Original: N ETWORK S IGNATURES FROM I MAGE R EPRESENTATION OF A DJACENCY M ATRICES : D EEP /T RANSFER L EARNING FOR S UBGRAPH C LASSIFICATION
Revised: N ETWORK S IGNATURES FROM I MAGE R EPRESENTATION OF A DJACENCY M ATRICES : D EEP /T RANSFER L EARNING FOR S UBGRAPH C LASSIFICATION

Original: Anonymous authors
Revised: Anonymous authors

Original: Paper under double-blind review
Revised: Paper under double-blind review

Original: A BSTRACT
Revised: A BSTRACT

Original: We propose a novel subgraph image representation for classiﬁcation of network fragments with the target being their parent networks.
Revised: We propose a novel subgraph image representation for classiﬁcation of network fragments with the target being their parent networks.

Original: The graph image representation is based on 2D image embeddings of adjacency matrices.
Revised: The graph image representation is based on 2D image embeddings of adjacency matrices.

Original: We use this image representation in two modes.
Revised: We use this image representation in two modes.

Original: First, as the input to a machine learning algorithm.
Revised: First, as the input to a machine learning algorithm.

Original: Second, as the input to a pure transfer learner.
Revised: Second, as the input to a pure transfer learner.

Original: Our conclusions from multiple datasets are that
Revised: Our conclusions from multiple datasets are that

Original: • 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.
Revised: • 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.

Original:  I NTRODUCTION
Revised:  I NTRODUCTION

Original: [Figure]
Revised: [Figure]

Original: Figure

Original: With the advent of big data, graphical representation of information has gained popularity.
Revised: With the advent of big data, graphical representation of information has gained popularity.

Original: Being able to classify graphs has applications in many domains.
Revised: Being able to classify graphs has applications in many domains.

Original: We ask, “Given a small piece of a parent network, is it possible to identify the nature of the parent network (Figure1)?”
Revised: We ask, “Given a small piece of a parent network, is it possible to identify the nature of the parent network (Figure1)?”

Original: We address this problem using structured image representations of graphs.
Revised: We address this problem using structured image representations of graphs.

Original: Adjacency matrices are notoriously bad for machine learning.
Revised: Adjacency matrices are notoriously bad for machine learning.

Original: It is easy to see why, from the unstructured image of a small fragment of a road network, in ﬁgure (a) below.
Revised: It is easy to see why, from the unstructured image of a small fragment of a road network, in ﬁgure (a) below.

Original: 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 ).
Revised: 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 ).

Original: Reordering the vertices (ﬁgure (b) below) gives a much more structured image for the same subgraph as in (a) .
Revised: Reordering the vertices (ﬁgure (b) below) gives a much more structured image for the same subgraph as in (a) .

Original: Now, the potential to learn distinguishing properties of the subgraph is evident.
Revised: Now, the potential to learn distinguishing properties of the subgraph is evident.

Original: We propose to exploit this very observation to solve a basic graph problem (see Figure 1).
Revised: We propose to exploit this very observation to solve a basic graph problem (see Figure 1).

Original: The datasets mentioned in Figure 1 are discussed in Section 
Revised: The datasets mentioned in Figure 1 are discussed in Section 2.

Original: (a) Unstructured image of adjacency matrix (road network)(b) Structured image of adjacency matrix (road network)
Revised: (a) Unstructured image of adjacency matrix (road network) of adjacency matrix (road network)

Original: We stress that both images are lossless representations of the same adjacency matrix.
Revised: We stress that both images are lossless representations of the same adjacency matrix.

Original: We use the structured image to classify subgraphs in two modes: (i) Deep learning models on the structured image representation as input.
Revised: We use the structured image to classify subgraphs in two modes: (i) Deep learning models on the structured image representation as input.

Original: (ii)
Revised: (ii)

Original: 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.
Revised: 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.

Original: Caffe outputs top-
Revised: Caffe outputs top-

Original: k categories that best describe the image.
Revised: k categories that best describe the image.

Original: For real world images, these
Revised: For real world images, these

Original: Caffe-descriptions are human friendly as seen in Figure 2a.
Revised: Caffe-descriptions are human friendly as seen in Figure 2a.

Original: However, for network-images, Caffegives a description which doesn’t really have intuitive meaning (Figure 2b). We map the Caffe- Classification Maximally Specific Score pug 0.
Revised: However, for network-images, Caffe

Original: bull mastiff 0. brabancon giffon 0. french bulldog 0. muzzle 0.
Revised: [Figure]

Original: Classiﬁcation
Revised: Classiﬁcation

Original: Score
Revised: Score

Original: Pug 0.

Original: Bull Mastiff 0. Brabancon Giffon 0. French Bulldog 0. Muzzle 0.
Revised: Window Screen

Original: [Figure]
Revised: [Figure]

Original: Classiﬁcation

Original: Score

Original: Window Screen 0.

Original: Digital Clock0.
Revised: Digital Clock

Original:  Window Shade 0.
Revised: [Figure] Window Shade [Figure]

Original: Scoreboard0.
Revised: Scoreboard

Original: Oscilloscope 0.

Original: [Figure]
Revised: [Figure]

Revised: a description which doesn’t really have intuitive meaning (

Revised: 2b) us compute network images similarity between description vectors

Revised: Section 2).

Original: 1. O UR C ONTRIBUTIONS
Revised: 1. O UR C ONTRIBUTIONS

Original: The signiﬁcant difference between our work and previous approaches is that we transform graph classiﬁcation into image classiﬁcation.
Revised: The signiﬁcant difference between our work and previous approaches is that we transform graph classiﬁcation into image classiﬁcation.

Original: We propose an image representation for the adjacency matrix.
Revised: We propose an image representation for the adjacency matrix.

Original: We use this representation as input to machine learning algorithms for graph classiﬁcation, yielding top performance.
Revised: We use this representation as input to machine learning algorithms for graph classiﬁcation, yielding top performance.

Original: We further show that this representation is powerful enough to serve as input to a pure transfer learner that has been trained in a completely unrelated image domain .
Revised: We further show that this representation is powerful enough to serve as input to a pure transfer learner that has been trained in a completely unrelated image domain .

Original: The Adjacency Matrix Image Representation.
Revised: The Adjacency Matrix Image Representation.

Original: Given a sample subgraph from a parent network, the ﬁrst step is to construct the image representation.
Revised: Given a sample subgraph from a parent network, the ﬁrst step is to construct the image representation.

Original: We illustrate the workﬂow below.
Revised: We illustrate the workﬂow below.

Original: Parent Network
Revised: [Figure]

Original: Sample Subgraph
Revised: Sample Subgraph

Original: Image Embedding
Revised: Image Embedding

Original: Raw Image
Revised: Raw [Figure]

Original: Image Structuring
Revised: Image Structuring

Original: Structured Image
Revised: Structured Image

Original: We use the novel method proposed in Wu et al.
Revised: We use the novel method proposed in Wu et al.

Original: (2016) which produces an adjacency matrix that is invariant to permutations of the vertices in the adjacency matrix.
Revised: (2016) which produces an adjacency matrix that is invariant to permutations of the vertices in the adjacency matrix.

Original: The image is simply a “picture” of this permutation-invariant adjacency matrix.
Revised: The image is simply a “picture” of this permutation-invariant adjacency matrix.

Original: Deep Learning Using the Adjacency Matrix Image Representation.
Revised: Deep Learning Using the Adjacency Matrix Image Representation.

