Tensor-based projection depth

Details Tensor-based projection depth Tensor-based projection depth

2012-01-05

arxiv.org/abs/1201.1146v1

Bernoulli 2011, Vol. 17, No. 4, 1386-1399

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/10-BEJ317 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/10-BEJ317

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.

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