nTD: Noise Adaptive Tensor Decomposition

Tensor decomposition is increasingly being used for many data analysis operations from clustering, trend detection, anomaly detection, to correlation analysis. However, as we argue in the paper, many of the tensor decomposition schemes are sensitive to noisy data, an inevitable problem in the real world that can lead to false conclusions. The problem is compounded by over-fitting when the data is sparse. Recent research has shown that it is possible to avoid overfitting by relying on probabilistic techniques. However, these have two major deficiencies: (a) firstly, they assume that all the data and intermediary results can fit in the main memory, and (b) they treat the entire tensor uniformly, ignoring potential non-uniformities in the noise distribution. To deal with these challenges, in this paper, we propose a Noise Adaptive Tensor Decomposition (nTD) method, which aims to tackle both of these challenges: in particular, nTD leverages a grid-based two-phase decomposition strategy for two complementary purposes: firstly, the partitioning helps ensure that the memory footprint of the decomposition is kept low; secondly (and more importantly) the noise profiles of the grid partitions enable us to develop a sample assignment strategy (or s-strategy) that best suits the noise distribution of the given tensor, leading to nTD method, which can leverage available rough knowledge regarding where in the tensor noise might be more prevalent. Experiments show that nTD’s performance is significantly better than conventional ALS-based CP decomposition on noisy tensors.