Original: We train deep image classiﬁers (discussed in Section 2.2) on our image representation 
Revised: We train deep image classiﬁers (discussed in Section 2.2) on our image representation as in Figure 3. [Figure]

Original: . Network Signatures from Deep Learning Classiﬁcation
Revised: Figure

Original: We compared performance with several methods, including graph kernel classiﬁers and classiﬁers based on standard topological features of the graph.
Revised: We compared performance with several methods, including graph kernel classiﬁers and classiﬁers based on standard topological features of the graph.

Original: Our image representation performs best.
Revised: Our image representation performs best.

Original: Transfer Learning Using the Adjacency Matrix Image Representation.
Revised: Transfer Learning Using the Adjacency Matrix Image Representation.

Original: When data is scarce or there are many missing labels, a popular option is transfer learning to leverage knowledge from some other domain.
Revised: When data is scarce or there are many missing labels, a popular option is transfer learning to leverage knowledge from some other domain.

Original: Typically the other domain is closely related to the target application.
Revised: Typically the other domain is closely related to the target application.

Original: It is unusual for learning in a completely unrelated domain to be transferable to a new target domain.
Revised: It is unusual for learning in a completely unrelated domain to be transferable to a new target domain.

Original: We show that our image representation is powerful enough that one can directly transfer learn from the real world image domain to the network domain (two completely unrelated domains).
Revised: We show that our image representation is powerful enough that one can directly transfer learn from the real world image domain to the network domain (two completely unrelated domains).

Original: That is, our image representation provides a link between these two domains enabling classiﬁcation in the graph domain to leverage the wealth of techniques available to the image domain.
Revised: That is, our image representation provides a link between these two domains enabling classiﬁcation in the graph domain to leverage the wealth of techniques available to the image domain.

Original: The image domain has mature pre-trained models based on massive data.
Revised: The image domain has mature pre-trained models based on massive data.

Original: For example, the opensource Caffe deep learning framework is a convolutional neural network trained on the ImageNet data which can recognize everyday objects like chairs, cats, dogs etc.
Revised: For example, the opensource Caffe deep learning framework is a convolutional neural network trained on the ImageNet data which can recognize everyday objects like chairs, cats, dogs etc.

Original: (Krizhevsky et al.
Revised: (Krizhevsky et al.

Original: We use Caffe as is .
Revised: We use Caffe as is .

Original: Caffe is a black box that provides a distribution over image classes which we refer to as the Caffe-classiﬁcation vector.
Revised: Caffe is a black box that provides a distribution over image classes which we refer to as the Caffe-classiﬁcation vector.

Original: The Caffe results are then mapped back into the source domain using a distance-based heuristic e.g. Jaccard distance and K -nearest neighbors.
Revised: The Caffe results are then mapped back into the source domain using a distance-based heuristic e.g. Jaccard distance and K -nearest neighbors as in Figure 4.

Original: [Equation]
Revised: [Figure]

Original: Images, not graphs , are passed through the Caffe deep neural network, and as we shall show, one can get good performance from as little as 10% of the training data used in the ab initio machine learning approach.

Original: It is quite stunning that such little training data together with un-tweaked transfer learning from a completely unrelated domain can perform so well.

Original: The reason is that our image representation provides very structured images (human-recognizable) for real world networks.

Original: Though these images are not traditional images like those used in training Caffe, Caffe still maps the different structured images to different distributions over its known classes, hence we are able to transfer this knowledge from Caffe to graph classiﬁcation.

Original: 1. R ELATED W ORK
Revised: 1. R ELATED W ORK

Original: Wu et al.
Revised: Wu et al.

Original: (2016) introduced the problem we study: Can one identify the parent network from a small subgraph?
Revised: (2016) introduced the problem we study: Can one identify the parent network from a small subgraph?

Original: How much does local information reveal about the parent graph at the global level?
Revised: How much does local information reveal about the parent graph at the global level?

Original: We approach the problem from the supervised setting and the unsupervised transfer learning setting.
Revised: We approach the problem from the supervised setting and the unsupervised transfer learning setting.

Original: There is previous work on similar problems using graph kernels (Kashima & Inokuchi (2002);
Revised: There is previous work on similar problems using graph kernels (Kashima & Inokuchi (2002);

Original: Kashima et al.
Revised: Kashima et al.

Original: Kudo et al.
Revised: Kudo et al.

Original: Such methods use kernels to compute similarities between graphs and then algorithms like SVM for classiﬁcation.
Revised: Such methods use kernels to compute similarities between graphs and then algorithms like SVM for classiﬁcation.

Original: Choosing kernels is not straightforward and is certainly not a one-size-ﬁts-all process.
Revised: Choosing kernels is not straightforward and is certainly not a one-size-ﬁts-all process.

Original: Further, these kernel methods do not scale well for very large graphs.
Revised: Further, these kernel methods do not scale well for very large graphs.

Original: We compare with one such method proposed by Shervashidze et al.
Revised: We compare with one such method proposed by Shervashidze et al.

Original: Another approach is to constuct feature vectors from topological attributes of the subgraph (Li et al.
Revised: Another approach is to constuct feature vectors from topological attributes of the subgraph (Li et al.

Original: The topological characteristics of social networks have been extensively studied by Ahn et al.
Revised: The topological characteristics of social networks have been extensively studied by Ahn et al.

Original: ; Ferrara & Fiumara (2012); Sridharan (2011).
Revised: ; Ferrara & Fiumara (2012); Sridharan (2011).

Original: The shortcomings of this approach are that it is difﬁcult to come up with a master set of features that can be used to represent graphs from different domains.
Revised: The shortcomings of this approach are that it is difﬁcult to come up with a master set of features that can be used to represent graphs from different domains.

Original: For example, assortativity could be an important feature in social networks while being of little signiﬁcance in case of road networks.
Revised: For example, assortativity could be an important feature in social networks while being of little signiﬁcance in case of road networks.

Original: It is hard to identify beforehand what features need to be computed for a given problem, thus leading to a trial and error scenario.
Revised: It is hard to identify beforehand what features need to be computed for a given problem, thus leading to a trial and error scenario.

Original: One of the methods we compare is logistic regression.
Revised: One of the methods we compare is logistic regression.

Original: Transfer learning is useful when a classiﬁcation task in one domain can leverage knowledge learned in a related domain (see Pan & Yang (2010) for an extensive survey).
Revised: Transfer learning is useful when a classiﬁcation task in one domain can leverage knowledge learned in a related domain (see Pan & Yang (2010) for an extensive survey).

Original: Raina et al.
Revised: Raina et al.

Original: (2007) introduced a method called self-taught learning which takes advantage of irrelevant unlabeled data to boost performance.
Revised: (2007) introduced a method called self-taught learning which takes advantage of irrelevant unlabeled data to boost performance.

Original: Zhu et al.
Revised: Zhu et al.

Original: (2011) discuss heterogeneous transfer learning wherein they use information from text data to improve image classiﬁcation performance.
Revised: (2011) discuss heterogeneous transfer learning where they use information from text data to improve image classiﬁcation performance.

Original: Quattoni et al.
Revised: Quattoni et al.

Original: (2008) create a new representation from kernel distances to large unlabeled data points before performing image classiﬁcation using a small subset of reference prototypes.
Revised: (2008) create a new representation from kernel distances to large unlabeled data points before performing image classiﬁcation using a small subset of reference prototypes.

