def simplified_algo(R, iterations, warp=0):
S = best_embedding_on_sphere(R, ndim=3)
R_order = scale_score(R).astype('int16')
for i in range(iterations): # @UnusedVariable
C = np.dot(S.T, S)
C_sorted = np.sort(C.flat)
R = C_sorted[R_order]
S = best_embedding_on_sphere(R, ndim=3)
if warp > 0:
base_D = distances_from_directions(S)
diameter = base_D.max()
min_ratio = 0.1
max_ratio = np.pi / diameter
ratios = np.exp(np.linspace(np.log(min_ratio),
np.log(max_ratio), warp))
scores = []
guesses = []
for ratio in ratios:
Cwarp = cosines_from_distances(base_D * ratio)
Sw = best_embedding_on_sphere(Cwarp, ndim=3)
Cw_order = scale_score(cosines_from_directions(Sw))
scores.append(correlation_coefficient(Cw_order, R_order))
guesses.append(Sw)
best = np.argmax(scores)
print('Best warp: %d (%f)' % (best, ratios[best]))
S = guesses[best]
return S
def simplified_algo(R, iterations, warp=0):
S = best_embedding_on_sphere(R, ndim=3)
R_order = scale_score(R).astype('int16')
for i in range(iterations): # @UnusedVariable
C = np.dot(S.T, S)
C_sorted = np.sort(C.flat)
R = C_sorted[R_order]
S = best_embedding_on_sphere(R, ndim=3)
if warp > 0:
base_D = distances_from_directions(S)
diameter = base_D.max()
min_ratio = 0.1
max_ratio = np.pi / diameter
ratios = np.exp(np.linspace(np.log(min_ratio), np.log(max_ratio),
warp))
scores = []
guesses = []
for ratio in ratios:
Cwarp = cosines_from_distances(base_D * ratio)
Sw = best_embedding_on_sphere(Cwarp, ndim=3)
Cw_order = scale_score(cosines_from_directions(Sw))
scores.append(correlation_coefficient(Cw_order, R_order))
guesses.append(Sw)
best = np.argmax(scores)
print('Best warp: %d (%f)' % (best, ratios[best]))
S = guesses[best]
return S
def seq():
N = 180
iterations = 10
nradii = 100
radii = np.linspace(5, 180, nradii)
K = 1
for radius_deg, i in itertools.product(radii, range(K)):
print radius_deg, i
# Generate a random symmetric matrix
# x = np.random.rand(N, N)
S = random_directions_bounded(3, np.radians(radius_deg), N)
C = np.dot(S.T, S)
alpha = 1
f = lambda x: np.exp(-alpha * (1 - x))
# f = lambda x : x
R = f(C)
# Normalize in [0,1]
R1 = (R - R.min()) / (R.max() - R.min())
# Normalize in [-1,1]
R2 = (R1 - 0.5) * 2
S1 = simplified_algo(R1, iterations)
S1w = simplified_algo(R1, iterations, warp=50)
S2 = simplified_algo(R2, iterations)
s1 = spearman(cosines_from_directions(S1), R1)
s1w = spearman(cosines_from_directions(S1w), R1)
s2 = spearman(cosines_from_directions(S2), R2)
e1 = np.degrees(overlap_error_after_orthogonal_transform(S, S1))
e1w = np.degrees(overlap_error_after_orthogonal_transform(S, S1w))
e2 = np.degrees(overlap_error_after_orthogonal_transform(S, S2))
r0 = np.degrees(distribution_radius(S))
r1 = np.degrees(distribution_radius(S1))
r1w = np.degrees(distribution_radius(S1w))
r2 = np.degrees(distribution_radius(S2))
yield dict(R0=r0,
R1=r1,
R1w=r1w,
R2=r2,
e1=e1,
e2=e2,
s1=s1,
s2=s2,
s1w=s1w,
e1w=e1w)
def seq():
N = 180
iterations = 10
nradii = 100
radii = np.linspace(5, 180, nradii)
K = 1
for radius_deg, i in itertools.product(radii, range(K)):
print radius_deg, i
# Generate a random symmetric matrix
# x = np.random.rand(N, N)
S = random_directions_bounded(3, np.radians(radius_deg), N)
C = np.dot(S.T, S)
alpha = 1
f = lambda x: np.exp(-alpha * (1 - x))
# f = lambda x : x
R = f(C)
# Normalize in [0,1]
R1 = (R - R.min()) / (R.max() - R.min())
# Normalize in [-1,1]
R2 = (R1 - 0.5) * 2
S1 = simplified_algo(R1, iterations)
S1w = simplified_algo(R1, iterations, warp=50)
S2 = simplified_algo(R2, iterations)
s1 = spearman(cosines_from_directions(S1), R1)
s1w = spearman(cosines_from_directions(S1w), R1)
s2 = spearman(cosines_from_directions(S2), R2)
e1 = np.degrees(overlap_error_after_orthogonal_transform(S, S1))
e1w = np.degrees(overlap_error_after_orthogonal_transform(S, S1w))
e2 = np.degrees(overlap_error_after_orthogonal_transform(S, S2))
r0 = np.degrees(distribution_radius(S))
r1 = np.degrees(distribution_radius(S1))
r1w = np.degrees(distribution_radius(S1w))
r2 = np.degrees(distribution_radius(S2))
yield dict(R0=r0, R1=r1, R1w=r1w, R2=r2, e1=e1, e2=e2,
s1=s1, s2=s2,
s1w=s1w, e1w=e1w)
