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|
| import numpy as np |
| from scipy.optimize import linprog |
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| def wasserstein_distance(p, q, D): |
| A_eq = [] |
| for i in range(len(p)): |
| A = np.zeros_like(D) |
| A[i, :] = 1 |
| A_eq.append(A.reshape(-1)) |
| for i in range(len(q)): |
| A = np.zeros_like(D) |
| A[:, i] = 1 |
| A_eq.append(A.reshape(-1)) |
| A_eq = np.array(A_eq) |
| b_eq = np.concatenate([p, q]) |
| D = D.reshape(-1) |
| result = linprog(D, A_eq=A_eq[:-1], b_eq=b_eq[:-1]) |
| return result.fun |
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|
| def word_rotator_distance(x, y): |
| x_norm = (x**2).sum(axis=1, keepdims=True)**0.5 |
| y_norm = (y**2).sum(axis=1, keepdims=True)**0.5 |
| p = x_norm[:, 0] / x_norm.sum() |
| q = y_norm[:, 0] / y_norm.sum() |
| D = 1 - np.dot(x / x_norm, (y / y_norm).T) |
| return wasserstein_distance(p, q, D) |
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| def word_mover_distance(x, y): |
| p = np.ones(x.shape[0]) / x.shape[0] |
| q = np.ones(y.shape[0]) / y.shape[0] |
| D = np.sqrt(np.square(x[:, None] - y[None, :]).mean(axis=2)) |
| return wasserstein_distance(p, q, D) |
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| def word_rotator_similarity(x, y): |
| return 1 - word_rotator_distance(x, y) |
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| def word_mover_similarity(x, y): |
| return 1 - word_mover_distance(x, y) |
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