Original: The rest of the paper is organized as follows.
Revised: The rest of the paper is organized as follows.

Original: In Section 2 we give more details of our approaches to subgraph classiﬁcation.
Revised: In Section 2 we give more details of our approaches to subgraph classiﬁcation.

Original: Section 3 present the results comparing the performance of our approach with other approaches.
Revised: Section 3 present the results comparing the performance of our approach with other approaches.

Original: We conclude in Section 4 with some possible future directions.
Revised: We conclude in Section 4 with some possible future directions.

Original:  M ETHODOLOGY
Revised:  M ETHODOLOGY

Original: Given fragments of a large network we ﬁrst obtain the structured image representation.
Revised: Given fragments of a large network we ﬁrst obtain the structured image representation.

Original: In the transfer setting, we pass these training samples to the classiﬁers and record the results.
Revised: In the transfer setting, we pass these training samples to the classiﬁers and record the results.

Original: In the unsupervised setting, we feed the training samples to Caffe framework and obtain the label-vectors.
Revised: In the unsupervised setting, we feed the training samples to Caffe framework and obtain the label-vectors.

Original: To classify a test subgraph, we ﬁrst obtain its label-vector through Caffe, compute the distance between the test vector and the training vectors, and classify using majority class of the nearest (cid:0) k vectors.
Revised: To classify a test subgraph, we ﬁrst obtain its label-vector through Caffe, compute the distance between the test vector and the training vectors, and classify using majority class of the nearest − k vectors.

Original: We explain each step in detail below.
Revised: We explain each step in detail below.

Original: 2. I MAGE EMBEDDINGS OF GRAPHS
Revised: 2. I MAGE EMBEDDINGS OF GRAPHS

Original: An adjacency matrix of a graph can be thought of as a monochrome image with 1s corresponding to dark pixels and 0s corresponding to white pixels.
Revised: An adjacency matrix of a graph can be thought of as a monochrome image with 1s corresponding to dark pixels and 0s corresponding to white pixels.

Original: This observation, however, is of limited practical use since it is not permutation invariant.
Revised: This observation, however, is of limited practical use since it is not permutation invariant.

Original: We utilize a novel technique for producing a permutationinvariant ordering of the adjacency matrix, ﬁrst given in Wu et al.
Revised: We utilize a novel technique for producing a permutationinvariant ordering of the adjacency matrix, ﬁrst given in Wu et al.

Original: The authors describe several ways to sort an adjacency matrix like page rank, degree based sorting, etc.
Revised: The authors describe several ways to sort an adjacency matrix like page rank, degree based sorting, etc.

Original: They show that the BFS-like approach introduced works best.
Revised: They show that the BFS-like approach introduced works best.

Original: The ordering starts with the node of highest degree (ties are broken using k -neighborhood size for k = 2 , then k = 3 , : : : ).
Revised: The ordering starts with the node of highest degree (ties are broken using k -neighborhood size for k = 2 , then k = 3 , . . . ).

Original: Subsequently, the ordering proceeds based on a combination of shortest paths and degrees.
Revised: Subsequently, the ordering proceeds based on a combination of shortest paths and degrees.

Original: Details can be found in Wu et al.
Revised: Details can be found in Wu et al.

Original: The ordering scheme results in permutation-invariant adjacency matrices from which we obtain structured images.
Revised: The ordering scheme results in permutation-invariant adjacency matrices from which we obtain structured images.

Original: We observe that the image embeddings have enough structure so that even the human eye can distinguish between different networks without much effort.
Revised: We observe that the image embeddings have enough structure so that even the human eye can distinguish between different networks without much effort.

Original: This is the intuition behind our approach.
Revised: This is the intuition behind our approach.

Original: Neural networks are highly successful in recognizing real world objects that have high structural properties.
Revised: Neural networks are highly successful in recognizing real world objects that have high structural properties.

Original: For example, all dogs have similar features although they are individually different.
Revised: For example, all dogs have similar features although they are individually different

Original:  2. D EEP L EARNING FOR E XTRACTING N ETWORK S IGNATURES
Revised: . 2. D EEP L EARNING FOR E XTRACTING N ETWORK S IGNATURES

Original: Our primary objective is to use deep learning to learn to classify subgraphs to their parent networks using our image representation of the subgraph.
Revised: Our primary objective is to use deep learning to learn to classify subgraphs to their parent networks using our image representation of the subgraph.

Original: However, we also tested a wide variety of other methods as outlined in the table below (more details are in the Appendix, including the references).
Revised: However, we also tested a wide variety of other methods as outlined in the table below (more details are in the Appendix, including the references).

Original: ID Method DBN Deep Belief Network: layers of Restricted Boltzmann Machines CNN Convolutional Neural Network: deep, feed-forward neural networks SdA Stacked denoising Auto-Encoder: NN layers trained as auto-encoders DCNN Diffusion CNN: directly learns graph representations GK Graph Kernel Methods: uses sequence

Original: [Table]
Revised: [Table]

Revised: DBN Deep Belief Network: layers of Restricted Boltzmann Machines CNN Convolutional Neural Network: deep, feed-forward neural networks SdA Stacked denoising Auto-Encoder: NN layers trained as auto-encoders DCNN Diffusion CNN: directly learns graph representations GK Graph Kernel Methods: uses sequence of subgraphs to capture features LR Logistic Regression: benchmark regression using 15 “standard” features

Original: All these methods are tested in a standard supervised learning framework where n training examples ( x i ; y i ) are given (the input x i and y i the target label).
Revised: All these methods are tested in a standard supervised learning framework where n training examples ( x i , y i ) are given (the input x i and y i the target label).

Original: For DBN, CNN and SdA, the input x i is our image representation of the subgraph.
Revised: For DBN, CNN and SdA, the input x i is our image representation of the subgraph.

Original: For DCNN and GK, the input x i is the graph itself, represented as an adjacency matrix.
Revised: For DCNN and GK, the input x i is the graph itself, represented as an adjacency matrix.

Original: For LR, the input x i is a set of 15 classical features (assortativity, clustering coefﬁcient, etc.).
Revised: For LR, the input x i is a set of 15 classical features (assortativity, clustering coefﬁcient, etc.).

Original: 2. C AFFE - BASED I MAGE C LASSIFICATION U SING T RANSFER L EARNING
Revised: 2. C AFFE - BASED I MAGE C LASSIFICATION U SING T RANSFER L EARNING

Original: Caffe is a deep learning framework developed by Jia et al.
Revised: Caffe is a deep learning framework developed by Jia et al.

Original: (2014), Berkeley AI Research and by community contributors with expressive and modular architecture in mind.
Revised: (2014), Berkeley AI Research and by community contributors with expressive and modular architecture in mind.

Original: It has been extensively used in image classiﬁcation and ﬁlter visualization, learning handwritten digital data, and style recognition among other things as seen in Benanne (2014).
Revised: It has been extensively used in image classiﬁcation and ﬁlter visualization, learning handwritten digital data, and style recognition among other things as seen in Benanne (2014).

Original: We use a pre-trained model that is trained on a crowd-sourced labeled data set ImageNet.
Revised: We use a pre-trained model that is trained on a crowd-sourced labeled data set ImageNet.

Original: As of 2016, ImageNet had more than 10 million hand-annotated images.
Revised: As of 2016, ImageNet had more thanmillion hand-annotated images.

