Related papers: k-means requires exponentially many iterations eve…

K-means clustering is an unsupervised clustering method that requires an initial decision of number of clusters. One method to determine the number of clusters is the elbow method, a heuristic method that relies on visual representation.…

We design a new algorithm for the Euclidean $k$-means problem that operates in the local model of differential privacy. Unlike in the non-private literature, differentially private algorithms for the $k$-means objective incur both additive…

We consider the problem of approximate $K$-means clustering with outliers and side information provided by same-cluster queries and possibly noisy answers. Our solution shows that, under some mild assumptions on the smallest cluster size,…

The price of explainability for a clustering task can be defined as the unavoidable loss,in terms of the objective function, if we force the final partition to be explainable. Here, we study this price for the following clustering problems:…

The $k$-means algorithm is arguably the most popular nonparametric clustering method but cannot generally be applied to datasets with incomplete records. The usual practice then is to either impute missing values under an assumed…

$k-$means Clustering requires as input the exact value of $k$, the number of clusters. Two challenges are open: (i) Is there a data-determined definition of $k$ which is provably correct and (ii) Is there a polynomial time algorithm to find…

We propose a novel clustering model encompassing two well-known clustering models: k-center clustering and k-median clustering. In the Hybrid k-Clusetring problem, given a set P of points in R^d, an integer k, and a non-negative real r, our…

K-Medoids(KM) is a standard clustering method, used extensively on semi-metric data.Error analyses of KM have traditionally used an in-sample notion of error,which can be far from the true error and suffer from generalization gap. We…

Application of K-Means algorithm is restricted by the fact that the number of clusters should be known beforehand. Previously suggested methods to solve this problem are either ad hoc or require parametric assumptions and complicated…

Given a set of $n$ points in the Euclidean plane, such that just $k$ points are strictly inside the convex hull of the whole set, we want to find the shortest tour visiting every point. The fastest known algorithm for the version when $k$…

$k$-means clustering is a fundamental problem in unsupervised learning. The problem concerns finding a partition of the data points into $k$ clusters such that the within-cluster variation is minimized. Despite its importance and wide…

The $k$-center problem is to choose a subset of size $k$ from a set of $n$ points such that the maximum distance from each point to its nearest center is minimized. Let $Q=\{Q_1,\ldots,Q_n\}$ be a set of polygons or segments in the…

We study the computational complexity of some explainable clustering problems in the framework proposed by [Dasgupta et al., ICML 2020], where explainability is achieved via axis-aligned decision trees. We consider the $k$-means,…

$k$-means algorithm is one of the most classical clustering methods, which has been widely and successfully used in signal processing. However, due to the thin-tailed property of the Gaussian distribution, $k$-means algorithm suffers from…

Clustering algorithms are a cornerstone of machine learning applications. Recently, a quantum algorithm for clustering based on the k-means algorithm has been proposed by Kerenidis, Landman, Luongo and Prakash. Based on their work, we…

Machine learning algorithms perform well on identifying patterns in many different datasets due to their versatility. However, as one increases the size of the dataset, the computation time for training and using these statistical models…

In this paper, we study clustering with respect to the k-modes objective function, a natural formulation of clustering for categorical data. One of the main contributions of this paper is to establish the connection between k-modes and…

Clustering is one of the most fundamental and important tasks in data mining. Traditional clustering algorithms, such as K-means, assign every data point to exactly one cluster. However, in real-world datasets, the clusters may overlap with…

Given a quadratic map Q : K^n -> K^k defined over a computable subring D of a real closed field K, and a polynomial p(Y_1,...,Y_k) of degree d, we consider the zero set Z=Z(p(Q(X)),K^n) of the polynomial p(Q(X_1,...,X_n)). We present a…

The $K$-means algorithm is extended to allow for partitioning of skewed groups. Our algorithm is called TiK-Means and contributes a $K$-means type algorithm that assigns observations to groups while estimating their skewness-transformation…