  In this technical report, we analyze Legendre decomposition for non-negative
tensor in theory and application. In theory, the properties of dual parameters
and dually flat manifold in Legendre decomposition are reviewed, and the
process of tensor projection and parameter updating is analyzed. In
application, a series of verification experiments and clustering experiments
with parameters on submanifold were carried out, hoping to find an effective
lower dimensional representation of the input tensor. The experimental results
show that the parameters on submanifold have no ability to be directly used as
low-rank representations. Combined with analysis, we connect Legendre
decomposition with neural networks and low-rank representation applications,
and put forward some promising prospects.
