Clustering algorithms are useful tools for data mining, compression, probability density es- timation, and many other important tasks. However, most clustering algorithms require the user to specify the number of clusters (called k), and it is not always clear what is the best value for k. Figure 1 shows examples where k has been improperly chosen. Choosing k is often an ad hoc decision based on prior knowledge, assumptions, and practical experience. Choosing k is made more difficult when the data has many dimensions, even when clusters are well-separated. Center-based clustering algorithms (in particular k-means and Gaussian expectation- maximization) usually assume that each cluster adheres to a unimodal distribution, such as Gaussian. With these methods, only one center should be used to model each subset of data that follows a unimodal distribution. If multiple centers are used to describe data drawn from one mode, the centers are a needlessly complex description of the data, and in fact the multiple centers capture the truth about the subset less well than one center. In this paper we present a simple algorithm called G-means that discovers an appropriate k using a statistical test for deciding whether to split a k-means center into two centers.

When clustering a dataset, the right number k of clusters to use is often not obvious, and choosing k automatically is a hard algorithmic problem. Inthis paper we present an improved algorithm for learning k while clustering. The G-means algorithm is based on a statistical test for the hypothesis that a subset of data follows a Gaussian distribution. G-means runs k-means with increasing k in a hierarchical fashion until the test accepts thehypothesis that the data assigned to each k-means center are Gaussian. Two key advantages are that the hypothesis test does not limit the covariance of the data and does not compute a full covariance matrix. Additionally, G-means only requires one intuitive parameter, the standard statisticalsignificance level α. We present results from experiments showing that the algorithm works well, and better than a recent method based on the BIC penalty for model complexity. In these experiments, we show that the BIC is ineffective as a scoring function, since it does not penalize strongly enough the model's complexity.

When clustering a dataset, the right number k of clusters to use is often not obvious, and choosing k automatically is a hard algorithmic problem. In this paper we present an improved algorithm for learning k while clustering. The G-means algorithm is based on a statistical test for the hypothesis that a subset of data follows a Gaussian distribution. G-means runs k-means with increasing k in a hierarchical fashion until the test accepts the hypothesis that the data assigned to each k-means center are Gaussian. Two key advantages are that the hypothesis test does not limit the covariance of the data and does not compute a full covariance matrix. Additionally, G-means only requires one intuitive parameter, the standard statistical significance level α. We present results from experiments showing that the algorithm works well, and better than a recent method based on the BIC penalty for model complexity. In these experiments, we show that the BIC is ineffective as a scoring function, since it does not penalize strongly enough the model's complexity.

When clustering a dataset, the right number k of clusters to use is often not obvious, and choosing k automatically is a hard algorithmic problem. In this paper we present an improved algorithm for learning k while clustering. The G-means algorithm is based on a statistical test for the hypothesis that a subset of data follows a Gaussian distribution. G-means runs k-means with increasing k in a hierarchical fashion until the test accepts the hypothesis that the data assigned to each k-means center are Gaussian. Two key advantages are that the hypothesis test does not limit the covariance of the data and does not compute a full covariance matrix. Additionally, G-means only requires one intuitive parameter, the standard statistical significance level α. We present results from experiments showing that the algorithm works well, and better than a recent method based on the BIC penalty for model complexity. In these experiments, we show that the BIC is ineffective as a scoring function, since it does not penalize strongly enough the model's complexity.