Related papers: Asymptotics for The $k$-means
Clustering is a popular form of unsupervised learning for geometric data. Unfortunately, many clustering algorithms lead to cluster assignments that are hard to explain, partially because they depend on all the features of the data in a…
Many clustering algorithms exist that estimate a cluster centroid, such as K-means, K-medoids or mean-shift, but no algorithm seems to exist that clusters data by returning exactly K meaningful modes. We propose a natural definition of a…
The $k$-means clustering algorithm and its variant, the spherical $k$-means clustering, are among the most important and popular methods in unsupervised learning and pattern detection. In this paper, we explore how the spherical $k$-means…
One key use of k-means clustering is to identify cluster prototypes which can serve as representative points for a dataset. However, a drawback of using k-means cluster centers as representative points is that such points distort the…
Most convex and nonconvex clustering algorithms come with one crucial parameter: the $k$ in $k$-means. To this day, there is not one generally accepted way to accurately determine this parameter. Popular methods are simple yet theoretically…
Comparison of three kind of the clustering and find cost function and loss function and calculate them. Error rate of the clustering methods and how to calculate the error percentage always be one on the important factor for evaluating the…
The recent framework of compressive statistical learning aims at designing tractable learning algorithms that use only a heavily compressed representation-or sketch-of massive datasets. Compressive K-Means (CKM) is such a method: it…
The classical $k$-means algorithm for partitioning $n$ points in $\mathbb{R}^d$ into $k$ clusters is one of the most popular and widely spread clustering methods. The need to respect prescribed lower bounds on the cluster sizes has been…
K-Means clustering algorithm is one of the most commonly used clustering algorithms because of its simplicity and efficiency. K-Means clustering algorithm based on Euclidean distance only pays attention to the linear distance between…
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…
Many clustering methods, including k-means, require the user to specify the number of clusters as an input parameter. A variety of methods have been devised to choose the number of clusters automatically, but they often rely on strong…
Clustering, a fundamental activity in unsupervised learning, is notoriously difficult when the feature space is high-dimensional. Fortunately, in many realistic scenarios, only a handful of features are relevant in distinguishing clusters.…
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…
In this paper, the decades-old clustering method k-means is revisited. The original distortion minimization model of k-means is addressed by a pure stochastic minimization procedure. In each step of the iteration, one sample is tentatively…
The Euclidean k-means problem is arguably the most widely-studied clustering problem in machine learning. While the k-means objective is NP-hard in the worst-case, practitioners have enjoyed remarkable success in applying heuristics like…
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…
In addition to finding meaningful clusters, centroid-based clustering algorithms such as K-means or mean-shift should ideally find centroids that are valid patterns in the input space, representative of data in their cluster. This is…
We provide necessary and sufficient conditions for the uniqueness of the k-means set of a probability distribution. This uniqueness problem is related to the choice of k: depending on the underlying distribution, some values of this…
A new cluster analysis method, $K$-quantiles clustering, is introduced. $K$-quantiles clustering can be computed by a simple greedy algorithm in the style of the classical Lloyd's algorithm for $K$-means. It can be applied to large and…
We consider the problem of estimating the number of clusters (k) in a dataset. We propose a non-parametric approach to the problem that utilizes similarity graphs to construct a robust statistic that effectively captures similarity…