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# Author: Mathieu Blondel | |
# License: BSD | |
import numpy as np | |
def find_r(w,k): | |
d = w.shape[0] | |
beta= np.r_[np.Inf,np.sort(np.abs(w))[::-1]] | |
tmp = np.sum(beta[k:d+1]) | |
for r in range(0,k): # from r = 0 to k-1 | |
if r == k-1: | |
break | |
if (beta[k-r-1] > tmp / (r+1)) and tmp / (r+1) >= beta[k-r]: | |
break | |
else: | |
tmp += beta[k-r-1] | |
return r, tmp, beta[1:] | |
def k_support_norm(w, k, squared=False): | |
r, tmp, beta = find_r(w, k) | |
sqnorm = np.sum(beta[0:k-r-1] ** 2) | |
sqnorm += (tmp ** 2) / (r+1) | |
if squared: | |
return 0.5 * sqnorm | |
else: | |
return np.sqrt(sqnorm) | |
# Naive implementation with two loops. | |
def k_support_norm2(w, k, squared=False): | |
d = len(w) | |
ind = np.argsort(np.abs(w))[::-1] | |
beta = np.abs(w[ind]) | |
beta = np.r_[np.Inf, beta] | |
for r in range(0, k): # from r = 0 to k-1 | |
tmp = 0 | |
for i in range(k-r, d+1): # from i = k-r | |
tmp += beta[i] | |
if beta[k-r-1] > tmp / (r+1) and tmp / (r+1) >= beta[k-r]: | |
break | |
sqnorm = np.sum(beta[1:k-r] ** 2) | |
sqnorm += (tmp ** 2) / (r+1) | |
if squared: | |
return 0.5 * sqnorm | |
else: | |
return np.sqrt(sqnorm) | |
def dual_k_support_norm(w, k, squared=False): | |
ind = np.argsort(np.abs(w))[::-1] | |
sqnorm = np.sum(w[ind][:k] ** 2) | |
if squared: | |
return 0.5 * sqnorm | |
else: | |
return np.sqrt(sqnorm) | |
if __name__ == '__main__': | |
rng = np.random.RandomState(None) | |
a = rng.randn(10) | |
k = 3 | |
# Non-sparse vector | |
print(k_support_norm(a, k)) | |
print(k_support_norm2(a, k)) | |
print(dual_k_support_norm(a, k)) | |
# k-sparse vector | |
ind = np.argsort(np.abs(a)) | |
a[ind[k:]] = 0 | |
print(k_support_norm(a, k)) | |
print(k_support_norm2(a, k)) | |
print(dual_k_support_norm(a, k)) | |
import matplotlib.pyplot as plt | |
xs = np.linspace(-2, 2, 100) | |
plt.figure() | |
values = [k_support_norm(np.array([x, 0.5, -0.7]), k=2, squared=True) for x in xs] | |
plt.plot(xs, values) | |
plt.show() | |
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