document: Clustering seasonality patterns in the presence of errors Clustering is a very well studied problem that attempts to group similar data points . Most traditional clustering algorithms assume that the data is provided without measurement error . Often , however , real world data sets have such errors and one can obtain estimates of these errors . We present a clustering method that incorporates information contained in these error estimates . We present a new distance function that is based on the distribution of errors in data . Using a Gaussian model for errors , the distance function follows a Chi-Square distribution and is easy to compute . This distance function is used in hierarchical clustering to discover meaningful clusters . The distance function is scale-invariant so that clustering results are independent of units of measuring data . In the special case when the error distribution is the same for each attribute of data points , the rank order of pair-wise distances is the same for our distance function and the Euclidean distance function . The clustering method is applied to the seasonality estimation problem and experimental results are presented for the retail industry data as well as for simulated data , where it outperforms classical clustering methods .
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