identifying clusters or clustering is an important aspect of data analysis. it is the task of grouping a set of objects in such a way those objects in the same group/cluster are more similar in some sense or another. it is a main task of exploratory data mining, and a common technique for statistical data analysis this paper proposed an improved version of k-means algorithm, namely persistent k...

Due to the progressive growth of the amount of data available in a wide variety of scientific fields, it has become more difficult to manipulate and analyze such information. Even though datasets have grown in size, the K-means algorithm remains as one of the most popular clustering methods, in spite of its dependency on the initial settings and high computational cost, especially in terms of d...

This paper shows that one can be competitive with the kmeans objective while operating online. In this model, the algorithm receives vectors v1, . . . , vn one by one in an arbitrary order. For each vector vt the algorithm outputs a cluster identifier before receiving vt+1. Our online algorithm generates Õ(k) clusters whose k-means cost is Õ(W ∗) where W ∗ is the optimal k-means cost using k cl...

Over half a century old and showing no signs of aging, k-means remains one of the most popular data processing algorithms. As is well-known, a proper initialization of k-means is crucial for obtaining a good final solution. The recently proposed k-means++ initialization algorithm achieves this, obtaining an initial set of centers that is provably close to the optimum solution. A major downside ...

We provide a clustering algorithm that approximately optimizes the k-means objective, in the one-pass streaming setting. We make no assumptions about the data, and our algorithm is very light-weight in terms of memory, and computation. This setting is applicable to unsupervised learning on massive data sets, or resource-constrained devices. The two main ingredients of our theoretical work are: ...

In this paper, we compare three initialization schemes for the KMEANS clustering algorithm: 1) random initialization (KMEANSRAND), 2) KMEANS++, and 3) KMEANSD++. Both KMEANSRAND and KMEANS++ have a major that the value of k needs to be set by the user of the algorithms. (Kang 2013) recently proposed a novel use of determinantal point processes for sampling the initial centroids for the KMEANS a...

The k-means++ seeding algorithm is one of the most popular algorithms that is used for finding the initial k centers when using the k-means heuristic. The algorithm is a simple sampling procedure and can be described as follows: Pick the first center randomly from among the given points. For i > 1, pick a point to be the i center with probability proportional to the square of the Euclidean dist...

Resumen. Sin lugar a duda el algoritmo K-means es el más utilizado en la comunidad de aprendizaje no supervisado. Desafortunadamente es muy sensible a la selección de los centroides iniciales. Debido a ello, se han propuesto un gran número de métodos para la selección de los centros iniciales. En este artículo se presenta un algoritmo de agrupamiento que tiene como base al algoritmo K-means, en...

Utilizing the sample size of a dataset, the random cluster model is employed in order to derive an estimate of the mean number of K-Means clusters to form during classification of a dataset.