability distribution in the case that for each sample point in the discrete sample space its (unnormalized) probability mass is revealed.…

We initiate the study of the following general clustering problem. We seek to partition a given set $P$ of data points into $k$ clusters by finding a set $X$ of $k$ centers and assigning each data point to one of the centers. The cost of a…

Proportional fairness criteria inspired by democratic ideals of proportional representation have received growing attention in the clustering literature. Prior work has investigated them in two separate paradigms. Chen et al. [ICML 2019]…

Clustering algorithms remain valuable tools for grouping and summarizing the most important aspects of data. Example areas where this is the case include image segmentation, dimension reduction, signals analysis, model order reduction,…