An Arithmetic-Based Deterministic Centroid Initialization Method for the k-Means Clustering Algorithm

One of the greatest challenges in k-means clustering is positioning the initial cluster centers, or centroids, as close to optimal as possible, and doing so in an amount of time deemed reasonable. Traditional fc-means utilizes a randomization process for initializing these centroids, and poor initialization can lead to increased numbers of required clustering iterations to reach convergence, and a greater overall runtime. This research proposes a simple, arithmetic-based deterministic centroid initialization method which is much faster than randomized initialization. Preliminary experiments suggest that this collection of methods, referred to herein as the sharding centroid initialization algorithm family, often outperforms random initialization in terms of the required number of iterations for convergence and overall time-related metrics and is competitive or better in terms of the reported mean sum of squared errors (SSE) metric. Surprisingly, the sharding algorithms often manage to report more advantageous mean SSE values in the instances where their performance is slower than random initialization

Inference and Evaluation of the Multinomial Mixture Model for Text Clustering

In this article, we investigate the use of a probabilistic model for unsupervised clustering in text collections. Unsupervised clustering has become a basic module for many intelligent text processing applications, such as information retrieval, text classification or information extraction. The model considered in this contribution consists of a mixture of multinomial distributions over the word counts, each component corresponding to a different theme. We present and contrast various estimation procedures, which apply both in supervised and unsupervised contexts. In supervised learning, this work suggests a criterion for evaluating the posterior odds of new documents which is more statistically sound than the "naive Bayes" approach. In an unsupervised context, we propose measures to set up a systematic evaluation framework and start with examining the Expectation-Maximization (EM) algorithm as the basic tool for inference. We discuss the importance of initialization and the influence of other features such as the smoothing strategy or the size of the vocabulary, thereby illustrating the difficulties incurred by the high dimensionality of the parameter space. We also propose a heuristic algorithm based on iterative EM with vocabulary reduction to solve this problem. Using the fact that the latent variables can be analytically integrated out, we finally show that Gibbs sampling algorithm is tractable and compares favorably to the basic expectation maximization approach

A Comparative Study of Efficient Initialization Methods for the K-Means Clustering Algorithm

K-means is undoubtedly the most widely used partitional clustering algorithm. Unfortunately, due to its gradient descent nature, this algorithm is highly sensitive to the initial placement of the cluster centers. Numerous initialization methods have been proposed to address this problem. In this paper, we first present an overview of these methods with an emphasis on their computational efficiency. We then compare eight commonly used linear time complexity initialization methods on a large and diverse collection of data sets using various performance criteria. Finally, we analyze the experimental results using non-parametric statistical tests and provide recommendations for practitioners. We demonstrate that popular initialization methods often perform poorly and that there are in fact strong alternatives to these methods.Comment: 17 pages, 1 figure, 7 table

Linear, Deterministic, and Order-Invariant Initialization Methods for the K-Means Clustering Algorithm

Over the past five decades, k-means has become the clustering algorithm of choice in many application domains primarily due to its simplicity, time/space efficiency, and invariance to the ordering of the data points. Unfortunately, the algorithm's sensitivity to the initial selection of the cluster centers remains to be its most serious drawback. Numerous initialization methods have been proposed to address this drawback. Many of these methods, however, have time complexity superlinear in the number of data points, which makes them impractical for large data sets. On the other hand, linear methods are often random and/or sensitive to the ordering of the data points. These methods are generally unreliable in that the quality of their results is unpredictable. Therefore, it is common practice to perform multiple runs of such methods and take the output of the run that produces the best results. Such a practice, however, greatly increases the computational requirements of the otherwise highly efficient k-means algorithm. In this chapter, we investigate the empirical performance of six linear, deterministic (non-random), and order-invariant k-means initialization methods on a large and diverse collection of data sets from the UCI Machine Learning Repository. The results demonstrate that two relatively unknown hierarchical initialization methods due to Su and Dy outperform the remaining four methods with respect to two objective effectiveness criteria. In addition, a recent method due to Erisoglu et al. performs surprisingly poorly.Comment: 21 pages, 2 figures, 5 tables, Partitional Clustering Algorithms (Springer, 2014). arXiv admin note: substantial text overlap with arXiv:1304.7465, arXiv:1209.196