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<!DOCTYPE html>

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<title>ot.datasets — POT Python Optimal Transport 0.9.7 documentation</title>

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POT Python Optimal Transport

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<li class="breadcrumb-item active">ot.datasets</li>

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<h1>Source code for ot.datasets</h1><div class="highlight"><pre>

"""

Simple example datasets

"""

# Author: Remi Flamary <remi.flamary@unice.fr>

#

# License: MIT License

import numpy as np

import scipy as sp

from scipy.stats import ortho_group, multivariate_normal

from .utils import check_random_state, deprecated

def make_1D_gauss(n, m, s):

"""return a 1D histogram for a gaussian distribution (`n` bins, mean `m` and std `s`)

Parameters

----------

n : int

number of bins in the histogram

m : float

mean value of the gaussian distribution

s : float

standard deviation of the gaussian distribution

Returns

-------

h : ndarray (`n`,)

1D histogram for a gaussian distribution

"""

x = np.arange(n, dtype=np.float64)

h = np.exp(-((x - m) ** 2) / (2 * s**2))

return h / h.sum()</div>

@deprecated()

def get_1D_gauss(n, m, sigma):

"""Deprecated see make_1D_gauss"""

return make_1D_gauss(n, m, sigma)

def make_2D_samples_gauss(n, m, sigma, random_state=None):

r"""Return `n` samples drawn from 2D gaussian :math:`\mathcal{N}(m, \sigma)`

Parameters

----------

n : int

number of samples to make

m : ndarray, shape (2,)

mean value of the gaussian distribution

sigma : ndarray, shape (2, 2)

covariance matrix of the gaussian distribution

random_state : int, RandomState instance or None, optional (default=None)

If int, random_state is the seed used by the random number generator;

If RandomState instance, random_state is the random number generator;

If None, the random number generator is the RandomState instance used

by `np.random`.

Returns

-------

X : ndarray, shape (`n`, 2)

n samples drawn from :math:`\mathcal{N}(m, \sigma)`.

"""

generator = check_random_state(random_state)

if np.isscalar(sigma):

sigma = np.array(

[

sigma,

]

)

if len(sigma) > 1:

P = sp.linalg.sqrtm(sigma)

res = generator.randn(n, 2).dot(P) + m

else:

res = generator.randn(n, 2) * np.sqrt(sigma) + m

return res</div>

@deprecated()

def get_2D_samples_gauss(n, m, sigma, random_state=None):

"""Deprecated see make_2D_samples_gauss"""

return make_2D_samples_gauss(n, m, sigma, random_state=None)

def make_data_classif(dataset, n, nz=0.5, theta=0, p=0.5, random_state=None, **kwargs):

"""Dataset generation for classification problems

Parameters

----------

dataset : str

type of classification problem (see code)

n : int

number of training samples

nz : float

noise level (>0)

p : float

proportion of one class in the binary setting

random_state : int, RandomState instance or None, optional (default=None)

If int, random_state is the seed used by the random number generator;

If RandomState instance, random_state is the random number generator;

If None, the random number generator is the RandomState instance used

by `np.random`.

Returns

-------

X : ndarray, shape (n, d)

`n` observation of size `d`

y : ndarray, shape (n,)

labels of the samples.

"""

generator = check_random_state(random_state)

if dataset.lower() == "3gauss":

y = np.floor((np.arange(n) * 1.0 / n * 3)) + 1

x = np.zeros((n, 2))

# class 1

x[y != 3, :] += 1.5 * nz * generator.randn(sum(y != 3), 2)

x[y == 3, :] += 2 * nz * generator.randn(sum(y == 3), 2)

elif dataset.lower() == "3gauss2":

y[y == 4] = 3

# class 1

x[y != 3, :] += nz * generator.randn(sum(y != 3), 2)

rot = np.array(

[[np.cos(theta), np.sin(theta)], [-np.sin(theta), np.cos(theta)]]

