Semi-supervised classification and betweenness computation on large, sparse, directed graphs

Abstract

a b s t r a c tThis work addresses graph-based semi-supervised classification and betweenness computation in large, sparse, networks (several millions of nodes). The objective of semi-supervised classification is to assign a label to unlabeled nodes using the whole topology of the graph and the labeling at our disposal. Two approaches are developed to avoid explicit computation of pairwise proximity between the nodes of the graph, which would be impractical for graphs containing millions of nodes. The first approach directly computes, for each class, the sum of the similarities between the nodes to classify and the labeled nodes of the class, as suggested initially in [1,2]. Along this approach, two algorithms exploiting different state-ofthe-art kernels on a graph are developed. The same strategy can also be used in order to compute a betweenness measure. The second approach works on a trellis structure built from biased random walks on the graph, extending an idea introduced in [3]. These random walks allow to define a biased bounded betweenness for the nodes of interest, defined separately for each class. All the proposed algorithms have a linear computing time in the number of edges while providing good results, and hence are applicable to large sparse networks. They are empirically validated on medium-size standard data sets and are shown to be competitive with state-of-the-art techniques. Finally, we processed a novel data set, which is made available for benchmarking, for multi-class classification in a large network: the U.S. patents citation network containing 3M nodes (of six different classes) and 38M edges. The three proposed algorithms achieve competitive results (around 85% classification rate) on this large network-they classify the unlabeled nodes within a few minutes on a standard workstation.

A bag-of-paths framework for network data analysis

“…Curiously, the spectral method applied to the three kernels (the Markov diffusion kernel (MD), the regularized commute time kernel (RCT) and the regularized Laplacian kernel (RL)) provides bad performances (all three kernels perform significantly worse than the two baselines). This is especially odd, as these kernels obtained good results when used in a sum-of-similarities context [31,66] -see the results obtained by the sum-of-similarities based on the RCT Table 4: Ranking of the different classification methods according to Borda's method (the higher score, the better). Table 3 which is not statistically different from the best method.…”

“…• A sum-of-similarities (SoS) algorithm based on the regularized commute time kernel, which provided good results on large datasets in [66]; see this paper for details. This is our second baseline method, denoted as SoS.…”

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“…21 for the definition of RWR), and applied it to address the classification problem [74]. With this method both complexities of time and space can be reduced.…”

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“…Instead of considering samples as I.I.D observations, graph-based learning takes the relationships/correlations between samples to ensure effective learning. For example, graph-based approaches have been popularly used to propagate labels in semi-supervised learning [24][25][26], where training samples are connected through one or multiple graphs. A recent method [27] considers preserving global and local structures inside the training data for feature selection.…”