This week, I use Manifold Ranking and Euclidean Distance to predict the label of certain nodes, and compared the results of these two methods.
The data is from Hong's work, it's a tensor in size 8131*64, which is an image data onto 64 dimensions. Also, I have the ground truth to every node, it is a dictionary that stores the labels for each node. The data structure is shown below.
At first, I thought that the Manifold Ranking should have higher precision in prediction of the labels than just use their Euclidean Distance. Because as the result of two-moon structure data in the paper we have discussed shows, the Manifold Ranking can give more related nodes higher weights. However, the results of real data are opposite.
In fact, in the terms of predicting, the precision of prediction uses the Euclidean Distance is higher than using the Manifold Ranking, moreover, the Manifold Ranking consumes much more time for calculations.
Because of the running time of the Manifold Ranking Algorithm, I have to randomly choose sample nodes to do the prediction. The random seed is the time, so every time the samples are different. Then choose the nearest 5 nodes, use their label to vote to get the predicted label of the query node, so the 5 nodes have the same weight.
My next step is to use the Analytical Solution to improve the running time of the program, and give the nodes different weights to get an average score of these two methods, not just prediction.
Aug 2nd, 2019 Update
After discussing with Hong, we tend to use another strategy to do the comparison.
The strategy is that to choose the nearest n node to one of the query nodes, if the i-th nearest node has the same label as the ground truth, then add 1/i score to this query node. Get score for all the query nodes, get the average score of all the query node for these two different methods.
As the figure shown above, the score of Manifold Ranking is lower than Euclidean Distance at small amount of nodes which participate in the score progress. However, as the amount of participating nodes become larger and larger, the score of Manifold Ranking will become higher than the Euclidean Distance.