  Several diseases of parkinsonian syndromes present similar symptoms at early
stage and no objective widely used diagnostic methods have been approved until
now. Positron emission tomography (PET) with $^{18}$F-FDG was shown to be able
to assess early neuronal dysfunction of synucleinopathies and tauopathies.
Tensor factorization (TF) based approaches have been applied to identify
characteristic metabolic patterns for differential diagnosis. However, these
conventional dimension-reduction strategies assume linear or multi-linear
relationships inside data, and are therefore insufficient to distinguish
nonlinear metabolic differences between various parkinsonian syndromes. In this
paper, we propose a Deep Projection Neural Network (DPNN) to identify
characteristic metabolic pattern for early differential diagnosis of
parkinsonian syndromes. We draw our inspiration from the existing TF methods.
The network consists of a (i) compression part: which uses a deep network to
learn optimal 2D projections of 3D scans, and a (ii) classification part: which
maps the 2D projections to labels. The compression part can be pre-trained
using surplus unlabelled datasets. Also, as the classification part operates on
these 2D projections, it can be trained end-to-end effectively with limited
labelled data, in contrast to 3D approaches. We show that DPNN is more
effective in comparison to existing state-of-the-art and plausible baselines.
