We run experiments showing that algorithm clarans (, 2005) finds better K-medoids solutions than the Voronoi iteration algorithm. This finding, along with the similarity between the Voronoi iteration algorithm and Lloyd's K-means algorithm, suggests that clarans may be an effective K-means initializer. We show that this is the case, with clarans outperforming other seeding algorithms on 23 23 datasets with a mean decrease over K-means++ of 30 for initialization mse and 3 or final mse. We describe how the complexity and runtime of clarans can be improved, making it a viable initialization scheme for large datasets.
Alternatives to have been considered which resemble the swapping approach of . One is by @cite_5 , where points are randomly selected and reassigned. @cite_4 show how this heuristic can result in better clustering when there are few points per cluster.
@cite_5 @cite_4
2199495299 201974436 1981081578 1916116059
In k-means clustering we are given a set of n data points in d-dimensional space Rd and an integer k, and the problem is to determine a set of k points in &#211C;d, called centers, to minimize the mean squared distance from each data point to its nearest center. No exact polynomial-time algorithms are known for this problem. Although asymptotically efficient approximation algorithms exist, these algorithms are not practical due to the extremely high constant factors involved. There are many heuristics that are used in practice, but we know of no bounds on their performance.We consider the question of whether there exists a simple and practical approximation algorithm for k-means clustering. We present a local improvement heuristic based on swapping centers in and out. We prove that this yields a (9+e)-approximation algorithm. We show that the approximation factor is almost tight, by giving an example for which the algorithm achieves an approximation factor of (9-e). To establish the practical value of the heuristic, we present an empirical study that shows that, when combined with Lloyd's algorithm, this heuristic performs quite well in practice. Multi-view clustering, which seeks a partition of the data in multiple views that often provide complementary information to each other, has received considerable attention in recent years. In real life clustering problems, the data in each view may have considerable noise. However, existing clustering methods blindly combine the information from multi-view data with possibly considerable noise, which often degrades their performance. In this paper, we propose a novel Markov chain method for Robust Multi-view Spectral Clustering (RMSC). Our method has a flavor of lowrank and sparse decomposition, where we firstly construct a transition probability matrix from each single view, and then use these matrices to recover a shared low-rank transition probability matrix as a crucial input to the standard Markov chain method for clustering. The optimization problem of RMSC has a low-rank constraint on the transition probability matrix, and simultaneously a probabilistic simplex constraint on each of its rows. To solve this challenging optimization problem, we propose an optimization procedure based on the Augmented Lagrangian Multiplier scheme. Experimental results on various real world datasets show that the proposed method has superior performance over several state-of-the-art methods for multi-view clustering. This paper presents a detailed empirical study of 12 generative approaches to text clustering, obtained by applying four types of document-to-cluster assignment strategies (hard, stochastic, soft and deterministic annealing (DA) based assignments) to each of three base models, namely mixtures of multivariate Bernoulli, multinomial, and von Mises-Fisher (vMF) distributions. A large variety of text collections, both with and without feature selection, are used for the study, which yields several insights, including (a) showing situations wherein the vMF-centric approaches, which are based on directional statistics, fare better than multinomial model-based methods, and (b) quantifying the trade-off between increased performance of the soft and DA assignments and their increased computational demands. We also compare all the model-based algorithms with two state-of-the-art discriminative approaches to document clustering based, respectively, on graph partitioning (CLUTO) and a spectral coclustering method. Overall, DA and CLUTO perform the best but are also the most computationally expensive. The vMF models provide good performance at low cost while the spectral coclustering algorithm fares worse than vMF-based methods for a majority of the datasets. Hartigan’s method for k-means clustering is the following greedy heuristic: select a point, and optimally reassign it. This paper develops two other formulations of the heuristic, one leading to a number of consistency properties, the other showing that the data partition is always quite separated from the induced Voronoi partition. A characterization of the volume of this separation is provided. Empirical tests verify not only good optimization performance relative to Lloyd’s method, but also good running time.