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Greedy Furthest Point Sampling
"""
Programmer: Chris Tralie
Purpose: To demonstrate a greedy furthest point sampling, which is a general technique
for getting good points that are "spread out" and cover the dataset well
"""
import numpy as np
import matplotlib.pyplot as plt
from sklearn.metrics.pairwise import pairwise_distances
def getGreedyPerm(D):
"""
A Naive O(N^2) algorithm to do furthest points sampling
Parameters
----------
D : ndarray (N, N)
An NxN distance matrix for points
Return
------
tuple (list, list)
(permutation (N-length array of indices),
lambdas (N-length array of insertion radii))
"""
N = D.shape[0]
#By default, takes the first point in the list to be the
#first point in the permutation, but could be random
perm = np.zeros(N, dtype=np.int64)
lambdas = np.zeros(N)
ds = D[0, :]
for i in range(1, N):
idx = np.argmax(ds)
perm[i] = idx
lambdas[i] = ds[idx]
ds = np.minimum(ds, D[idx, :])
return (perm, lambdas)
def makeVideoExample():
t = np.linspace(0, 2*np.pi, 101)[0:100]
X1 = np.zeros((len(t), 2))
X1[:, 0] = np.cos(t)
X1[:, 1] = np.sin(t)
t = np.linspace(0, 2*np.pi, 1001)[0:1000]
X2 = np.zeros((len(t), 2))
X2[:, 0] = 2*np.cos(t)+5
X2[:, 1] = 2*np.sin(t)
X3 = np.zeros((len(t), 2))
X3[:, 0] = 3*np.cos(t)
X3[:, 1] = 3*np.sin(t)+3
X = np.concatenate((X1, X2, X3), 0)
D = pairwise_distances(X, metric='euclidean')
(perm, lambdas) = getGreedyPerm(D)
xlims = [np.min(X[:, 0]) - lambdas[1], np.max(X[:, 0]) + lambdas[1]]
ylims = [np.min(X[:, 1]) - lambdas[1], np.max(X[:, 1]) + lambdas[1]]
plt.figure(figsize=(8, 4))
for i in range(50):
plt.clf()
plt.subplot(121)
plt.plot(X[:, 0], X[:, 1], '.')
plt.hold(True)
R = lambdas[i+1]
plt.scatter(X[perm[0:i+1], 0], X[perm[0:i+1], 1], 50, 'k')
t = np.linspace(0, 2*np.pi, 100)
cx = R*np.cos(t)
cy = R*np.sin(t)
for k in range(0, i+1):
plt.plot(cx + X[perm[k], 0], cy + X[perm[k], 1], 'b')
plt.xlim(xlims)
plt.ylim(ylims)
plt.axis('off')
plt.subplot(122)
plt.scatter(X[perm[0:i+1], 0], X[perm[0:i+1], 1])
plt.xlim(xlims)
plt.ylim(ylims)
plt.axis('off')
plt.savefig("%i.jpg"%i)
if __name__ == '__main__':
makeVideoExample()
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@ctralie ctralie commented May 7, 2018

out

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