def test_sparse_alpha_knn_graph():
data = datasets.make_swiss_roll()[0]
k = 5
a = 0.45
thresh = 0.01
bandwidth_scale = 1.3
pdx = squareform(pdist(data, metric="euclidean"))
knn_dist = np.partition(pdx, k, axis=1)[:, :k]
epsilon = np.max(knn_dist, axis=1) * bandwidth_scale
pdx = (pdx.T / epsilon).T
K = np.exp(-1 * pdx**a)
K = K + K.T
W = np.divide(K, 2)
np.fill_diagonal(W, 0)
G = pygsp.graphs.Graph(W)
G2 = build_graph(
data,
n_pca=None, # n_pca,
decay=a,
knn=k - 1,
thresh=thresh,
bandwidth_scale=bandwidth_scale,
random_state=42,
use_pygsp=True,
)
assert np.abs(G.W - G2.W).max() < thresh
assert G.N == G2.N
assert isinstance(G2, graphtools.graphs.kNNGraph)
def test_knn_graph():
k = 3
n_pca = 20
pca = PCA(n_pca, svd_solver='randomized', random_state=42).fit(data)
data_nu = pca.transform(data)
pdx = squareform(pdist(data_nu, metric='euclidean'))
knn_dist = np.partition(pdx, k, axis=1)[:, :k]
epsilon = np.max(knn_dist, axis=1)
K = np.empty_like(pdx)
for i in range(len(pdx)):
K[i, pdx[i, :] <= epsilon[i]] = 1
K[i, pdx[i, :] > epsilon[i]] = 0
K = K + K.T
W = np.divide(K, 2)
np.fill_diagonal(W, 0)
G = pygsp.graphs.Graph(W)
G2 = build_graph(data, n_pca=n_pca,
decay=None, knn=k, random_state=42,
use_pygsp=True)
assert(G.N == G2.N)
assert(np.all(G.d == G2.d))
assert((G.W != G2.W).nnz == 0)
assert((G2.W != G.W).sum() == 0)
assert(isinstance(G2, graphtools.graphs.kNNGraph))
def test_mnn_graph_matrix_gamma():
X, sample_idx = generate_swiss_roll()
bs = 0.8
gamma = np.array([
[1, bs], # 0
[bs, 1]
]) # 3
k = 10
a = 20
metric = 'euclidean'
beta = 0
samples = np.unique(sample_idx)
K = np.zeros((len(X), len(X)))
K[:] = np.nan
K = pd.DataFrame(K)
for si in samples:
X_i = X[sample_idx == si] # get observations in sample i
for sj in samples:
X_j = X[sample_idx == sj] # get observation in sample j
pdx_ij = cdist(X_i, X_j, metric=metric) # pairwise distances
kdx_ij = np.sort(pdx_ij, axis=1) # get kNN
e_ij = kdx_ij[:, k] # dist to kNN
pdxe_ij = pdx_ij / e_ij[:, np.newaxis] # normalize
k_ij = np.exp(-1 * (pdxe_ij**a)) # apply alpha-decaying kernel
if si == sj:
K.iloc[sample_idx == si, sample_idx == sj] = k_ij * \
(1 - beta) # fill out values in K for NN on diagonal
else:
# fill out values in K for NN on diagonal
K.iloc[sample_idx == si, sample_idx == sj] = k_ij
K = np.array(K)
matrix_gamma = pd.DataFrame(np.zeros((len(sample_idx), len(sample_idx))))
for ix, si in enumerate(set(sample_idx)):
for jx, sj in enumerate(set(sample_idx)):
matrix_gamma.iloc[sample_idx == si, sample_idx == sj] = gamma[ix,
jx]
W = np.array((matrix_gamma * np.minimum(K, K.T)) +
((1 - matrix_gamma) * np.maximum(K, K.T)))
np.fill_diagonal(W, 0)
G = pygsp.graphs.Graph(W)
G2 = graphtools.Graph(X,
