k-means++ is a seeding technique for the k-means method with an expected approximation ratio of O(log k), where k denotes the number of clusters. Examples are known on which the expected approximation ratio of k-means++ is Ω(log k), showing that the upper bound is asymptotically tight. However, it remained open whether k-means++ yields an O(1)-approximation with probability 1/poly(k) or even wi...

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. In spite of its dependency on the initial settings and the large number of distance computations that it can require to converge, the K-means algorithm remains as one of the most popular clustering methods for massive data...

The k-means++ algorithm is the state of the art algorithm to solve k-Means clustering problems as the computed clusterings are O(log k) competitive in expectation. However, its seeding step requires k inherently sequential passes through the full data set making it hard to scale to massive data sets. The standard remedy is to use the k-means‖ algorithm which reduces the number of sequential rou...

We run experiments showing that algorithm clarans (Ng et al., 2005) finds better Kmedoids solutions than the standard algorithm. This finding, along with the similarity between the standard K-medoids and K-means algorithms, suggests that clarans may be an effective K-means initializer. We show that this is the case, with clarans outperforming other popular seeding algorithms on 23/23 datasets w...

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...

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...