In this work, we study the k-means cost function. The (Euclidean) k-means problem can be described as follows: given a dataset X ⊆ R and a positive integer k, find a set of k centers C ⊆ R such that Φ(C,X) def = ∑ x∈X minc∈C ||x− c|| 2 is minimized. Let ∆k(X) def = minC⊆Rd Φ(C,X) denote the cost of the optimal k-means solution. It is simple to observe that for any dataset X, ∆k(X) decreases as ...

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 ...

Due to intensity overlaps between interested objects caused by noise and intensity inhomogeneity, image segmentation is still an open problem. In this paper, we propose a framework to segment images in the well-known image model in which intensities of the observed image are viewed as a product of the true image and the bias field. In the proposed framework, a CUDA accelerated non-local means 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...

The aim of the contribution is the discussion of some types and classes of means on ordinal scales, especially kernel and shift invariant ordinal means, weighted ordinal means based on weighted divisible t–conorms (t–norms) and dissimilarity based ordinal means. Moreover, several types of ordinal arithmetic means are introduced.

We propose a definition for geometric mean of k positive (semi) definite matrices. We show that our definition is the only one in the literature that has the properties that one would expect from a geometric mean, and that our geometric mean generalizes many inequalities satisfied by the geometric mean of two positive semidefinite matrices. We prove some new properties of the geometric mean of ...

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 ...