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...

Clustering sets of histograms has become popular thanks to the success of the generic method of bag-of-X used in text categorization and in visual categorization applications. In this paper, we investigate the use of a parametric family of distortion measures, called the α-divergences, for clustering histograms. Since it usually makes sense to deal with symmetric divergences in information retr...

Data mining has been defined as "The nontrivial extraction of implicit, previously unknown, and potentially useful information from data". Clustering is the automated search for group of related observations in a data set. The K-Means method is one of the most commonly used clustering techniques for a variety of applications. This paper proposes a method for making the K-Means algorithm more ef...

Many datasets include feature values that are missing but may be acquired at a cost. In this paper, we consider the clustering task for such datasets, and address the problem of acquiring missing feature values that improve clustering quality in a cost-effective manner. Since acquiring all missing information may be unnecessarily expensive, we propose a framework for iteratively selecting featu...

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...

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....

Does K-Means reasonably divides the data into k groups is an important question that arises when one works on Image Segmentation? Which color space one should choose and how to ascertain that the k we determine is valid? The purpose of this study was to explore the answers to aforementioned questions. We perform K-Means on a number of 2-cluster, 3cluster and k-cluster color images (k>3) in RGB ...