  We aim at capturing high-order statistics of feature vectors formed by a
neural network, and propose end-to-end second- and higher-order pooling to form
a tensor descriptor. Tensor descriptors require a robust similarity measure due
to low numbers of aggregated vectors and the burstiness phenomenon, when a
given feature appears more/less frequently than statistically expected. The
Heat Diffusion Process (HDP) on a graph Laplacian is closely related to the
Eigenvalue Power Normalization (EPN) of the covariance/autocorrelation matrix,
whose inverse forms a loopy graph Laplacian. We show that the HDP and the EPN
play the same role, i.e., to boost or dampen the magnitude of the eigenspectrum
thus preventing the burstiness. We equip higher-order tensors with EPN which
acts as a spectral detector of higher-order occurrences to prevent burstiness.
We also prove that for a tensor of order r built from d dimensional feature
descriptors, such a detector gives the likelihood if at least one higher-order
occurrence is 'projected' into one of binom(d,r) subspaces represented by the
tensor; thus forming a tensor power normalization metric endowed with
binom(d,r) such 'detectors'. For experimental contributions, we apply several
second- and higher-order pooling variants to action recognition, provide
previously not presented comparisons of such pooling variants, and show
state-of-the-art results on HMDB-51, YUP++ and MPII Cooking Activities.
