We prove in this paper that the expected value of the objective function of the k-means++ algorithm for samples converges to population expected value. As k-means++, for samples, provides with constant factor approximation for k-means objectives, such an approximation can be achieved for the population with increase of the sample size. This result is of potential practical relevance when one is...

This is the Supplementary Information to Paper ”k-variates++: more pluses in the kmeans++”, appearing in the proceedings of ICML 2016. Notation “main file” indicates reference to the paper.

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 k-means-u algorithm which starts from a result of k-means++ and attempts to improve it with a sequence of non-local “jumps” alternated by runs of standard k-means....

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 the given points. For i > 1, pick a point to be the i center with probability proportional to the square of the Euclidean distance o...

Even though virtualization provides a lot of advantages in cloud computing, it does not provide effective performance isolation between the virtualization machines. In other words, the performance may get affected due the interferences caused by co-virtual machines. This can be achieved by the proper management of resource allocations between the Virtual Machines running simultaneously. This pa...

We introduce a bimodal epistemic logic intended to capture knowledge as truth in all epistemically alternative states and belief as a generalized ‘majority ’ quantifier, interpreted as truth in many (a ‘majority ’ of the) epistemically alternative states. This doxastic interpretation is of interest in KR applications and it also has an independent philosophical and technical interest. The logic...

This paper presents an RK-means clustering algorithm which is developed for reliable data grouping by introducing a new reliability evaluation to the K-means clustering algorithm. The conventional K-means clustering algorithm has two shortfalls: 1) the clustering result will become unreliable if the assumed number of the clusters is incorrect; 2) during the update of a cluster center, all the d...

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...