This paper presents a generalized version of the conventional k-means clustering algorithm [Proceedings of 5th Berkeley Symposium on Mathematical Statistics and Probability, 1, University of California Press, Berkeley, 1967, p. 281]. Not only is this new one applicable to ellipse-shaped data clusters without dead-unit problem, but also performs correct clustering without pre-assigning the exact...

k-means++ [5] seeding procedure is a simple sampling based algorithm that is used to quickly find k centers which may then be used to start the Lloyd’s method. There has been some progress recently on understanding this sampling algorithm. Ostrovsky et al. [10] showed that if the data satisfies the separation condition that ∆k−1(P ) ∆k(P ) ≥ c (∆i(P ) is the optimal cost w.r.t. i centers, c > 1...

We investigate, theoretically and empirically, the effectiveness of kernel K-means++ samples as landmarks in the Nyström method for low-rank approximation of kernel matrices. Previous empirical studies (Zhang et al., 2008; Kumar et al., 2012) observe that the landmarks obtained using (kernel) K-means clustering define a good lowrank approximation of kernel matrices. However, the existing work d...

The Lloyd’s algorithm, also known as the k-means algorithm, is one of the most popular algorithms for solving the k-means clustering problem in practice. However, it does not give any performance guarantees. This means that there are datasets on which this algorithm can behave very badly. One reason for poor performance on certain datasets is bad initialization. The following simple sampling ba...

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...

In this paper we propose to jointly consider Segmental Dynamic Time Warping and distance clustering for the unsupervised learning of acoustic events. As a result, the computational complexity increases only linearly with the dababase size compared to a quadratic increase in a sequential setup, where all pairwise SDTW distances between segments are computed prior to clustering. Further, we discu...

This study presents the results of an experimental study of two document clustering techniques which are kmeans and k-means++. In particular, we compare the two main approaches in crime document clustering. The drawback of k-means is that the user needs to define the centroid point. This becomes more critical when dealing with document clustering because each center point represented by a word ...

In this paper we present an online unsupervised method based on clustering to find defects in concrete structures using hammering. First, the initial dataset of sound samples is roughly clustered using the k-means algorithm with the k-means++ seeding procedure in order to find the cluster best representative of the structure. Then the regular model for the hammering sound, the centroid of this ...