Related papers: On Clusters that are Separated but Large
Designing efficient, effective, and consistent metric clustering algorithms is a significant challenge attracting growing attention. Traditional approaches focus on the stability of cluster centers; unfortunately, this neglects the…
A distributed algorithm performs local computations on pieces of input and communicates the results through given communication links. When processing a massive graph in a distributed algorithm, local outputs must be configured as a…
When you first heard people speak of Piles of PCs, the first thing that came to mind may have been a cluttered computer room with processors, monitors, and snarls of cables all around. Collections of computers have undoubtedly become more…
In this paper, we consider the problem of partitioning a small data sample of size $n$ drawn from a mixture of $2$ sub-gaussian distributions. Our work is motivated by the application of clustering individuals according to their population…
We present a scalable algorithm for the individually fair ($p$, $k$)-clustering problem introduced by Jung et al. and Mahabadi et al. Given $n$ points $P$ in a metric space, let $\delta(x)$ for $x\in P$ be the radius of the smallest ball…
We consider the problem of Gaussian mixture clustering in the high-dimensional limit where the data consists of $m$ points in $n$ dimensions, $n,m \rightarrow \infty$ and $\alpha = m/n$ stays finite. Using exact but non-rigorous methods…
This paper studies the fair range clustering problem in which the data points are from different demographic groups and the goal is to pick $k$ centers with the minimum clustering cost such that each group is at least minimally represented…
Improving the explainability of the results from machine learning methods has become an important research goal. Here, we study the problem of making clusters more interpretable by extending a recent approach of [Davidson et al., NeurIPS…
Clustering is a fundamental data processing task used for grouping records based on one or more features. In the vertically partitioned setting, data is distributed among entities, with each holding only a subset of those features. A key…
Due to the progressive growth of the amount of data available in a wide variety of scientific fields, it has become more difficult to ma- nipulate and analyze such information. Even though datasets have grown in size, the K-means algorithm…
We classify the subsets of a group by their sizes, formalize the basic methods of partitions and apply them to partition a group to subsets of prescribed sizes.
Analysis of higher-order organizations, usually small connected subgraphs called motifs, is a fundamental task on complex networks. This paper studies a new problem of testing higher-order clusterability: given query access to an undirected…
We present a $k$-means-based clustering algorithm, which optimizes the mean square error, for given cluster sizes. A straightforward application is balanced clustering, where the sizes of each cluster are equal. In the $k$-means assignment…
This paper investigates two fundamental descriptors of data, i.e., density distribution versus mass distribution, in the context of clustering. Density distribution has been the de facto descriptor of data distribution since the…
Given two sets of points $A$ and $B$ in a normed plane, we prove that there are two linearly separable sets $A'$ and $B'$ such that $\mathrm{diam}(A')\leq \mathrm{diam}(A)$, $\mathrm{diam}(B')\leq \mathrm{diam}(B)$, and $A'\cup B'=A\cup B.$…
It is well known that most of the common clustering objectives are NP-hard to optimize. In practice, however, clustering is being routinely carried out. One approach for providing theoretical understanding of this seeming discrepancy is to…
We study supervised learning problems using clustering constraints to impose structure on either features or samples, seeking to help both prediction and interpretation. The problem of clustering features arises naturally in text…
The randomized $k$-number partitioning problem is the task to distribute $N$ i.i.d. random variables into $k$ groups in such a way that the sums of the variables in each group are as similar as possible. The restricted $k$-partitioning…
We introduce and address a novel distributed clustering problem where each participant has a private dataset containing only a subset of all available features, and some features are included in multiple datasets. This scenario occurs in…
Clustering is widely used in different field such as biology, psychology, and economics. Most traditional clustering algorithms are limited to handling datasets that contain either numeric or categorical attributes. However, datasets with…