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运行结果
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main函数
import matplotlib.pyplot as plt
import numpy as np
mean1 = [0, 0]
cov1 = [[5, 0], [-5, 10]] # diagonal covariance
mean2 = [10, 0]
cov2 = [[5, 0], [5, 10]] # diagonal covariance
x1, y1 = np.random.multivariate_normal(mean1, cov1, 5000).T
x2, y2 = np.random.multivariate_normal(mean2, cov2, 5000).T
plt.scatter(x1, y1, c='r', alpha=0.1)
plt.scatter(x2, y2, c='b', alpha=0.1)
plt.axis('equal')
plt.show()
source = np.vstack([x1, y1]).T
target = np.vstack([x2, y2]).T
from utils.mmd_numpy_sklearn import mmd_linear, mmd_poly, mmd_rbf
def cal_dis(source, target, function):
d1 = function(source, target)
d2 = function(target, source)
d3 = function(source, source)
d4 = function(target, target)
print('D1-{:.2f}; D2-{:.2f}; D3-{:.2f}; D4-{:.2f}.'.format(d1, d2, d3, d4))
cal_dis(source, target, mmd_linear)
cal_dis(source, target, mmd_poly)
cal_dis(source, target, mmd_rbf)
- mmd函数
# Compute MMD (maximum mean discrepancy) using numpy and scikit-learn.
import numpy as np
from sklearn import metrics
def mmd_linear(X, Y):
"""MMD using linear kernel (i.e., k(x,y) = )
Note that this is not the original linear MMD, only the reformulated and faster version.
The original version is:
def mmd_linear(X, Y):
XX = np.dot(X, X.T)
YY = np.dot(Y, Y.T)
XY = np.dot(X, Y.T)
return XX.mean() + YY.mean() - 2 * XY.mean()
Arguments:
X {[n_sample1, dim]} -- [X matrix]
Y {[n_sample2, dim]} -- [Y matrix]
Returns:
[scalar] -- [MMD value]
"""
delta = X.mean(0) - Y.mean(0)
return delta.dot(delta.T)
def mmd_rbf(X, Y, gamma=1.0):
"""MMD using rbf (gaussian) kernel (i.e., k(x,y) = exp(-gamma * ||x-y||^2 / 2))
Arguments:
X {[n_sample1, dim]} -- [X matrix]
Y {[n_sample2, dim]} -- [Y matrix]
Keyword Arguments:
gamma {float} -- [kernel parameter] (default: {1.0})
Returns:
[scalar] -- [MMD value]
"""
XX = metrics.pairwise.rbf_kernel(X, X, gamma)
YY = metrics.pairwise.rbf_kernel(Y, Y, gamma)
XY = metrics.pairwise.rbf_kernel(X, Y, gamma)
return XX.mean() + YY.mean() - 2 * XY.mean()
def mmd_poly(X, Y, degree=2, gamma=1, coef0=0):
"""MMD using polynomial kernel (i.e., k(x,y) = (gamma + coef0)^degree)
Arguments:
X {[n_sample1, dim]} -- [X matrix]
Y {[n_sample2, dim]} -- [Y matrix]
Keyword Arguments:
degree {int} -- [degree] (default: {2})
gamma {int} -- [gamma] (default: {1})
coef0 {int} -- [constant item] (default: {0})
Returns:
[scalar] -- [MMD value]
"""
XX = metrics.pairwise.polynomial_kernel(X, X, degree, gamma, coef0)
YY = metrics.pairwise.polynomial_kernel(Y, Y, degree, gamma, coef0)
XY = metrics.pairwise.polynomial_kernel(X, Y, degree, gamma, coef0)
return XX.mean() + YY.mean() - 2 * XY.mean()
if __name__ == '__main__':
a = np.arange(1, 10).reshape(3, 3)
b = [[7, 6, 5], [4, 3, 2], [1, 1, 8], [0, 2, 5]]
b = np.array(b)
print(a)
print(b)
print(mmd_linear(a, b)) # 6.0
print(mmd_rbf(a, b)) # 0.5822
print(mmd_poly(a, b)) # 2436.5
- 参考文献
- https://numpy.org/doc/stable/reference/random/generated/numpy.random.multivariate_normal.html
- https://github.com/jindongwang/transferlearning/blob/master/code/distance/mmd_numpy_sklearn.py
