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pro vyhledávání: '"Blömer, Johannes"'
The fuzzy $K$-means problem is a popular generalization of the well-known $K$-means problem to soft clusterings. We present the first coresets for fuzzy $K$-means with size linear in the dimension, polynomial in the number of clusters, and poly-logar
Externí odkaz:
http://arxiv.org/abs/1612.07516
Training the parameters of statistical models to describe a given data set is a central task in the field of data mining and machine learning. A very popular and powerful way of parameter estimation is the method of maximum likelihood estimation (MLE
Externí odkaz:
http://arxiv.org/abs/1603.06478
The $k$-means algorithm is one of the most widely used clustering heuristics. Despite its simplicity, analyzing its running time and quality of approximation is surprisingly difficult and can lead to deep insights that can be used to improve the algo
Externí odkaz:
http://arxiv.org/abs/1602.08254
The fuzzy $K$-means problem is a generalization of the classical $K$-means problem to soft clusterings, i.e. clusterings where each points belongs to each cluster to some degree. Although popular in practice, prior to this work the fuzzy $K$-means pr
Externí odkaz:
http://arxiv.org/abs/1512.05947
Autor:
Blömer, Johannes, Kohn, Kathlén
We study the geometry and complexity of Voronoi cells of lattices with respect to arbitrary norms. On the positive side, we show for strictly convex and smooth norms that the geometry of Voronoi cells of lattices in any dimension is similar to the Eu
Externí odkaz:
http://arxiv.org/abs/1512.00720
Autor:
Blömer, Johannes, Bujna, Kathrin
We present new initialization methods for the expectation-maximization algorithm for multivariate Gaussian mixture models. Our methods are adaptions of the well-known $K$-means++ initialization and the Gonzalez algorithm. Thereby we aim to close the
Externí odkaz:
http://arxiv.org/abs/1312.5946
In this paper we provide a new analysis of the SEM algorithm. Unlike previous work, we focus on the analysis of a single run of the algorithm. First, we discuss the algorithm for general mixture distributions. Second, we consider Gaussian mixture mod
Externí odkaz:
http://arxiv.org/abs/1310.5034
Autor:
Blömer, Johannes, Naewe, Stefanie
In this paper, we present a deterministic algorithm for the closest vector problem for all l_p-norms, 1 < p < \infty, and all polyhedral norms, especially for the l_1-norm and the l_{\infty}-norm. We achieve our results by introducing a new lattice p
Externí odkaz:
http://arxiv.org/abs/1104.3720
Publikováno v:
Ackermann, M. R., Bl\"omer, J., Kuntze, D., and Sohler, C. (2014). Analysis of Agglomerative Clustering. Algorithmica, 69(1):184-215
The diameter $k$-clustering problem is the problem of partitioning a finite subset of $\mathbb{R}^d$ into $k$ subsets called clusters such that the maximum diameter of the clusters is minimized. One early clustering algorithm that computes a hierarch
Externí odkaz:
http://arxiv.org/abs/1012.3697