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, ...

Designing tools that support group formation is a challenging goal for both the areas of adaptive and collaborative e-learning environments. Group formation may be used for a variety of purposes such as for grouping students that could potentially benefit from cooperation based on their individual characteristics or needs, for mediating peer help by matching peer learners, for facilitating inst...

This paper shows that one can be competitive with the kmeans objective while operating online. In this model, the algorithm receives vectors v1, . . . , vn one by one in an arbitrary order. For each vector vt the algorithm outputs a cluster identifier before receiving vt+1. Our online algorithm generates Õ(k) clusters whose k-means cost is Õ(W ∗) where W ∗ is the optimal k-means cost using k cl...

In this paper we present a new clustering method based on k-means that has been implemented on a video surveillance system. Rekmeans does not require to specify in advance the number of clusters to search for and is more precise than k-means in clustering data coming from multiple Gaussian distributions with different co-variances, while maintaining real-time performance. Experiments on real an...

K-means (MacQueen, 1967) [1] is one of the simplest unsupervised learning algorithms that solve the well-known clustering problem. The procedure follows a simple and easy way to classify a given data set to a predefined, say K number of clusters. Determination of K is a difficult job and it is not known that which value of K can partition the objects as per our intuition. To overcome this probl...

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...

The k-means++ seeding algorithm is one of the most popular algorithms that is used for finding the initial k centers when using the k-means heuristic. The algorithm is a simple sampling procedure and can be described as follows: Pick the first center randomly from among the given points. For i > 1, pick a point to be the i center with probability proportional to the square of the Euclidean dist...

Much work has sought to discern the different types of cloud regimes, typically via Euclidean k-means clustering of histograms. However, these methods ignore the underlying similarity structure of cloud types. Wasserstein k-means clustering is a promising candidate for utilizing this structure during clustering, but existing algorithms do not scale well and lack the quality guarantees of the Eu...

Identifying clusters is an important aspect of data analysis. This paper proposes a noveldata clustering algorithm to increase the clustering accuracy. A novel game theoretic self-organizingmap (NGTSOM ) and neural gas (NG) are used in combination with Competitive Hebbian Learning(CHL) to improve the quality of the map and provide a better vector quantization (VQ) for clusteringdata. Different ...

In this paper we propose a new evolutionary clustering algorithm named E-means. E-means is an Evolutionary extension of k-means algorithm that is composed by a revised k-means algorithm and an evolutionary approach to Gaussian mixture model, which estimates automatically the number of clusters and the optimal mean for each cluster. More specifically, the proposed Emeans algorithm defines an ent...