Problem 1 (30 points total) node2vec We will use the implementation of node2vec available in github, https://github.com/aditya-grover/ node2vec to create vector representations for each node in G encoded in cell_graph.edgelist. 1) (Clustering on Node2Vec Features (10 points)) First, use default parameters and follow the instruc tions in the README on the graph in cell_graph.edgelist. This will create a 128dimensional vector for each node. Cluster the nodes based on these vectors and compare to the ground truth labels in the last column of Levine_matrix.csv using NMI. Compare your results to Problem 2, question 3. Does an embedding of the graph offer any apparent advantages in classifying cells? 2) (Parameters, part 1 (5 points)) Try a few different values for the number of dimensions --dimensions, such that some of them are less than 128, and some of them are more than 128. Cluster cells again with the embeddings obtained in different dimensions. Again, you can compute the NMI between the cluster assignments and the ground truth labels. Comment on some observations, and show a plot of NMI plotted against the number of dimensions used. 3) (Parameters, part 2 (5 points)) Recall that the parameters p and q control the 'breadth' vs 'depth of the walk'. Choose one of these parameters to vary, and repeat the previous question using the default 128 dimensions, but varying values for either p or q. Comment on some observations, and show a plot of NMI against p or q (whichever one you chose). 4) (Cell Classication, Part II (10 points)) Repeat Problem 2, question (5). However, instead of using only X as the feature matrix, we are going to combine the marker expressions with node2vec features. Let N be your matrix generated through node2Vec. Create a new matrix called X : [X|N]. That is, you will simply concatenate X and N. Formulate the same classication problem from Problem 2, question (5) to classify Tcells from monocytes. Again, report your ROC curve. Comment on the performance, especially in comparison to the results obtained in Problem 2