We propose a novel subgraph image representation for classification of network fragments with the target being their parent networks. The graph image representation is based on 2D image embeddings of adjacency matrices. We use this image representation in two modes. First, as the input to a machine learning algorithm. Second, as the input to a pure transfer learner. Our conclusions from multiple datasets are that
• deep learning using structured image features performs the best compared to graph kernel and classical features based methods; and, • pure transfer learning works effectively with minimum interference from the user and is robust against small data.
With the advent of big data, graphical representation of information has gained popularity. Being able to classify graphs has applications in many domains. We ask, "Given a small piece of a parent network, is it possible to identify the nature of the parent network (Figure1)?" We address this problem using structured image representations of graphs.
Adjacency matrices are notoriously bad for machine learning. It is easy to see why, from the unstructured image of a small fragment of a road network, in figure (a) below. Though the road network is structured, the random image would convey little or no information to machine learning algorithms (in the image, a black pixel at position (i, j) corresponds to an edge between nodes i and j). Reordering the vertices (figure (b) below) gives a much more structured image for the same subgraph as in (a). Now, the potential to learn distinguishing properties of the subgraph is evident. We propose to exploit this very observation to solve a basic graph problem (see Figure 1). The datasets mentioned in Figure 1 are discussed in Section 2.4. We stress that both images are lossless representations of the same adjacency matrix. We use the structured image to classify subgraphs in two modes: (i) Deep learning models on the structured image representation as input. (ii) The structured image representation is used as input to a transfer learner (Caffe: see Section 2.3) in a pure transfer learning setting without any change to the Caffe algorithm. Caffe outputs top-k categories that best describe the image. For real world images, these Caffe-descriptions are human friendly as seen in Figure 2a. However, for network-images, Caffe Figure 2: An image of a dog and a structured image of a Facebook graph sample vs their corresponding maximally specific classification vectors returned by Caffe gives a description which doesn't really have intuitive meaning (Figure 2b). We map the Caffedescriptions to vectors. This allows us to compute similarity between network images using the similarity between Caffe description-vectors (see Section 2).
The paper proposed a subgraph image representation and validate it in image classification and transfer learning problems. The image presentation is a minor extension based on a method of producing permutation-invariant adjacency matrix. The experimental results supports the claim.
It is very positive that the figures are very helpful for delivering the information.
The work seems to be a little bit incremental. The proposed image representation is mainly based on a previous work of permutation-invariant adjacency matrix. A novelty of this work seems to be transforming a graph into an image. By the proposed representation, the authors are able to apply image classification methods (supervised or unsupervised) to subgraph classification. 
It will be better if the authors could provide more details in the methodology or framework section.
The experiments on 9 networks support the claims that the image embedding approaches with their image representation of the subgraph outperform the graph kernel and classical features based methods. It seem to be promising when using transfer learning.
The last two process figures in 1.1 can be improved. No caption or figure number is provided.
It will be better to make the notations easy to understand and avoid any notation in a sentence without explanation nearby.
For example:
"the test example is correctly classified if and only if its ground truth matches C."(P5)
"We carry out this exercise 4 times and set n to 8, 16, 32 and 64 respectively."(P6)
Some minor issues:
"Zhu et al.(2011) discuss heterogeneous transfer learning where in they use..."(P3)
"Each label vector (a tuple of label, label-probability pairs)." (incomplete sentence?P5)