Legendre Decomposition for Tensors
This is an incremental improvement for researchers in tensor analysis and machine learning, offering a new decomposition method with theoretical guarantees.
The authors tackled the problem of nonnegative tensor decomposition by introducing Legendre decomposition, which uniquely minimizes KL divergence and empirically achieves more accurate tensor reconstruction compared to existing methods.
We present a novel nonnegative tensor decomposition method, called Legendre decomposition, which factorizes an input tensor into a multiplicative combination of parameters. Thanks to the well-developed theory of information geometry, the reconstructed tensor is unique and always minimizes the KL divergence from an input tensor. We empirically show that Legendre decomposition can more accurately reconstruct tensors than other nonnegative tensor decomposition methods.