)

m1 = np.array([-1, 1])

m2 = np.array([1, -1])

y = np.floor((np.arange(n) * 1.0 / n * 2)) + 1

n1 = np.sum(y == 1)

n2 = np.sum(y == 2)

x[y == 1, :] = make_2D_samples_gauss(n1, m1, nz, random_state=generator)

x[y == 2, :] = make_2D_samples_gauss(n2, m2, nz, random_state=generator)

x = x.dot(rot)

y = np.concatenate((np.ones(int(p * n)), np.zeros(int((1 - p) * n))))

x = np.hstack((0 * y[:, None] - 0, 1 - 2 * y[:, None])) + nz * generator.randn(

len(y), 2

)

if ("bias" not in kwargs) and ("b" not in kwargs):

kwargs["bias"] = np.array([0, 2])

x[:, 0] += kwargs["bias"][0]

x[:, 1] += kwargs["bias"][1]

else:

x = np.array(0)

y = np.array(0)

print("unknown dataset")

return x, y.astype(int)</div>

@deprecated()

def get_data_classif(dataset, n, nz=0.5, theta=0, random_state=None, **kwargs):

"""Deprecated see make_data_classif"""

return make_data_classif(dataset, n, nz=0.5, theta=0, random_state=None, **kwargs)

def make_gauss_hd(

ns, nt, p=100, dim=5, m_diff=3.0, a=(10.0, 15.0), b=(3.0, 3.0), sub_the_same=False

):

"""Generation of source and target domains from Gaussian HD distributions

Parameters

----------

ns : int

number of samples (source)

nt : int

number of samples (target)

p : int

dimension of the ambient space the data live in

dim : (int,int) or int

the intrinsic dimensions of the source and target Gaussian HD distriutions. If a single int the intrinsic dimension is assumed to be the same

m_diff : float

the shift in the first coordinate of the means of the Gaussian HD distributions, i.e. ms_0 and mt_0, respectively (see code)

a : (float, float)

positive floating numbers corresponding to the isotropic variances in the principal subspace, for the source and target distributions, respectively. The same as \delta in :ref:`[1] <references-make_gauss-hd>`, Proposition 2.2

b : (float, float)

positive floating numbers corresponding to the isotropic variance outside the principal subspace for the source and target distributions, respectively.

sub_the_same : bool

should the source/target Gaussian HD distributions live in the same principal subspace?

Returns

-------

Xs : ndarray, shape (ns, p)

`ns` observations of size `p` (source)

Xt : ndarray, shape (nt, p)

`nt` observations of size `p` (destination)

pmts : list

a list containing the parameters of the Gaussian HD distributions

.. _references-make_gauss_hd:

References

----------

.. [1] Bouveyron, C. & Corneli, M. ("Scaling Optimal Transport to High-Dimensional Gaussian Distributions")

"""

d = (dim, dim) if isinstance(dim, int) else dim

mu = np.zeros((2, p))

S = []

mu[1, 0] = m_diff

Q = [ortho_group.rvs(p) for _ in range(2)]

if sub_the_same:

Q[1] = Q[0]

S.append(

Q[0]

@ np.diag(np.hstack((np.full(d[0], a[0]), np.full(p - d[0], b[0]))))

@ Q[0].T

)

S.append(

Q[1]

@ np.diag(np.hstack((np.full(d[1], a[1]), np.full(p - d[1], b[1]))))

@ Q[1].T

)

Xs = multivariate_normal.rvs(mean=mu[0], cov=S[0], size=ns)

Xt = multivariate_normal.rvs(mean=mu[1], cov=S[1], size=ns)

ms = mu[0]

mt = mu[1]

ds = d[0]

dt = d[1]

sigma2_s = np.array(b[0])

sigma2_t = np.array(b[1])

ls = np.repeat(a[0], ds) - sigma2_s

lt = np.repeat(a[1], dt) - sigma2_t

Us = Q[0][:, :ds]

Ut = Q[1][:, :dt]

ds = np.array([ds])

dt = np.array([dt])

prmts = {

"ms": ms,

"mt": mt,

"sigma2_s": sigma2_s,

"sigma2_t": sigma2_t,

"ls": ls,

"lt": lt,

"Us": Us,

"Ut": Ut,

"ds": ds,

"dt": dt,

"Cs": S[0],

"Ct": S[1],

}

return Xs, Xt, prmts</div>

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