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...

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: ...

We consider the popular k-means problem in d-dimensional Euclidean space. Recently Friggstad, Rezapour, Salavatipour [FOCS’16] and Cohen-Addad, Klein, Mathieu [FOCS’16] showed that the standard local search algorithm yields a p1`εq-approximation in time pn ̈kq Opdq , giving the first polynomialtime approximation scheme for the problem in low-dimensional Euclidean space. While local search achiev...

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...

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...