Original: The massive volume combined with a deep convolutional neural network gives us ﬁne-grained discriminatory power for images.
Revised: The massive volume combined with a deep convolutional neural network gives us ﬁne-grained discriminatory power for images.

Original: Given an image, the output of our Caffe-based image classiﬁcation function is a vector of (label, label-probability) tuples, sorted in decreasing order of probabilities.
Revised: Given an image, the output of our Caffe-based image classiﬁcation function is a vector of (label, label-probability) tuples, sorted in decreasing order of probabilities.

Original: An example of the output for a real image is shown in Figure 2a.
Revised: An example of the output for a real image is shown in Figure 2a.

Original: Although Caffe has not been trained on image embeddings of graphs, such images nonetheless produce vectors that have sufﬁcient discriminatory information that we extract using the post processing step (see Section 2.3.1).
Revised: Although Caffe has not been trained on image embeddings of graphs, such images nonetheless produce vectors that have sufﬁcient discriminatory information that we extract using the post processing step (see Section 2.3.1).

Original: An example of a vector corresponding to a Facebook network sample is shown in Figure 2b.
Revised: An example of a vector corresponding to a Facebook network sample is shown in Figure 2b.

Original: Caffe provides either maximally accurate or maximally speciﬁc classiﬁcation.
Revised: Caffe provides either maximally accurate or maximally speciﬁc classiﬁcation.

Original: We use the maximally speciﬁc categorization option in Caffe for our work.
Revised: We use the maximally speciﬁc categorization option in Caffe for our work.

Original: Further, while we have shown cardinalityvectors for brevity in Figure 2, we use cardinality-10 vectors in our experiments.
Revised: Further, while we have shown cardinalityvectors for brevity in Figure 2, we use cardinality-10 vectors in our experiments.

Original: 2.3. P OST - PROCESSING FOR G RAPH C LASSIFICATION
Revised: 2.3. P OST - PROCESSING FOR G RAPH C LASSIFICATION

Original: Caffe provides a set of label vectors L i for each training network x i .
Revised: Caffe provides a set of label vectors L i for each training network x i .

Original: Each label vector (a tuple of label, label-probability pairs).
Revised: Each label vector is a tuple of (label, label-probability pairs) as deemed by Caffe.

Original: In this work, we ignore the probabilities, and treat each vector as an unordered list of labels (strings).
Revised: In this work, we ignore the probabilities, and treat each vector as an unordered list of labels (strings).

Original: Each training vector also has a ground truth parent label.
Revised: Each training vector also has a ground truth parent label.

Original: We use Jaccard similarity to compute a similarity metric between two label-vectors L j and L k :
Revised: We use Jaccard similarity to compute a similarity metric between two label-vectors L j and L k :

Original: [Equation]
Revised: [Equation]

Original: We leave for future work the use of more sophisticated metrics which could use the probabilities from Caffe - our goal is to demonstrate the potential of even this simplest possible approach.
Revised: We leave for future work the use of more sophisticated metrics which could use the probabilities from Caffe - our goal is to demonstrate the potential of even this simplest possible approach.

Original: For a test graph, we get the label-vector T from Caffe and then compute the k nearest training vectors using the Jaccard distance d ( L i ; T ) to each training vector L i and classify using the majority class  among these k nearest training vectors (ties are broken randomly).
Revised: For a test graph, we get the label-vector T from Caffe and then compute the k nearest training vectors using the Jaccard distance d ( L i , T ) to each training vector L i and classify using the majority class C among these k nearest training vectors (ties are broken randomly).

Original: The test example is correctly classiﬁed if and only if its ground truth matches C .
Revised: The test example is correctly classiﬁed if and only if its ground truth matches C .

Original: One advantage of the k nearest neighbor approach is that it seamlessly extends to an arbitrary number of parent network classes.
Revised: One advantage of the k nearest neighbor approach is that it seamlessly extends to an arbitrary number of parent network classes.

Original: 2. D ATASETS
Revised: 2. D ATASETS

Original: We used a variety of datasets ranging from citation networks to social networks to e-commerce networks (see Table 1 and the brief descriptions in the Appendix).
Revised: We used a variety of datasets ranging from citation networks to social networks to e-commerce networks (see Table 1 and the brief descriptions in the Appendix).

Original: Our deep networks learn signatures from the image representation of each graph class.
Revised: Our deep networks learn signatures from the image representation of each graph class.

Original: To gein some insight into these network signatures, we show the top principal component of the images of each network.
Revised: To gein some insight into these network signatures, we show the top principal component of the images of each network.

Original: This process is very similar to the one carried out in Turk & Pentland (1991).
Revised: This process is very similar to the one carried out in Turk & Pentland (1991).

Original: We grouped all the samples into their respective (9) categories.
Revised: We grouped all the samples into their respective (9) categories.

Original: Then, we vectorized each sample; i.e., we reshaped each sample from n (cid:2) n to 1 (cid:2) n 2 .
Revised: Then, we vectorized each sample; i.e., we reshaped each sample from n × n to 1 × n 2 .

Original: We then performed principal component analysis on the vectorized dataset.
Revised: We then performed principal component analysis on the vectorized dataset.

Original: We show the top principal component for each network in Figure 3a.
Revised: We show the top principal component for each network in Figure 5a.

Original: In Figure 3b [Table] we show the structured image representations of sample 64-node subgraphs from each of the 9 datasets.
Revised: In Figure 5b, we show the structured image representations of sample 64-node subgraphs from each of the 9 datasets.

Original: These are adjacency matrices that have gone through the structuring process described in Section 2.1.
Revised: These are adjacency matrices that have gone through the structuring process described in Section 2.1.

Original: Observe that the images for different graphs are well structured and quite different.
Revised: Observe that the images for different graphs are well structured and quite different.

Original: This is why the deep networks are able to perform well at classifying the subgraphs, as we will see later in Section 3.
Revised: This is why the deep networks are able to perform well at classifying the subgraphs, as we will see later in Section 3.

Original: Our approach leverages the structure as well as the distinctness of the image representations.
Revised: Our approach leverages the structure as well as the distinctness of the image representations.

Original: [Table]
Revised: [Table]

Revised: [Figure]

Original:  E XPERIMENTAL S ETUP AND R ESULTS
Revised:  E XPERIMENTAL S ETUP AND R ESULTS

Original: In this section we will describe our experimental setup and present the results we obtained from the two approaches we have described in the earlier sections.
Revised: In this section we will describe our experimental setup and present the results we obtained from the two approaches we have described in the earlier sections.

Original: [Figure]

Original: 3. S UPERVISED C LASSIFICATION USING D EEP I MAGE C LASSIFIERS
Revised: 3. S UPERVISED C LASSIFICATION USING D EEP I MAGE C LASSIFIERS

Original: We perform the graph classiﬁcation task using the above mentioned 9 parent networks.
Revised: We perform the graph classiﬁcation task using the above mentioned 9 parent networks.

Original: We perform a random walk on each of these networks 5 ; 000 times and we stop when we get the requiredn number of nodes per sample.
Revised: We perform a random walk on each of these networks 5 , 000 times and we stop when we get the required number of nodes per sample denoted by n .

Original: We carry out this exercise 4 times and set n to 8 , 16 , 32 andrespectively.
Revised: We carry out this exercise 4 times and set n to 8 , 16 , 32 andrespectively.

Original: So, with 9 networks and 5 ; 000 samples per network, we create 4 datasets with 45 ;samples each.
Revised: So, with 9 networks and 5 , 000 samples per network, we create 4 datasets with 45 ,samples each.

