Many-body Approximation for Non-negative Tensors
This work addresses tensor decomposition challenges for researchers in machine learning and data analysis, offering an incremental improvement over existing methods.
The paper tackles the problem of decomposing non-negative tensors by introducing a many-body approximation method that avoids the global optimization and rank selection difficulties of traditional low-rank approaches, demonstrating its effectiveness in tensor completion and approximation tasks.
We present an alternative approach to decompose non-negative tensors, called many-body approximation. Traditional decomposition methods assume low-rankness in the representation, resulting in difficulties in global optimization and target rank selection. We avoid these problems by energy-based modeling of tensors, where a tensor and its mode correspond to a probability distribution and a random variable, respectively. Our model can be globally optimized in terms of the KL divergence minimization by taking the interaction between variables (that is, modes), into account that can be tuned more intuitively than ranks. Furthermore, we visualize interactions between modes as tensor networks and reveal a nontrivial relationship between many-body approximation and low-rank approximation. We demonstrate the effectiveness of our approach in tensor completion and approximation.