sdml_expr.py

import numpy as np
from scipy.sparse.csgraph import laplacian
from sklearn.utils import check_random_state
from scipy.sparse import coo_matrix
from numpy.testing import assert_array_almost_equal

RNG = check_random_state(0)

def test_loss_sdml():
    n_samples = 10
    n_dims = 5
    X = RNG.randn(n_samples, n_dims)
    c = np.array([[1, 2], [3, 6], [2, 3], [4, 2], [5, 3]])
    n_pairs = len(c)
    pairs = X[c]
    y = RNG.choice([-1, 1], (n_pairs))

    # original computation of the expression
    adj = coo_matrix((y, (c[:, 0], c[:, 1])), shape=(n_samples,) * 2)
    adj_sym = adj + adj.T
    L = laplacian(adj_sym, normed=False)
    expr_1 = X.T.dot(L.dot(X))

    # equivalent way to do it with already formed pairs
    diff = pairs[:, 0] - pairs[:, 1]
    expr_2 = (diff.T * y).dot(diff)

    assert_array_almost_equal(expr_1, expr_2)



def test_loss_sdml_with_duplicates():
    n_samples = 10
    n_dims = 5
    X = RNG.randn(n_samples, n_dims)
    c = np.array([[1, 2], [3, 6], [2, 3], [4, 2], [5, 3], [5, 3]])
    pairs = X[c]
    y = [-1, 1, 1, 1, 1, 1]


    # original computation of the expression
    adj = coo_matrix((y, (c[:, 0], c[:, 1])), shape=(n_samples,) * 2)
    adj_sym = adj + adj.T
    L = laplacian(adj_sym, normed=False)
    expr_1 = X.T.dot(L.dot(X))

    # equivalent way to do it with pairs already formed
    diff = pairs[:, 0] - pairs[:, 1]
    expr_2 = (diff.T * y).dot(diff)

    assert_array_almost_equal(expr_1, expr_2)

if __name__ == '__main__':
    test_loss_sdml()
    test_loss_sdml_with_duplicates()

This snippet tests the computation of the expression of SDML algorithm here: https://github.com/metric-learn/metric-learn/blob/master/metric_learn/sdml.py#L54 , in a way that uses only already formed pairs. Note that it works also if some pairs are duplicated (indeed when the adjacency matrix is computed and there is duplicated pairs, the weight of the connection is the addition (ex: =3 if pair duplicated 3 times).