Original: Each dataset is of the size 45 ; 000 (cid:2) n (cid:2) n .
Revised: Each dataset is of the size 45 , 000 × n × n .

Original: For a given dataset, we randomly chose 33% of the dataset for validation and set aside 33% of the dataset for testing.
Revised: For a given dataset, we randomly chose 33% of the dataset for validation and set aside 33% of the dataset for testing.

Original: The accuracy score is deﬁned as the ratio of the sum of the principal diagonal entries of the confusion matrix over the sum of all the entries of the confusion matrix (sometimes called the error matrix Stehman (1997)).
Revised: The accuracy score is deﬁned as the ratio of the sum of the principal diagonal entries of the confusion matrix over the sum of all the entries of the confusion matrix (sometimes called the error matrix Stehman (1997)).

Original: A confusion matrix C is such that C i;j is equal to the number of observations known to be in class i but predicted ( confused ) to be in class j .
Revised: A confusion matrix C is such that C i,j is equal to the number of observations known to be in class i but predicted ( confused ) to be in class j .

Original: We report the best accuracy score for each classiﬁer in the following table.
Revised: We report the best accuracy score for each classiﬁer in the following table.

Original: CNN
Revised: CNN

Original: SdA
Revised: SdA

Original: [Table] [Table]
Revised: DBN DCNN

Original: [Table]
Revised: GK LR

Revised: Acc.

Original: [Table]
Revised: [Table]

Original: CNN was the best performing classiﬁer while DCNN and GK were the poorest performers.
Revised: CNN was the best performing classiﬁer while DCNN and GK were the poorest performers.

Original: This shows that off-the-shelf deep learning with graph image features with no tuning of the classiﬁer is better than any other method we tested.
Revised: This shows that off-the-shelf deep learning with graph image features with no tuning of the classiﬁer is better than any other method we tested.

Original: Figure 4 summarizes the performance of all the methods we tested concisely.
Revised: Figure 6 summarizes the performance of all the methods we tested concisely.

Original: As expected, we obtained higher accuracy in classiﬁcation as the number of nodes per sample n increased.
Revised: As expected, we obtained higher accuracy in classiﬁcation as the number of nodes per sample n increased.

Original: Note that straight line in the ﬁgure refers to the accuracy achieved for random guessing of the classes.
Revised: Note that straight line in the ﬁgure refers to the accuracy achieved for random guessing of the classes.

Original: We would like to point out the fact that even with only 8 nodes, we were able to do signiﬁcantly better than random while being better than graph kernel methods and the feature based logistic regression classiﬁer.
Revised: We would like to point out the fact that even with only 8 nodes, we were able to do signiﬁcantly better than random while being better than graph kernel methods and the feature based logistic regression classiﬁer.

Original: We would like to note that although LR performs okay, it is very hard to choose the features when graphs come from different domains.
Revised: We would like to note that although LR performs okay, it is very hard to choose the features when graphs come from different domains.

Original: One set of features that worked best in one scenario may not be the best in another.
Revised: One set of features that worked best in one scenario may not be the best in another.

Original: So, when using an untuned CNN that requires very little effort from the user handily outperforms these cumbersome methods, it is an easy choice to make.
Revised: So, when using an untuned CNN that requires very little effort from the user handily outperforms these cumbersome methods, it is an easy choice to make.

Original: This is one of the biggest observations of our study.
Revised: This is one of the biggest observations of our study.

Original: We also mixed the samples with different n ’s to create hybrid datasets.
Revised: We also mixed the samples with different n ’s to create hybrid datasets.

Original: We observed that the performance of the classiﬁcation was better when the mixture had more samples with higher n .
Revised: We observed that the performance of the classiﬁcation was better when the mixture had more samples with higher n .

Original: This is inline with our expectation and the results in Figure 4.
Revised: This is inline with our expectation and the results in Figure 6.

Original: Interested readers can refer to the Appendix for more details.
Revised: Interested readers can refer to the Appendix for more details.

Original: Graph kernel and feature-based methods performed better than DCNN, but not as well as the image embedding based methods.
Revised: Graph kernel and feature-based methods performed better than DCNN, but not as well as the image embedding based methods.

Original: Kernel methods are complex and usually slow and the fact that they have performed poorly do not make them attractive.
Revised: Kernel methods are complex and usually slow and the fact that they have performed poorly do not make them attractive.

Original: One may notice that the accuracy scores for LR are very comparable to SdA. However, we would like to remark that LR is a lossy method since it approximates the graph and boils it down to a handful of features.
Revised: One may notice that the accuracy scores for LR are very comparable to SdA. However, we would like to remark that LR is a lossy method since it approximates the graph and boils it down to a handful of features.

Original: It is very hard to decide which features must be used and the choice may vary for graphs in different domains in order to get optimal results.
Revised: It is very hard to decide which features must be used and the choice may vary for graphs in different domains in order to get optimal results.

Original: However, our approach is completely lossless .
Revised: However, our approach is completely lossless .

Original: The structured image representation of the graph has every bit of the information the adjacency matrix does.
Revised: The structured image representation of the graph has every bit of the information the adjacency matrix does.

Original: So, we would not have to make any compromises to get the best out of the data.
Revised: So, we would not have to make any compromises to get the best out of the data.

Original: [Figure]
Revised: [Figure]

Original: We would like to make a note about DCNN.
Revised: We would like to make a note about DCNN.

Original: Out of the 4 neural network classiﬁcation models we have used in this work, DCNN is the only one that takes a graph as an input instead of images.
Revised: Out of the 4 neural network classiﬁcation models we have used in this work, DCNN is the only one that takes a graph as an input instead of images.

Original: In fact, it takes two inputs: an adjacency matrix and a design matrix.
Revised: In fact, it takes two inputs: an adjacency matrix and a design matrix.

Original: The design matrix contains information about each node in the adjacency matrix.
Revised: The design matrix contains information about each node in the adjacency matrix.

Original: For example, information like average degree, clustering co-efﬁcient etc. can be provided in the design matrix.
Revised: For example, information like average degree, clustering co-efﬁcient etc. can be provided in the design matrix.

Original: In order to make the comparison between DCNN and the other classiﬁcation models as fair as possible, we speciﬁed the values of the pixels in the image embedding in our design matrices throughout our experiments.
Revised: In order to make the comparison between DCNN and the other classiﬁcation models as fair as possible, we speciﬁed the values of the pixels in the image embedding in our design matrices throughout our experiments.

Original: When other information (assortativity, centrality etc.) were provided we observed no signiﬁcant increase in performance.
Revised: When other information (assortativity, centrality etc.) were provided we observed no signiﬁcant increase in performance.

Original: This is because these properties can be calculated from the graph which is already an input.
Revised: This is because these properties can be calculated from the graph which is already an input.

Original: The neural network is expected to have learned these features already.
Revised: The neural network is expected to have learned these features already.

Original: [Figure] C LASSIFICATION USING T RANSFER L EARNING
Revised: 3. U NSUPERVISED C LASSIFICATION USING T RANSFER L EARNING

Original: In this section we present our experimental results of our second approach to graph classiﬁcation: transfer learning.
Revised: In this section we present our experimental results of our second approach to graph classiﬁcation: transfer learning.

Original: We show that our transfer learning approach is highly resilient to sparse training data.
Revised: We show that our transfer learning approach is highly resilient to sparse training data.

