| * Joint OT matrix and mapping estimation [8]. | ||
| * Wasserstein Discriminant Analysis [11] (requires autograd + pymanopt). | ||
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| * Gromov-Wasserstein distances [12] |
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| [11] Flamary, R., Cuturi, M., Courty, N., & Rakotomamonjy, A. (2016). [Wasserstein Discriminant Analysis](https://arxiv.org/pdf/1608.08063.pdf). arXiv preprint arXiv:1608.08063. | ||
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| [12] Peyré, Gabriel, Marco Cuturi, and Justin Solomon, [Gromov-Wasserstein averaging of kernel and distance matrices](http://proceedings.mlr.press/v48/peyre16.html) International Conference on Machine Learning (ICML). 2016. |
| """ | ||
| ==================== | ||
| Gromov-Wasserstein example | ||
| ==================== |
| import numpy as np | ||
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| import ot | ||
| import matplotlib.pylab as pl |
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| """ | ||
| Sample two Gaussian distributions (2D and 3D) | ||
| ==================== |
| For demonstration purpose, we sample two Gaussian distributions in 2- and 3-dimensional spaces. | ||
| """ | ||
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| n = 30 # nb samples |
| Returns the value of L(a,b)=(1/2)*|a-b|^2 | ||
| """ | ||
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| return (1 / 2) * (a - b)**2 |
| return b | ||
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| tens = -np.dot(h1(C1), T).dot(h2(C2).T) | ||
| tens = tens - tens.min() |
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| Parameters | ||
| ---------- | ||
| C1 : np.ndarray(ns,ns) |
| cpt = 0 | ||
| err = 1 | ||
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| while (err > stopThr and cpt < numItermax): |
…test function
| """ | ||
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| def smacof_mds(C, dim, maxIter=3000, eps=1e-9): |
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| Parameters | ||
| ---------- | ||
| C : np.ndarray(ns,ns) |
| ---------- | ||
| C : np.ndarray(ns,ns) | ||
| dissimilarity matrix | ||
| dim : Integer |
| dissimilarity matrix | ||
| dim : Integer | ||
| dimension of the targeted space | ||
| maxIter : Maximum number of iterations of the SMACOF algorithm for a single run |
| Ct01 = [0 for i in range(2)] | ||
| for i in range(2): | ||
| Ct01[i] = ot.gromov.gromov_barycenters(N, [Cs[0], Cs[1]], [ | ||
| ps[0], ps[1]], p, lambdast[i], 'square_loss', 5e-4, numItermax=100, stopThr=1e-3) |
| triangle = spi.imread('../data/triangle.png').astype(np.float64) / 256 | ||
| fleche = spi.imread('../data/coeur.png').astype(np.float64) / 256 | ||
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| shapes = [carre, rond, triangle, fleche] |
| 'It.', 'Err') + '\n' + '-' * 19) | ||
| print('{:5d}|{:8e}|'.format(cpt, err)) | ||
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| cpt = cpt + 1 |
Nicolas Courty added 2 commits
September 1, 2017 15:37
| square = spi.imread('../data/carre.png').astype(np.float64) / 256 | ||
| circle = spi.imread('../data/rond.png').astype(np.float64) / 256 | ||
| triangle = spi.imread('../data/triangle.png').astype(np.float64) / 256 | ||
| arrow = spi.imread('../data/coeur.png').astype(np.float64) / 256 |
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| xs = ot.datasets.get_2D_samples_gauss(n_samples, mu_s, cov_s) | ||
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| xt = xs[::-1] |
| npos : ndarray, shape (R, dim) | ||
| Embedded coordinates of the interpolated point cloud (defined with one isometry) | ||
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| """ | ||
| Sample two Gaussian distributions (2D and 3D) | ||
| ============================================= | ||
| The Gromov-Wasserstein distance allows to compute distances with samples that do not belong to the same metric space. |
| tens : ndarray, shape (ns, nt) | ||
| \mathcal{L}(C1,C2) \otimes T tensor-matrix multiplication result | ||
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| ===================================== | ||
| Gromov-Wasserstein Barycenter example | ||
| ===================================== | ||
| This example is designed to show how to use the Gromov-Wassertsein distance |
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| def smacof_mds(C, dim, max_iter=3000, eps=1e-9): | ||
| """ | ||
| Returns an interpolated point cloud following the dissimilarity matrix C using SMACOF |
| Embedded coordinates of the interpolated point cloud (defined with one isometry) | ||
| """ | ||
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| rng = np.random.RandomState(seed=3) |
| ---------- | ||
| p : ndarray, shape (N,) | ||
| weights in the targeted barycenter | ||
| lambdas : list of the S spaces' weights |
| sample weights in the S spaces | ||
| p : ndarray, shape(N,) | ||
| weights in the targeted barycenter | ||
| lambdas : list of the S spaces' weights |
| lambdas = np.asarray(lambdas, dtype=np.float64) | ||
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| # Initialization of C : random SPD matrix | ||
| xalea = np.random.randn(N, 2) |
