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Management metrics of complex software systems exhibit stable correlations which can enable fault detection and diagnosis. Current approaches use specific analytic forms, typically linear, for modeling correlations. In practice, more complex nonlinear relationships exist between metrics. Moreover, most intermetric correlations form clusters rather than simple pairwise correlations. These clusters provide additional information and offer the possibility for optimization. In this paper, we address these issues by using Normalized Mutual Information (NMI) as a similarity measure to identify clusters of correlated metrics, without assuming any specific form for the metric relationships. We show how to apply the Wilcoxon Rank-Sum test on the entropy measures to detect errors in the system. We also present three diagnosis algorithms to locate faulty components: RatioScore, based on the Jaccard coefficient, SigScore, which incorporates knowledge of component dependencies, and BayesianScore, which uses Bayesian inference to assign a fault probability to each component. We evaluate our approach in the context of a complex enterprise application, and show that 1) stable, nonlinear correlations exist and can be captured with our approach; 2) we can detect a large fraction of faults with a low false positive rate (we detect up to 18 of the 22 faults we injected); and 3) we improve the diagnosis with our new diagnosis algorithms.