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.