knn=k + 1,
decay=a,
beta=1 - beta,
kernel_symm='gamma',
gamma=gamma,
distance=metric,
sample_idx=sample_idx,
thresh=0,
use_pygsp=True)
assert G.N == G2.N
assert np.all(G.d == G2.d)
assert (G.W != G2.W).nnz == 0
assert (G2.W != G.W).sum() == 0
assert isinstance(G2, graphtools.graphs.MNNGraph)
def test_knn_graph_sparse():
k = 3
n_pca = 20
pca = TruncatedSVD(n_pca, random_state=42).fit(data)
data_nu = pca.transform(data)
pdx = squareform(pdist(data_nu, metric="euclidean"))
knn_dist = np.partition(pdx, k, axis=1)[:, :k]
epsilon = np.max(knn_dist, axis=1)
K = np.empty_like(pdx)
for i in range(len(pdx)):
K[i, pdx[i, :] <= epsilon[i]] = 1
K[i, pdx[i, :] > epsilon[i]] = 0
K = K + K.T
W = np.divide(K, 2)
np.fill_diagonal(W, 0)
G = pygsp.graphs.Graph(W)
G2 = build_graph(
sp.coo_matrix(data),
n_pca=n_pca,
decay=None,
knn=k - 1,
random_state=42,
use_pygsp=True,
)
assert G.N == G2.N
np.testing.assert_allclose(G2.W.toarray(), G.W.toarray())
assert isinstance(G2, graphtools.graphs.kNNGraph)
def test_knn_graph_anisotropy():
k = 3
a = 13
n_pca = 20
anisotropy = 0.9
thresh = 1e-4
data_small = data[np.random.choice(len(data), len(data) // 2, replace=False)]
pca = PCA(n_pca, svd_solver="randomized", random_state=42).fit(data_small)
data_small_nu = pca.transform(data_small)
pdx = squareform(pdist(data_small_nu, metric="euclidean"))
knn_dist = np.partition(pdx, k, axis=1)[:, :k]
epsilon = np.max(knn_dist, axis=1)
weighted_pdx = (pdx.T / epsilon).T
K = np.exp(-1 * weighted_pdx ** a)
K[K < thresh] = 0
K = K + K.T
K = np.divide(K, 2)
d = K.sum(1)
W = K / (np.outer(d, d) ** anisotropy)
np.fill_diagonal(W, 0)
G = pygsp.graphs.Graph(W)
G2 = build_graph(
data_small,
n_pca=n_pca,
thresh=thresh,
decay=a,
knn=k - 1,
random_state=42,
use_pygsp=True,
anisotropy=anisotropy,
)
assert isinstance(G2, graphtools.graphs.kNNGraph)
assert G.N == G2.N
np.testing.assert_allclose(G.dw, G2.dw, atol=1e-14, rtol=1e-14)
np.testing.assert_allclose((G2.W - G.W).data, 0, atol=1e-14, rtol=1e-14)
def test_knn_graph_multiplication_symm():
k = 3
n_pca = 20
pca = PCA(n_pca, svd_solver="randomized", random_state=42).fit(data)
data_nu = pca.transform(data)
pdx = squareform(pdist(data_nu, metric="euclidean"))
knn_dist = np.partition(pdx, k, axis=1)[:, :k]
epsilon = np.max(knn_dist, axis=1)
K = np.empty_like(pdx)
for i in range(len(pdx)):
K[i, pdx[i, :] <= epsilon[i]] = 1
K[i, pdx[i, :] > epsilon[i]] = 0
W = K * K.T
np.fill_diagonal(W, 0)
G = pygsp.graphs.Graph(W)
G2 = build_graph(
data,
n_pca=n_pca,
decay=None,
knn=k - 1,
random_state=42,
use_pygsp=True,
kernel_symm="*",
)
assert G.N == G2.N
np.testing.assert_equal(G.dw, G2.dw)
assert (G.W - G2.W).nnz == 0
assert (G2.W - G.W).sum() == 0
