This paper presents a methodology and a system, named LogMaster, for mining correlations of events that have multiple attributions, i.e., node ID, application ID, event type, and event severity, in logs of large-scale cluster systems. Different from traditional transactional data, e.g., supermarket purchases, system logs have their unique characteristic, and hence we propose several innovative approaches to mine their correlations. We present a simple metrics to measure correlations of events that may happen interleavedly. On the basis of the measurement of correlations, we propose two approaches to mine event correlations; meanwhile, we propose an innovative abstraction: event correlation graphs (ECGs) to represent event correlations, and present an ECGs based algorithm for predicting events. For two system logs of a production Hadoop-based cloud computing system at Research Institution of China Mobile and a production HPC cluster system at Los Alamos National Lab (LANL), we evaluate our approaches in three scenarios: (a) predicting all events on the basis of both failure and non-failure events; (b) predicting only failure events on the basis of both failure and non-failure events; (c) predicting failure events after removing non-failure events.