def test_dense_svd():
dense = DenseTensor(np.random.random(size=(10, 15)))
sparse = dense.to_sparse()
print repr(data(dense.svd().u))
dense_svd_u = np.abs(data(dense.svd().u))
sparse_svd_u = np.abs(data(sparse.svd().u))
assert np.all(np.abs(dense_svd_u - sparse_svd_u) < 0.0001)
def aspace_mds():
from csc.conceptnet.analogyspace import conceptnet_2d_from_db
cnet = conceptnet_2d_from_db('en')
aspace = cnet.normalized().svd(k=100)
labels = cnet.label_list(0)
ptmatrix = data(aspace.u)
ptmatrix *= data(aspace.svals)
proj = mds(ptmatrix)
result = proj.project(data(aspace.u))
return LabeledView(DenseTensor(result), [labels, None])
def aspace_mds():
from csc.conceptnet.analogyspace import conceptnet_2d_from_db
cnet = conceptnet_2d_from_db('en')
aspace = cnet.normalized().svd(k=100)
labels = cnet.label_list(0)
ptmatrix = data(aspace.u)
ptmatrix *= data(aspace.svals)
proj = mds(ptmatrix)
result = proj.project(data(aspace.u))
return LabeledView(DenseTensor(result), [labels, None])
def mds(matrix, k=2):
if isinstance(matrix, Tensor):
matrix = data(matrix.to_dense())
# Find Landmark points
N = matrix.shape[0]
landmarks = _getLandmarkPoints(N)
num_landmarks = len(landmarks)
landmark_matrix = matrix[landmarks]
sqdistances = compute_distances(landmark_matrix, landmark_matrix)
# Do normal MDS on landmark points
means = np.mean(sqdistances, axis=1) # this is called mu_n in the paper
global_mean = np.mean(means) # this is called mu in the paper
# this is called B in the paper
distances_balanced = -(sqdistances - means[np.newaxis, :] -
means[:, np.newaxis] + global_mean) / 2
# find the eigenvectors and eigenvalues with our all-purpose hammer
# for the paper, Lambda = lambda, Q = V
Q, Lambda, Qt = np.linalg.svd(distances_balanced)
k = min(k, len(Lambda))
mdsarray_sharp = Q[:, :k] # called L^sharp transpose in the paper
mdsarray = mdsarray_sharp * np.sqrt(Lambda)[
np.newaxis, :k] # called L transpose in the paper
# Make Triangulation Object
return MDSProjection(landmark_matrix, mdsarray_sharp, means)
def mds(matrix, k=2):
if isinstance(matrix, Tensor):
matrix = data(matrix.to_dense())
# Find Landmark points
N = matrix.shape[0]
landmarks = _getLandmarkPoints(N)
num_landmarks = len(landmarks)
landmark_matrix = matrix[landmarks]
sqdistances = compute_distances(landmark_matrix, landmark_matrix)
# Do normal MDS on landmark points
means = np.mean(sqdistances, axis=1) # this is called mu_n in the paper
global_mean = np.mean(means) # this is called mu in the paper
# this is called B in the paper
distances_balanced = -(sqdistances - means[np.newaxis,:] - means[:,np.newaxis] + global_mean)/2
# find the eigenvectors and eigenvalues with our all-purpose hammer
# for the paper, Lambda = lambda, Q = V
Q, Lambda, Qt = np.linalg.svd(distances_balanced)
k = min(k, len(Lambda))
mdsarray_sharp = Q[:,:k] # called L^sharp transpose in the paper
mdsarray = mdsarray_sharp * np.sqrt(Lambda)[np.newaxis,:k] # called L transpose in the paper
# Make Triangulation Object
return MDSProjection(landmark_matrix, mdsarray_sharp, means)
def test_dense_data():
t1 = LabeledView(DenseTensor(zeros((2, 2))), [['a', 'b'], ['c', 'd']])
assert isinstance(data(t1), ndarray)
def test_dense_data():
t1 = LabeledView(DenseTensor(zeros((2,2))), [['a', 'b'], ['c', 'd']])
assert isinstance(data(t1), ndarray)
