Our code was written and tested using Python 3.6.7, but most version of Python 3 should work. Libraries used are:
- numpy 1.15.4
- scipy 1.2.0
- scikit-learn 0.20.2
- networkx 2.2 [only for MDS, not needed for metric learning]
The code should run out of the box, assuming dependencies are installed.
To run k-means clustering tests on metric learning, use the following syntax:
python3 metric_learning.py --dataset DATASET --lmbd LAMBDA --reg REG --clus
Similarly, for k-nearest neighbor classification, use the following:
python3 metric_learning.py --dataset DATASET --K k --lmbd LAMBDA --reg REG --clf
k is used in classification tests to specify the k in k-nearest neighbor. Reg should be a float between 0.0 and 1.0 and specifies the regularization term in the loss function. Lambda should be a float, and specifies how much scaling is penalized during optimization. Dataset names available out of the box are: football, polbooks, karate, adjnoun, helicoid and 20newsgroup.
To approximate the distance function on a manifold, one must compute the arc length integrand as a function of paths (as described in the paper). Plugging this integrand into the function learn_distance in learn_manifold_distance.py will yield an approximation of the true manifold distance (see paper for empirical rate of convergence)
Minimizing the MDS loss function in generalized_mds.py requires the functions fxn_mfd, fxn_mfd_dist, and (optionally) fxn_integrand, as described above. It also requires a nxn distance matrix D (where n is the number of points to be embedded, and Dij is the distance between the ith and jth points), an initialized matrix of embedded points (which may be generated randomly), and the desired embedding dimension.