assert isinstance(G2, graphtools.graphs.kNNGraph)
def test_knn_graph_fixed_bandwidth():
k = None
decay = 5
bandwidth = 10
bandwidth_scale = 1.3
n_pca = 20
thresh = 1e-4
pca = PCA(n_pca, svd_solver="randomized", random_state=42).fit(data)
data_nu = pca.transform(data)
pdx = squareform(pdist(data_nu, metric="euclidean"))
K = np.exp(-1 * np.power(pdx / (bandwidth * bandwidth_scale), decay))
K[K < thresh] = 0
K = K + K.T
W = np.divide(K, 2)
np.fill_diagonal(W, 0)
G = pygsp.graphs.Graph(W)
G2 = build_graph(
data,
n_pca=n_pca,
decay=decay,
bandwidth=bandwidth,
bandwidth_scale=bandwidth_scale,
knn=k,
random_state=42,
thresh=thresh,
search_multiplier=2,
use_pygsp=True,
)
assert isinstance(G2, graphtools.graphs.kNNGraph)
np.testing.assert_array_equal(G.N, G2.N)
np.testing.assert_array_equal(G.d, G2.d)
np.testing.assert_allclose((G.W - G2.W).data,
np.zeros_like((G.W - G2.W).data),
atol=1e-14)
bandwidth = np.random.gamma(20, 0.5, len(data))
K = np.exp(-1 * (pdx.T / (bandwidth * bandwidth_scale)).T**decay)
K[K < thresh] = 0
K = K + K.T
W = np.divide(K, 2)
np.fill_diagonal(W, 0)
G = pygsp.graphs.Graph(W)
G2 = build_graph(
data,
n_pca=n_pca,
decay=decay,
bandwidth=bandwidth,
bandwidth_scale=bandwidth_scale,
knn=k,
random_state=42,
thresh=thresh,
use_pygsp=True,
)
assert isinstance(G2, graphtools.graphs.kNNGraph)
np.testing.assert_array_equal(G.N, G2.N)
np.testing.assert_allclose(G.dw, G2.dw, atol=1e-14)
np.testing.assert_allclose((G.W - G2.W).data,
np.zeros_like((G.W - G2.W).data),
atol=1e-14)
def test_shortest_path_constant():
data_small = data[np.random.choice(len(data), len(data) // 4, replace=False)]
G = build_graph(data_small, knn=5, decay=None)
P = graph_shortest_path(G.K)
# sklearn returns 0 if no path exists
P[np.where(P == 0)] = np.inf
# diagonal should actually be zero
np.fill_diagonal(P, 0)
np.testing.assert_equal(P, G.shortest_path(distance="constant"))
def test_exact_graph_callable_bandwidth():
decay = 2
knn = 5
def bandwidth(x):
return 2
n_pca = 20
thresh = 1e-4
pca = PCA(n_pca, svd_solver="randomized", random_state=42).fit(data)
data_nu = pca.transform(data)
pdx = squareform(pdist(data_nu, metric="euclidean"))
K = np.exp(-1 * (pdx / bandwidth(pdx))**decay)
K[K < thresh] = 0
K = K + K.T
W = np.divide(K, 2)
np.fill_diagonal(W, 0)
G = pygsp.graphs.Graph(W)
G2 = build_graph(
data,
n_pca=n_pca,
knn=knn - 1,
decay=decay,
bandwidth=bandwidth,
random_state=42,
thresh=thresh,
use_pygsp=True,
)
assert isinstance(G2, graphtools.graphs.TraditionalGraph)
assert G.N == G2.N
np.testing.assert_equal(G.dw, G2.dw)
assert (G2.W != G.W).sum() == 0
assert (G.W != G2.W).nnz == 0
def bandwidth(x):
return np.percentile(x, 10, axis=1)
K = np.exp(-1 * (pdx / bandwidth(pdx))**decay)