Original: We achieve a respectable accuracy even when only 10% of the data was used for training.
Revised: We achieve a respectable accuracy even when only 10% of the data was used for training.

Original: Caffe can be treated as a black-box that requires very little interference from the user.
Revised: Caffe can be treated as a black-box that requires very little interference from the user.

Original: This is signiﬁcant because when one does not have access to ample data to train their own neural networks, transfer learning can be a very quick and effective ﬁx to get the job done.
Revised: This is signiﬁcant because when one does not have access to ample data to train their own neural networks, transfer learning can be a very quick and effective ﬁx to get the job done.

Original: These are the other two big observations to take home from our work.
Revised: These are the other two big observations to take home from our work.

Original: We also carried out the following experiments: (a) differentiating networks of similar theme/type (i. Terrorist Net.
Revised: We also carried out the following experiments: (a) differentiating networks of similar theme/type (i. Terrorist Net.

Original: vs Facebook, ii.
Revised: vs Facebook, ii.

Original: Citation vs DBLP and iii.
Revised: Citation vs DBLP and iii.

Original: Web vs Wiki); and (b) multi-way  classiﬁcation.
Revised: Web vs Wiki); and (b) multi-way [Figure] classiﬁcation.

Original: The detailed results are relegated to the Appendix, but we note that accuracy scores were in the high 90s and 80s for (a) and around the 60s for (b).
Revised: The detailed results are relegated to the Appendix, but we note that accuracy scores were in the high 90s and 80s for (a) and around the 60s for (b).

Original: While the multi-class scores are not as glamorous as those presented in Section 3.1, they are still worth mentioning.
Revised: While the multi-class scores are not as glamorous as those presented in Section 3.1, they are still worth mentioning.

Original: [Figure] Figure 5 plots the accuracy numbers from the (a) set of experiments as we progressively increase the proportion of data used for training.
Revised: Figure 7 plots the accuracy numbers from the (a) set of experiments as we progressively increase the proportion of data used for training.

Original: Each point on the x -axis shows the percentage of available data that was used for training, the reminder used for testing.
Revised: Each point on the x -axis shows the percentage of available data that was used for training, the reminder used for testing.

Original: Note that the reduction of training percentage hardly impacts accuracy except for a slight dip when only 10% is used for training.
Revised: Note that the reduction of training percentage hardly impacts accuracy except for a slight dip when only 10% is used for training.

Original: Most learning techniques, especially deep neural networks are sensitive to training data volume.
Revised: Most learning techniques, especially deep neural networks are sensitive to training data volume.

Original: The relative insensitivity of our approach is likely due to the fact that we leverage pre-trained recognition engine in the image domain which has already been trained with a massive volume of images.
Revised: The relative insensitivity of our approach is likely due to the fact that we leverage pre-trained recognition engine in the image domain which has already been trained with a massive volume of images.

Original: This shows that the transfer learning approach is very robust and resilient to sparse training data.
Revised: This shows that the transfer learning approach is very robust and resilient to sparse training data.

Original: Finally, we study the impact of k , the neighborhood size for the majority rule, on accuracy.
Revised: Finally, we study the impact of k , the neighborhood size for the majority rule, on accuracy.

Original: We show the detailed analysis in the Appendix but the take away fact is that as long as k > 15 , we do not have to worry too much about tuning k , showing once again that the approach is robust.
Revised: We show the detailed analysis in the Appendix but the take away fact is that as long as k > 15 , we do not have to worry too much about tuning k , showing once again that the approach is robust.

Original:  C ONCLUSION AND F UTURE W ORK
Revised:  C ONCLUSION AND F UTURE W ORK

Original: Our experiments overwhelmingly show that the structured image representation of graphs achieves successful graph classiﬁcation with ease.
Revised: Our experiments overwhelmingly show that the structured image representation of graphs achieves successful graph classiﬁcation with ease.

Original: They are a lossless transformation because the image embeddings do not lose information compared to their corresponding adjacency matrices of the graph.
Revised: The image representation is lossless , that is the image embeddings contain all the information in the corresponding adjacency matrix.

Original: They also show that even with very little information about the parent network, neural networkclassiﬁcation models are able to extract network signatures.
Revised: Our results also show that even with very little information about the parent network, Deep network models are able to extract network signatures.

Original: Speciﬁcally, with just 64-node samples from networks with up to 1 million nodes, we were able to predict the parent network with > 90% accuracy while being signiﬁcantly better than random with only 8-node samples.
Revised: Speciﬁcally, with just 64-node samples from networks with up to 1 million nodes, we were able to predict the parent network with > 90% accuracy while being signiﬁcantly better than random with only 8-node samples.

Original: Further, we demonstrated that the image embedding approach provides many advantages over graph kernel and feature-based methods.
Revised: Further, we demonstrated that the image embedding approach provides many advantages over graph kernel and feature-based methods.

Original: We also presented an approach to graph classiﬁcation using transfer learning from a completely different domain.
Revised: We also presented an approach to graph classiﬁcation using transfer learning from a completely different domain.

Original: Our approach converts graphs into 2D image embeddings and uses a pre-trained image classiﬁer (Caffe) to obtain label-vectors.
Revised: Our approach converts graphs into 2D image embeddings and uses a pre-trained image classiﬁer (Caffe) to obtain label-vectors.

Original: In a range of experiments with real-world data sets, we have obtained accuracies from 70% to 94% for 2-way classiﬁcation and 61% for multi-way classiﬁcation.
Revised: In a range of experiments with real-world data sets, we have obtained accuracies from 70% to 94% for 2-way classiﬁcation and 61% for multi-way classiﬁcation.

Original: Further, our approach is highly resilient to training-to-test ratio, that is, can work with sparse training samples.
Revised: Further, our approach is highly resilient to training-to-test ratio, that is, can work with sparse training samples.

Original: Our results show that such an approach is very promising, especially for applications where training data is not readily available (e.g. terrorist networks).
Revised: Our results show that such an approach is very promising, especially for applications where training data is not readily available (e.g. terrorist networks).

Original: Future work includes improvements to the transfer learning by improving the distance function between label-vectors, as well as using the probabilities from Caffe.
Revised: Future work includes improvements to the transfer learning by improving the distance function between label-vectors, as well as using the probabilities from Caffe.

Original: Further, we would also look to generalize this approach to other domains, for example classifying radio frequency map samples using transfer learning.
Revised: Further, we would also look to generalize this approach to other domains, for example classifying radio frequency map samples using transfer learning.

Revised: Acknowledgments.

Revised: This research was supported by the Army Research Laboratory under Cooperative Agreement W911NF-09-2-0053 (the ARL-NSCTA).

Revised: The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the ofﬁcial policies, either expressed or implied, of the Army Research Laboratory or the U

Revised: S. Government.

Revised: The U.S. Government is authorized to reproduce and distribute reprints for government purposes notwithstanding any copyright notation here on

Original: A A PPENDIX A. C LASSIFIERS FOR E XTRACTING N ETWORK S IGNATURESDeep Belief Network (DBN)
Revised: A A PPENDIX A. C LASSIFIERS FOR E XTRACTING N ETWORK S IGNATURES

Revised: Deep Belief Network (DBN)

Original: DBNs (see: Hinton (2009)) consist of multiple layers of unsupervised Restricted Boltzmann Machines (RBMs) where the output of each RBM is used as input to the next.
Revised: DBNs (see: Hinton (2009)) consist of multiple layers of unsupervised Restricted Boltzmann Machines (RBMs) where the output of each RBM is used as input to the next.

