  The conventional definition of a depth function is vector-based. In this
paper, a novel projection depth (PD) technique directly based on tensors, such
as matrices, is instead proposed. Tensor projection depth (TPD) is still an
ideal depth function and its computation can be achieved through the iteration
of PD. Furthermore, we also discuss the cases for sparse samples and higher
order tensors. Experimental results in data classification with the two
projection depths show that TPD performs much better than PD for data with a
natural tensor form, and even when the data have a natural vector form, TPD
appears to perform no worse than PD.
