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Diffstat (limited to 'ot/sliced.py')
| -rw-r--r-- | ot/sliced.py | 181 |
1 files changed, 147 insertions, 34 deletions
diff --git a/ot/sliced.py b/ot/sliced.py index 4792576..d3dc3f2 100644 --- a/ot/sliced.py +++ b/ot/sliced.py @@ -1,61 +1,73 @@ """ -Sliced Wasserstein Distance. +Sliced OT Distances """ # Author: Adrien Corenflos <adrien.corenflos@aalto.fi> +# Nicolas Courty <ncourty@irisa.fr> +# Rémi Flamary <remi.flamary@polytechnique.edu> # # License: MIT License import numpy as np +from .backend import get_backend, NumpyBackend +from .utils import list_to_array -def get_random_projections(n_projections, d, seed=None): +def get_random_projections(d, n_projections, seed=None, backend=None, type_as=None): r""" Generates n_projections samples from the uniform on the unit sphere of dimension d-1: :math:`\mathcal{U}(\mathcal{S}^{d-1})` Parameters ---------- - n_projections : int - number of samples requested d : int dimension of the space + n_projections : int + number of samples requested seed: int or RandomState, optional Seed used for numpy random number generator + backend: + Backend to ue for random generation Returns ------- - out: ndarray, shape (n_projections, d) + out: ndarray, shape (d, n_projections) The uniform unit vectors on the sphere Examples -------- >>> n_projections = 100 >>> d = 5 - >>> projs = get_random_projections(n_projections, d) - >>> np.allclose(np.sum(np.square(projs), 1), 1.) # doctest: +NORMALIZE_WHITESPACE + >>> projs = get_random_projections(d, n_projections) + >>> np.allclose(np.sum(np.square(projs), 0), 1.) # doctest: +NORMALIZE_WHITESPACE True """ - if not isinstance(seed, np.random.RandomState): - random_state = np.random.RandomState(seed) + if backend is None: + nx = NumpyBackend() + else: + nx = backend + + if isinstance(seed, np.random.RandomState) and str(nx) == 'numpy': + projections = seed.randn(d, n_projections) else: - random_state = seed + if seed is not None: + nx.seed(seed) + projections = nx.randn(d, n_projections, type_as=type_as) - projections = random_state.normal(0., 1., [n_projections, d]) - norm = np.linalg.norm(projections, ord=2, axis=1, keepdims=True) - projections = projections / norm + projections = projections / nx.sqrt(nx.sum(projections**2, 0, keepdims=True)) return projections -def sliced_wasserstein_distance(X_s, X_t, a=None, b=None, n_projections=50, seed=None, log=False): +def sliced_wasserstein_distance(X_s, X_t, a=None, b=None, n_projections=50, p=2, + projections=None, seed=None, log=False): r""" - Computes a Monte-Carlo approximation of the 2-Sliced Wasserstein distance + Computes a Monte-Carlo approximation of the p-Sliced Wasserstein distance .. math:: - \mathcal{SWD}_2(\mu, \nu) = \underset{\theta \sim \mathcal{U}(\mathbb{S}^{d-1})}{\mathbb{E}}[\mathcal{W}_2^2(\theta_\# \mu, \theta_\# \nu)]^{\frac{1}{2}} + \mathcal{SWD}_p(\mu, \nu) = \underset{\theta \sim \mathcal{U}(\mathbb{S}^{d-1})}{\mathbb{E}}[\mathcal{W}_p^p(\theta_\# \mu, \theta_\# \nu)]^{\frac{1}{p}} where : @@ -74,8 +86,12 @@ def sliced_wasserstein_distance(X_s, X_t, a=None, b=None, n_projections=50, seed samples weights in the target domain n_projections : int, optional Number of projections used for the Monte-Carlo approximation + p: float, optional = + Power p used for computing the sliced Wasserstein + projections: shape (dim, n_projections), optional + Projection matrix (n_projections and seed are not used in this case) seed: int or RandomState or None, optional - Seed used for numpy random number generator + Seed used for random number generator log: bool, optional if True, sliced_wasserstein_distance returns the projections used and their associated EMD. @@ -100,10 +116,18 @@ def sliced_wasserstein_distance(X_s, X_t, a=None, b=None, n_projections=50, seed .. [31] Bonneel, Nicolas, et al. "Sliced and radon wasserstein barycenters of measures." Journal of Mathematical Imaging and Vision 51.1 (2015): 22-45 """ - from .lp import emd2_1d + from .lp import wasserstein_1d - X_s = np.asanyarray(X_s) - X_t = np.asanyarray(X_t) + X_s, X_t = list_to_array(X_s, X_t) + + if a is not None and b is not None and projections is None: + nx = get_backend(X_s, X_t, a, b) + elif a is not None and b is not None and projections is not None: + nx = get_backend(X_s, X_t, a, b, projections) + elif a is None and b is None and projections is not None: + nx = get_backend(X_s, X_t, projections) + else: + nx = get_backend(X_s, X_t) n = X_s.shape[0] m = X_t.shape[0] @@ -114,31 +138,120 @@ def sliced_wasserstein_distance(X_s, X_t, a=None, b=None, n_projections=50, seed X_t.shape[1])) if a is None: - a = np.full(n, 1 / n) + a = nx.full(n, 1 / n) if b is None: - b = np.full(m, 1 / m) + b = nx.full(m, 1 / m) d = X_s.shape[1] - projections = get_random_projections(n_projections, d, seed) + if projections is None: + projections = get_random_projections(d, n_projections, seed, backend=nx, type_as=X_s) + + X_s_projections = nx.dot(X_s, projections) + X_t_projections = nx.dot(X_t, projections) - X_s_projections = np.dot(projections, X_s.T) - X_t_projections = np.dot(projections, X_t.T) + projected_emd = wasserstein_1d(X_s_projections, X_t_projections, a, b, p=p) + res = (nx.sum(projected_emd) / n_projections) ** (1.0 / p) if log: - projected_emd = np.empty(n_projections) + return res, {"projections": projections, "projected_emds": projected_emd} + return res + + +def max_sliced_wasserstein_distance(X_s, X_t, a=None, b=None, n_projections=50, p=2, + projections=None, seed=None, log=False): + r""" + Computes a Monte-Carlo approximation of the max p-Sliced Wasserstein distance + + .. math:: + \mathcal{Max-SWD}_p(\mu, \nu) = \underset{\theta _in + \mathcal{U}(\mathbb{S}^{d-1})}{\max} [\mathcal{W}_p^p(\theta_\# + \mu, \theta_\# \nu)]^{\frac{1}{p}} + + where : + + - :math:`\theta_\# \mu` stands for the pushforwars of the projection :math:`\mathbb{R}^d \ni X \mapsto \langle \theta, X \rangle` + + + Parameters + ---------- + X_s : ndarray, shape (n_samples_a, dim) + samples in the source domain + X_t : ndarray, shape (n_samples_b, dim) + samples in the target domain + a : ndarray, shape (n_samples_a,), optional + samples weights in the source domain + b : ndarray, shape (n_samples_b,), optional + samples weights in the target domain + n_projections : int, optional + Number of projections used for the Monte-Carlo approximation + p: float, optional = + Power p used for computing the sliced Wasserstein + projections: shape (dim, n_projections), optional + Projection matrix (n_projections and seed are not used in this case) + seed: int or RandomState or None, optional + Seed used for random number generator + log: bool, optional + if True, sliced_wasserstein_distance returns the projections used and their associated EMD. + + Returns + ------- + cost: float + Sliced Wasserstein Cost + log : dict, optional + log dictionary return only if log==True in parameters + + Examples + -------- + + >>> n_samples_a = 20 + >>> reg = 0.1 + >>> X = np.random.normal(0., 1., (n_samples_a, 5)) + >>> sliced_wasserstein_distance(X, X, seed=0) # doctest: +NORMALIZE_WHITESPACE + 0.0 + + References + ---------- + + .. [35] Deshpande, I., Hu, Y. T., Sun, R., Pyrros, A., Siddiqui, N., Koyejo, S., ... & Schwing, A. G. (2019). Max-sliced wasserstein distance and its use for gans. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (pp. 10648-10656). + """ + from .lp import wasserstein_1d + + X_s, X_t = list_to_array(X_s, X_t) + + if a is not None and b is not None and projections is None: + nx = get_backend(X_s, X_t, a, b) + elif a is not None and b is not None and projections is not None: + nx = get_backend(X_s, X_t, a, b, projections) + elif a is None and b is None and projections is not None: + nx = get_backend(X_s, X_t, projections) else: - projected_emd = None + nx = get_backend(X_s, X_t) + + n = X_s.shape[0] + m = X_t.shape[0] + + if X_s.shape[1] != X_t.shape[1]: + raise ValueError( + "X_s and X_t must have the same number of dimensions {} and {} respectively given".format(X_s.shape[1], + X_t.shape[1])) + + if a is None: + a = nx.full(n, 1 / n) + if b is None: + b = nx.full(m, 1 / m) + + d = X_s.shape[1] + + if projections is None: + projections = get_random_projections(d, n_projections, seed, backend=nx, type_as=X_s) - res = 0. + X_s_projections = nx.dot(X_s, projections) + X_t_projections = nx.dot(X_t, projections) - for i, (X_s_proj, X_t_proj) in enumerate(zip(X_s_projections, X_t_projections)): - emd = emd2_1d(X_s_proj, X_t_proj, a, b, log=False, dense=False) - if projected_emd is not None: - projected_emd[i] = emd - res += emd + projected_emd = wasserstein_1d(X_s_projections, X_t_projections, a, b, p=p) - res = (res / n_projections) ** 0.5 + res = nx.max(projected_emd) ** (1.0 / p) if log: return res, {"projections": projections, "projected_emds": projected_emd} return res |