Original: (Hinton et al.
Revised: (Hinton et al.

Original: The RBMs can be trained greedily and a supervised back-propagation step can be used for ﬁne-tuning.
Revised: The RBMs can be trained greedily and a supervised back-propagation step can be used for ﬁne-tuning.

Original: Typically, DBNs have an input layer, hidden layer(s) and a ﬁnal output layer.
Revised: Typically, DBNs have an input layer, hidden layer(s) and a ﬁnal output layer.

Original: The input layer contains a node for each of the entries in the feature vector.
Revised: The input layer contains a node for each of the entries in the feature vector.

Original: For example, if the input is an image of size 8 (cid:2) 8 , then there will be 8 (cid:2) 8 = 64 nodes in the input layer.
Revised: For example, if the input is an image of size 8 × 8 , then there will be 8 × 8 = 64 nodes in the input layer.

Original: The hidden layers consist of RBMs where the output of each of RBMs are used as input to the next.
Revised: The hidden layers consist of RBMs where the output of each of RBMs are used as input to the next.

Original: Finally, the output layer contains a node for each class.
Revised: Finally, the output layer contains a node for each class.

Original: The probabilities of each class label is returned.
Revised: The probabilities of each class label is returned.

Original: The one with the highest probability is chosen as the overall classiﬁcation for the given input.
Revised: The one with the highest probability is chosen as the overall classiﬁcation for the given input.

Original: Convolutional Neural Network (CNN)
Revised: Convolutional Neural Network (CNN)

Original: CNNs are a category of neural networks that have been proven to be very effective in image classiﬁcation tasks.
Revised: CNNs are a category of neural networks that have been proven to be very effective in image classiﬁcation tasks.

Original: Although they have been extensively used on real world images, we believe it is essential to include CNNs in our experiments.
Revised: Although they have been extensively used on real world images, we believe it is essential to include CNNs in our experiments.

Original: The building blocks of a CNN are convolution layers, non-linear layers such as Rectiﬁed Linear
Revised: The building blocks of a CNN are convolution layers, non-linear layers such as Rectiﬁed Linear

Original: Units (ReLU), pooling layers and fully connected layers for classiﬁcation.
Revised: Units (ReLU), pooling layers and fully connected layers for classiﬁcation.

Original: Stacked De-Noising Auto-Encoder (SdA)
Revised: Stacked De-Noising Auto-Encoder (SdA)

Original: We implement the stacked de-noising auto-encoder (SdA) based on greedy training algorithm presented in Wu & Magdon-Ismail (2016).
Revised: We implement the stacked de-noising auto-encoder (SdA) based on greedy training algorithm presented in Wu & Magdon-Ismail (2016).

Original: In a regular multi-layer deep neural network, each layer is trained to ”reconstruct” the input from the previous layer.
Revised: In a regular multi-layer deep neural network, each layer is trained to ”reconstruct” the input from the previous layer.

Original: Then, the system is ﬁne tuned by using back-propagation.
Revised: Then, the system is ﬁne tuned by using back-propagation.

Original: In SdA, instead of the original input, a noisy input is fed to the system.
Revised: In SdA, instead of the original input, a noisy input is fed to the system.

Original: Diffusion-Convolutional Neural Network (DCNN)
Revised: -Convolutional Neural Network (DCNN)

Original: This model, introduced byAtwood &
Revised: This model, introduced by

Original:  Towsley (2016), works on the graphs themselves rather than the image embeddings of their adjacency matrices.
Revised: Atwood & Towsley (2016), works on the graphs themselves rather than the image embeddings of their adjacency matrices.

Original: DCNNs provide a ﬂexible representation of graphical data that encodes node features, edge features, and purely structural information with little preprocessing.
Revised: DCNNs provide a ﬂexible representation of graphical data that encodes node features, edge features, and purely structural information with little preprocessing.

Original: DCNNs learn diffusion-based representations from graph-structured data which is made possible by the new diffusion-convolution operation.
Revised: DCNNs learn diffusion-based representations from graph-structured data which is made possible by the new diffusion-convolution operation.

Original: Graph Kernel Approach
Revised: Graph Kernel Approach

Original: We use a graph kernel introduced in Shervashidze et al.
Revised: We use a graph kernel introduced in Shervashidze et al.

Original: (2011) which uses a rapid feature extraction scheme based on the Weisfeiler-Lehman test of isomorphism on graphs.
Revised: (2011) which uses a rapid feature extraction scheme based on the Weisfeiler-Lehman test of isomorphism on graphs.

Original: It maps the original graph to a sequence of graphs, whose node attributes capture topological and label information.
Revised: It maps the original graph to a sequence of graphs, whose node attributes capture topological and label information.

Original: We use the code provided here Ghisu as-is in our experiments.
Revised: We use the code provided here Ghisu as-is in our experiments.

Original: Feature-based Classiﬁcation
Revised: Feature-based Classiﬁcation

Original: We compute 15 classic features for every graph sample and use just these to perform classiﬁcation usinga linear model like logistic regression.
Revised: We compute 15 classic features for every graph sample and use just these to perform classiﬁcation using logistic regression.

Original: The said features are: transitivity, average clustering co-efﬁcient, average node connectivity, edge connectivity, average eccentricity, diameter, average shortest path, average degree, fraction of single-degree nodes, average closeness centrality, central points, density, average neighbor degree and top two eigen values of the adjacency matrix.
Revised: The said features are: transitivity, average clustering co-efﬁcient, average node connectivity, edge connectivity, average eccentricity, diameter, average shortest path, average degree, fraction of single-degree nodes, average closeness centrality, central points, density, average neighbor degree and top two eigen values of the adjacency matrix.

Original: A. D ATASETS Citation
Revised: A. D ATASETS Citation

Original: This citation network is from Arxiv HEP-PH (high energy physics phenomenology).
Revised: This citation network is from Arxiv HEP-PH (high energy physics phenomenology).

Original: If a paper i cites paper j , the graph contains a directed edge from i to j .
Revised: If a paper i cites paper j , the graph contains a directed edge from i to j .

Original: There are 34 ; 546 nodes with 421 ; 578 edges.
Revised: There are 34 , 546 nodes with 421 , 578 edges.

Original: See: Leskovec et al.
Revised: See: Leskovec et al.

Original: ; Gehrke et al.
Revised: ; Gehrke et al.

Original: Facebook
Revised: Facebook

Original: This social network contains ”friends lists” from Facebook.
Revised: This social network contains ”friends lists” from Facebook.

Original: There are 4039 people (nodes) and there is an undirected edge between nodes if they are friends.
Revised: There are 4039 people (nodes) and there is an undirected edge between nodes if they are friends.

Original: There are 88 ; 234 such edges.
Revised: There are 88 , 234 such edges.

Original: See: Leskovec & Mcauley (2012)
Revised: See: Leskovec & Mcauley (2012)

Original: Road Network
Revised: Road Network

Original: This is a road network of Pennsylvania.
Revised: This is a road network of Pennsylvania.

Original: Intersections and endpoints are represented by nodes, and the roads connecting these intersectionsor endpoints are represented by undirected edges.
Revised: Intersections and endpoints are represented by nodes, and the roads connecting these intersections are represented by undirected edges.

Original: There are 1 ; 088 ; 092 nodes and 1 ; 541 ; 898 edges in this network.
Revised: There are 1 , 088 , 092 nodes and 1 , 541 , 898 edges in this network.

