<p style='text-indent:20px;'>The <inline-formula><tex-math id="M2">\begin{document}$ k $\end{document}</tex-math></inline-formula>-means problem is a classical combinatorial optimization which has lots of applications in many fields such as machine learning, data mining, etc. We consider variant id="M3">\begin{document}$ the spherical space, that is, id="M4">...

Let us define some notation which will help us analyze the algorithm. L := A solution (k-subset) returned by Local Search. Copt := An optimal solution for the k-median problem. We will eventually show that Cost(L) ≤ 5 · Cost(Copt). For any p ∈ P,C ⊆ P, NN(p, C) := c̄ ∈ C that minimizes d(p, ·). So d(p,NN(p, C)) = d(p, C) by definition. Also, for any C ⊆ P, c̄ ∈ C, Cluster(C, c̄) := {q ∈ P | NN(q, ...

This paper investigates the following natural greedy procedure for clustering in the bi-criterion setting: iteratively grow a set of centers, in each round adding the center from a candidate set that maximally decreases clustering cost. In the case of k-medians and k-means, the key results are as follows. • When the method considers all data points as candidate centers, then selecting O(k log(1...

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The growth in interest in RGB-D devices (e.g. Microsoft Kinect or ASUS Xtion Pro) is based on their low price, as well as the wide range of possible applications. These devices can provide skeletal data consisting of 3D position, as well as orientation data, which can be further used for pose or action recognition. Data for 15 or 20 joints can be retrieved, depending on the libraries used. Rece...

Data clustering is a process of arranging similar data into groups. A clustering algorithm partitions a data set into several groups such that the similarity within a group is better than among groups. In this paper a hybrid clustering algorithm based on K-mean and K-harmonic mean (KHM) is described. The proposed algorithm is tested on five different datasets. The research is focused on fast an...

Clustering of relational data has so far received a lot less attention than classification of such data. In this paper we investigate a simple approach based on randomized propositionalization, which allows for applying standard clustering algorithms like KMeans to multi-relational data. We describe how random rules are generated and then turned into boolean-valued features. Clustering generall...

We present a simultaneous generalization of the well-known Karhunen-Loéve (PCA) and k-means algorithms. The basic idea lies in approximating the data with k affine subspaces of a given dimension n. In the case n = 0 we obtain the classical k-means, while for k = 1 we obtain PCA algorithm. Moreover, by our approach we can obtain clusters with different dimensionality which describe the structure...

The k-means algorithm is a widely used clustering technique. Here we will examine the performance of multiple implementations of the k-means algorithm in different settings. Our discussion will touch on the implementation of the algorithm in both python and C, and will also mention a 3rd party package for the k-means algorithm that is also written in C but provides python bindings. We will then...