K[K < thresh] = 0
K = K + K.T
W = np.divide(K, 2)
np.fill_diagonal(W, 0)
G = pygsp.graphs.Graph(W)
G2 = build_graph(
data,
n_pca=n_pca,
knn=knn - 1,
decay=decay,
bandwidth=bandwidth,
random_state=42,
thresh=thresh,
use_pygsp=True,
)
assert isinstance(G2, graphtools.graphs.TraditionalGraph)
assert G.N == G2.N
np.testing.assert_allclose(G.dw, G2.dw)
np.testing.assert_allclose((G2.W - G.W).data, 0, atol=1e-14)
def test_shortest_path_data():
data_small = data[np.random.choice(len(data), len(data) // 4, replace=False)]
G = build_graph(data_small, knn=5, decay=None)
D = squareform(pdist(G.data_nu)) * np.where(G.K.toarray() > 0, 1, 0)
P = graph_shortest_path(D)
# sklearn returns 0 if no path exists
P[np.where(P == 0)] = np.inf
# diagonal should actually be zero
np.fill_diagonal(P, 0)
np.testing.assert_allclose(P, G.shortest_path(distance="data"))
np.testing.assert_allclose(P, G.shortest_path())
def test_shortest_path_affinity():
data_small = data[np.random.choice(len(data),
len(data) // 4,
replace=False)]
G = build_graph(data_small, knn=5, decay=15)
D = -1 * np.where(G.K != 0, np.log(np.where(G.K != 0, G.K, np.nan)), 0)
P = graph_shortest_path(D)
# sklearn returns 0 if no path exists
P[np.where(P == 0)] = np.inf
# diagonal should actually be zero
np.fill_diagonal(P, 0)
np.testing.assert_allclose(P, G.shortest_path(distance="affinity"))
np.testing.assert_allclose(P, G.shortest_path())
def test_exact_graph_fixed_bandwidth():
decay = 2
knn = None
bandwidth = 2
n_pca = 20
pca = PCA(n_pca, svd_solver="randomized", random_state=42).fit(data)
data_nu = pca.transform(data)
pdx = squareform(pdist(data_nu, metric="euclidean"))
K = np.exp(-1 * (pdx / bandwidth)**decay)
K = K + K.T
W = np.divide(K, 2)
np.fill_diagonal(W, 0)
G = pygsp.graphs.Graph(W)
G2 = build_graph(
data,
n_pca=n_pca,
graphtype="exact",
knn=knn,
decay=decay,
bandwidth=bandwidth,
random_state=42,
thresh=0,
use_pygsp=True,
)
assert isinstance(G2, graphtools.graphs.TraditionalGraph)
assert G.N == G2.N
np.testing.assert_allclose(G.dw, G2.dw)
np.testing.assert_allclose((G2.W - G.W).data, 0, atol=1e-14)
bandwidth = np.random.gamma(5, 0.5, len(data))
K = np.exp(-1 * (pdx.T / bandwidth).T**decay)
K = K + K.T
W = np.divide(K, 2)
np.fill_diagonal(W, 0)
G = pygsp.graphs.Graph(W)
G2 = build_graph(
data,
n_pca=n_pca,
graphtype="exact",
knn=knn,
decay=decay,
bandwidth=bandwidth,
random_state=42,
thresh=0,
use_pygsp=True,
)
assert isinstance(G2, graphtools.graphs.TraditionalGraph)
assert G.N == G2.N
np.testing.assert_allclose(G.dw, G2.dw)
np.testing.assert_allclose((G2.W - G.W).data, 0, atol=1e-14)
def test_truncated_exact_graph_no_pca():
k = 3
a = 13
n_pca = None
thresh = 1e-4
data_small = data[np.random.choice(len(data),
