An increasing number of data applications such as monitoring weather data, data streaming, data web logs, and cloud data, are going online and are playing vital in our every-day life. The underlying data of such applications change very frequently, especially in the cloud environment. Many interesting events can be detected by discovering such data from different distributed sources and analyzing it for specific purposes (e.g., car accident detection or market analysis). However, several isolated events could be erroneous due to the fact that important data sets are either discarded or improperly analyzed as they contain missing data. Such events therefore need to be monitored globally and be detected jointly in order to understand their patterns and correlated relationships. In the context of current cloud computing infrastructure, no solutions exist for enabling the correlations between multi-source events in the presence of missing data. This paper addresses the problem of capturing the underlying latent structure of the data with missing entries based on association rules. This necessitate to factorize the data set with missing data. The paper proposes a novel model to handle high amount of data in cloud environment. It is a model of aggregated data that are confidences of association rules. We first propose a method to discover the association rules locally on each node of a cloud in the presence of missing rules. Afterward, we provide a tensor based model to perform a global correlation between all the local models of each node of the network. The proposed approach based on tensor decomposition, deals with a multi modal network where missing association rules are detected and their confidences are approximated. The approach is scalable in terms of factorizing multi-way arrays (i.e. tensor) in the presence of missing association rules. It is validated through experimental results which show its significance and viability in terms of detecting missing rules.