Related papers: An initialization method for the k-means using the…
K-means defines one of the most employed centroid-based clustering algorithms with performances tied to the data's embedding. Intricate data embeddings have been designed to push $K$-means performances at the cost of reduced theoretical…
The k-means objective is arguably the most widely-used cost function for modeling clustering tasks in a metric space. In practice and historically, k-means is thought of in a continuous setting, namely where the centers can be located…
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…
One of the most employed yet simple algorithm for cluster analysis is the k-means algorithm. k-means has successfully witnessed its use in artificial intelligence, market segmentation, fraud detection, data mining, psychology, etc., only to…
We combine K-means clustering with the least-squares kernel classification method. K-means clustering is used to extract a set of representative vectors for each class. The least-squares kernel method uses these representative vectors as a…
Clustering is a key task in machine learning, with $k$-means being widely used for its simplicity and effectiveness. While 1D clustering is common, existing methods often fail to exploit the structure of 1D data, leading to inefficiencies.…
Organizing data into semantically more meaningful is one of the fundamental modes of understanding and learning. Cluster analysis is a formal study of methods for understanding and algorithm for learning. K-mean clustering algorithm is one…
The Euclidean $k$-median problem is defined in the following manner: given a set $\mathcal{X}$ of $n$ points in $\mathbb{R}^{d}$, and an integer $k$, find a set $C \subset \mathbb{R}^{d}$ of $k$ points (called centers) such that the cost…
The $k$-Means algorithm is one of the most popular choices for clustering data but is well-known to be sensitive to the initialization process. There is a substantial number of methods that aim at finding optimal initial seeds for…
Traditionally, practitioners initialize the {\tt k-means} algorithm with centers chosen uniformly at random. Randomized initialization with uneven weights ({\tt k-means++}) has recently been used to improve the performance over this…
This paper introduces k-splits, an improved hierarchical algorithm based on k-means to cluster data without prior knowledge of the number of clusters. K-splits starts from a small number of clusters and uses the most significant data…
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 present a new clustering algorithm called k-means-u* which in many cases is able to significantly improve the clusterings found by k-means++, the current de-facto standard for clustering in Euclidean spaces. First we introduce the…
The classical center based clustering problems such as $k$-means/median/center assume that the optimal clusters satisfy the locality property that the points in the same cluster are close to each other. A number of clustering problems arise…
We propose a simple and efficient clustering method for high-dimensional data with a large number of clusters. Our algorithm achieves high-performance by evaluating distances of datapoints with a subset of the cluster centres. Our…
Spherical k-Means is frequently used to cluster document collections because it performs reasonably well in many settings and is computationally efficient. However, the time complexity increases linearly with the number of clusters k, which…
Clustering is a widely used and powerful machine learning technique, but its effectiveness is often limited by the need to specify the number of clusters, k, or by relying on thresholds that implicitly determine k. We introduce k*-means, a…
In the Euclidean $k$-Means problem we are given a collection of $n$ points $D$ in an Euclidean space and a positive integer $k$. Our goal is to identify a collection of $k$ points in the same space (centers) so as to minimize the sum of the…
The K-Means clustering using LLoyd's algorithm is an iterative approach to partition the given dataset into K different clusters. The algorithm assigns each point to the cluster based on the following objective function \[\ \min…
The input to the \emph{sets-$k$-means} problem is an integer $k\geq 1$ and a set $\mathcal{P}=\{P_1,\cdots,P_n\}$ of sets in $\mathbb{R}^d$. The goal is to compute a set $C$ of $k$ centers (points) in $\mathbb{R}^d$ that minimizes the sum…