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similarity based on angular difference is a better metric than euclidean distance, for the link predic- tion task. Average Cosine distance between multi hop neighbors 0.6 0.5 0.4 0.3 0.2 0.1 Degree vs distance ratio 0 1 2 3 4 5 0 #Hops Next, we plot the average cosine distances between k-hop neighbors while varying k. This gives us an idea of how well node2vec is able to preserve neighborhoods in the original graph. As is ex- pected, the distance increases linearly with the number of hops. Another plot of interest is seeing how the ratio of average neighbor vs non-neighbor distances changes for different degree nodes. Due to computational constraints, this data was gathered by randomly sampling nodes. There is an evident decreasing trend in the ratio as the degree increases. This can be explained by the fact that high degree nodes have a large set of nodes that can be reached with 2 hops, a even larger set reachable with 3 hops and so on. Hence these high-degree nodes have a "central" location in the graph and are close to a big set of nodes. Our node2vec em- bedding seems to capture this structure as well. In conclusion, node2vec does a very good job of capturing the network properties in our graph. Hence, we are justified in using it as a proxy for network structure in our recommendation tasks. 4.3 Link Prediction Using node2vec To generate recommendations and predict new edges, we frame the problem as a supervised learn- ing instance - specifically, as a classification task, where we wish to predict whether there exists an edge between a pair of nodes. Given two videos u, v and their corresponding to vector embed- dings f (u), f (v) we compute the vector f (u) − f (v) as input to our classifier. We also appended the cosine distance between f (u), f (v) to the input based on our analysis of the embeddings in the previous section. As the complete dataset contained a huge amount of edges (over 1.8 million) and due to a lack computing resources, it was infeasible to train over all node pairs. Hence, we created a training dataset by randomly sampling edges from the graph. We also added an equal number of randomly sampled non-edge vertex pairs to the dataset, to remove bias from our model. The first approach we tried was using a simple Logistic Regression model. Even after augmenting the dataset with some additional features like Euclidean distance, this was unable to converge to a useful solution, with accuracy hovering around 50%. This suggests the underlying function to be learned is a lot more complex than a linear model could learn. Hence, we resort to training a neural network. The neural network we train has an input layer of size 61, and 2 fully connected hidden layers of size 120 and 30. The output layer was a softmax layer of size 2, since our task was binary classification. Between all the layers, we used batch normalization to speed up training. Our trained network has an impressive accuracy of 97.3% on an independently drawn test set. Our results are summarized in Table 4.3. Table 2: Link Prediction Accuracies 6 20 15 10 5 00 50 100 150 200 250 300 Degree Model Logistic Regression (baseline) Neural Network without cosine distance Neural Network with cosine distance Accuracy 51.3% 83.1% 97.3% Cosine distance Non-neighbor distance/neighbor distancePDF Image | Recommending Related YouTube Videos
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