Original: See: Leskovec et al.
Revised: See: Leskovec et al.

Original: Web
Revised: Web

Original: Nodes in this network represent web pages and directed edges represent hyperlinks between them.
Revised: Nodes in this network represent web pages and directed edges represent hyperlinks between them.

Original: There are 875 ; 713 nodes and 5 ; 105 ; 039 edges.
Revised: There are 875 , 713 nodes and 5 , 105 , 039 edges.

Original: See: Leskovec et al.
Revised: See: Leskovec et al.

Original: Wikipedia
Revised: Wikipedia

Original: This is a Wikipedia hyperlink graph.
Revised: This is a Wikipedia hyperlink graph.

Original: A condensed version of Wikipedia was used in the collection of this dataset.
Revised: A condensed version of Wikipedia was used in the collection of this dataset.

Original: There are 4 ; 604 articles (nodes) with 119 ; 882 links (edges) between them.
Revised: There are 4 , 604 articles (nodes) with 119 , 882 links (edges) between them.

Original: See: West & Leskovec (2012);
Revised: See: West & Leskovec (2012);

Original: West et al.
Revised: West et al.

Original: Amazon
Revised: Amazon

Original: This is a product co-purchase network of amazon.com.
Revised: This is a product co-purchase network of amazon.com.

Original: The nodes are products sold on amazon.com.
Revised: The nodes are products sold on amazon.com.

Original: There is an undirected edge between two products if they are frequently co-purchased.
Revised: There is an undirected edge between two products if they are frequently co-purchased.

Original: There are 334 ; 863 nodes and 925 ; 872 edges.
Revised: There are 334 , 863 nodes and 925 , 872 edges.

Original: See: Leskovec et al.
Revised: See: Leskovec et al.

Original: DBLP
Revised: DBLP

Original: This is a co-authorship network.
Revised: This is a co-authorship network.

Original: It has authors for its nodes and there is an undirected edge between them if they have co-authored at least one paper.
Revised: It has authors for its nodes and there is an undirected edge between them if they have co-authored at least one paper.

Original: There are 317 ; 080 nodes and 1 ; 049 ;edges.
Revised: There are 317 , 080 nodes and 1 , 049 ,edges.

Original: See: Yang & Leskovec (2012)0.
Revised: See: Yang & Leskovec (2012)

Original: Terrorist Network
Revised: Terrorist Network

Original: We use the “Al Qaeda Operations Attack Series 1993-2003, Worldwide” dataset consisting of 271 nodes (participants of Al Qaeda terrorist group) with 756 links between them.
Revised: We use the “Al Qaeda Operations Attack Series 1993-2003, Worldwide” dataset consisting of 271 nodes (participants of Al Qaeda terrorist group) with 756 links between them.

Original: See: JJATT (2009)
Revised: See: JJATT (2009)

Original: Gowalla
Revised: Gowalla

Original: Gowalla was a location-based social networking website where users shared their locations by checking-in.
Revised: Gowalla was a location-based social networking website where users shared their locations by checking-in.

Original: The friendship network is undirected and consists of 196 ; 591 nodes and 950 ;edges.
Revised: The friendship network is undirected and consists of 196 , 591 nodes and 950 , 327 edges.

Original: See: Cho et al.
Revised: See: Cho et al.

Original: A. H YBRID D ATASETS
Revised: [Figure] D [Figure]

Original: We present the detailed results for different mixtures of datasets that we experimented with in the supervised setting.
Revised: We present the detailed results for different mixtures of datasets that we experimented with in the supervised setting.

Original: Although the performance deteriorates when different n ’s are mixed, the relative ordering of the methods w.r.t.
Revised: Although the performance deteriorates when different n ’s are mixed, the relative ordering of the methods w.r.t.

Original: their performances remains the same.
Revised: their performances remains the same.

Original: Table below shows the 4 cases and as Figure 6 shows, classiﬁcation accuracy increases as the contribution by samples with higher n increases. 
Revised: Table below shows the 4 cases and as Figure 8 shows, classiﬁcation accuracy increases as the contribution by samples with higher n increases. Nodes Case Case

Revised: Case

Revised: Case 25% 10% 40% 10% 25% 20% 30% 40% 25% 30% 20% 40% 25% 40% 10% 10%

Original: [Table]
Revised: [Figure]

Original: A. E XTENSIVE T RANSFER L EARNING R ESULTS

Original: We present the results from two sets of experiments: (a) telling apart networks of similar theme/type; and (b) multi-way classiﬁcation.
Revised: We present the results from two sets of experiments: (a) telling apart networks of similar theme/type; and (b) multi-way classiﬁcation.

Original: Tables 7a, 7b, and 7c show the results of classiﬁcation between similarly-themed networks.
Revised: Tables 9a, 9b, and 9c show the results of classiﬁcation between similarly-themed networks.

Original: We see that our approach is able to classify Wiki and Web with a very high accuracy of 95%.
Revised: We see that our approach is able to classify Wiki and Web with a very high accuracy of 95%.

Original: The other two are respectable as well, with 90% and 80% accuracies. 
Revised: The other two are respectable as well, with 90% and 80% accuracies. Data Prc. Rec.

Revised: F

Original:  [Table]
Revised: Ter. Net. [Table] [Table]

Revised: FB

Revised: [Table]

Revised: [Table]

Revised: [Table]

Revised: Acc.

Original:  [Figure] 
Revised: [Table] [Figure] Terrorist [Table]

Revised: vs Facebook

Revised: Data

Revised: Prc.

Revised: [Table]

Revised: F

Revised: Cit.

Revised: [Table]

Revised: DBLP 0.

Original: [Figure] 
Revised: [Figure] [Figure] [Figure] Data

Revised: Prc.

Revised: Rec.

Revised: F

Revised: Wiki 0.

Revised: Web 0.

Revised: Acc.

Original:  Table below shows that our approach does not do quite as well when it comes to multi-way classiﬁcation.
Revised: [Figure] Wiki vs Web [Figure] Table below shows that our approach does not do quite as well when it comes to multi-way classiﬁcation.

Original: While multi-way classiﬁcation is challenging in general, our particular approach of using the majority rule may be somewhat more impacted since now the correct class has to outnumber several other classes. 
Revised: While multi-way classiﬁcation is challenging in general, our particular approach of using the majority rule may be somewhat more impacted since now the correct class has to outnumber several other classes. Data Prc. Rec.

Original: [Table]
Revised: F Wiki 0. Web 0. DBLP 0.

Revised: Terrorist Net

Original:  Figure 8 shows the variation of accuracy results when k is varied in steps of 8 from k = 7 to k = 47 , with the base case k = 15 used for the tabulated results above included for comparison.
Revised: [Table] Citations [Table] Figure 10 shows the variation of accuracy results when k is varied in steps of 8 from k = 7 to k = 47 , with the base case k = 15 used for the tabulated results above included for comparison.

Original: As can be seen, except for a couple of cases with k = 7 providing a somewhat lower accuracy, the variation is within 1% of the base case.
Revised: As can be seen, except for a couple of cases with k = 7 providing a somewhat lower accuracy, the variation is within 1% of the base case.

Original: Thus, as long as k > 15 , we do not have to worry too much about tuning k , showing that the approach is robust.
Revised: Thus, as long as k > 15 , we do not have to worry too much about tuning k , showing that the approach is robust.