  In this paper, we focus on fraud detection on a signed graph with only a
small set of labeled training data. We propose a novel framework that combines
deep neural networks and spectral graph analysis. In particular, we use the
node projection (called as spectral coordinate) in the low dimensional spectral
space of the graph's adjacency matrix as input of deep neural networks.
Spectral coordinates in the spectral space capture the most useful topology
information of the network. Due to the small dimension of spectral coordinates
(compared with the dimension of the adjacency matrix derived from a graph),
training deep neural networks becomes feasible. We develop and evaluate two
neural networks, deep autoencoder and convolutional neural network, in our
fraud detection framework. Experimental results on a real signed graph show
that our spectrum based deep neural networks are effective in fraud detection.
