How can we find useful patterns and anomalies in large scale real-world data, such as network intrusion logs with (source-ip, target-ip, portnumber, timestamp), with multiple attributes? Tensors are suitable for modeling these multi-dimensional data, and widely used for the analysis of social networks, web data, network traffic, and in many other settings. However, current tensor decomposition methods do not scale for tensors with millions and billions of rows, columns and 'fibers', that often appear in real datasets.
In this project, we design and develop large scale tensor analysis algorithms. Our goal is to design algorithms so that the sparsity of real world tensors are fully exploited to boost the performance. The supported algorithms include PARAFAC decomposition, coupled matrix-tensor decomposition, Tucker decomposition, and nonnegative tensor decompositions.
Our proposed tools analyze various real world matrix or tensor data with the following applications.