len(data) // 10,
replace=False)]
pdx = squareform(pdist(data_small, metric="euclidean"))
knn_dist = np.partition(pdx, k, axis=1)[:, :k]
epsilon = np.max(knn_dist, axis=1)
weighted_pdx = (pdx.T / epsilon).T
K = np.exp(-1 * weighted_pdx**a)
K[K < thresh] = 0
W = K + K.T
W = np.divide(W, 2)
np.fill_diagonal(W, 0)
G = pygsp.graphs.Graph(W)
G2 = build_graph(
data_small,
thresh=thresh,
graphtype="exact",
n_pca=n_pca,
decay=a,
knn=k - 1,
random_state=42,
use_pygsp=True,
)
assert G.N == G2.N
np.testing.assert_equal(G.dw, G2.dw)
assert (G.W != G2.W).nnz == 0
assert (G2.W != G.W).sum() == 0
assert isinstance(G2, graphtools.graphs.TraditionalGraph)
G2 = build_graph(
sp.csr_matrix(data_small),
thresh=thresh,
graphtype="exact",
n_pca=n_pca,
decay=a,
knn=k - 1,
random_state=42,
use_pygsp=True,
)
assert G.N == G2.N
np.testing.assert_equal(G.dw, G2.dw)
assert (G.W != G2.W).nnz == 0
assert (G2.W != G.W).sum() == 0
assert isinstance(G2, graphtools.graphs.TraditionalGraph)
def test_knnmax():
data = datasets.make_swiss_roll()[0]
k = 5
k_max = 10
a = 0.45
thresh = 0
with warnings.catch_warnings():
warnings.filterwarnings("ignore", "K should be symmetric",
RuntimeWarning)
G = build_graph(
data,
n_pca=None, # n_pca,
decay=a,
knn=k - 1,
knn_max=k_max - 1,
thresh=0,
random_state=42,
kernel_symm=None,
)
assert np.all((G.K > 0).sum(axis=1) == k_max)
pdx = squareform(pdist(data, metric="euclidean"))
knn_dist = np.partition(pdx, k, axis=1)[:, :k]
knn_max_dist = np.max(np.partition(pdx, k_max, axis=1)[:, :k_max], axis=1)
epsilon = np.max(knn_dist, axis=1)
pdx_scale = (pdx.T / epsilon).T
K = np.where(pdx <= knn_max_dist[:, None], np.exp(-1 * pdx_scale**a), 0)
K = K + K.T
W = np.divide(K, 2)
np.fill_diagonal(W, 0)
G = pygsp.graphs.Graph(W)
G2 = build_graph(
data,
n_pca=None, # n_pca,
decay=a,
knn=k - 1,
knn_max=k_max - 1,
thresh=0,
random_state=42,
use_pygsp=True,
)
assert isinstance(G2, graphtools.graphs.kNNGraph)
assert G.N == G2.N
assert np.all(G.dw == G2.dw)
assert (G.W - G2.W).nnz == 0
def test_knn_graph():
k = 3
n_pca = 20
pca = PCA(n_pca, svd_solver="randomized", random_state=42).fit(data)
data_nu = pca.transform(data)
pdx = squareform(pdist(data_nu, metric="euclidean"))
knn_dist = np.partition(pdx, k, axis=1)[:, :k]
epsilon = np.max(knn_dist, axis=1)
K = np.empty_like(pdx)
for i in range(len(pdx)):
K[i, pdx[i, :] <= epsilon[i]] = 1
K[i, pdx[i, :] > epsilon[i]] = 0
K = K + K.T
W = np.divide(K, 2)
np.fill_diagonal(W, 0)
G = pygsp.graphs.Graph(W)
G2 = build_graph(data,
n_pca=n_pca,
decay=None,
knn=k - 1,
random_state=42,
use_pygsp=True)
assert G.N == G2.N
np.testing.assert_equal(G.dw, G2.dw)
assert (G.W - G2.W).nnz == 0
assert (G2.W - G.W).sum() == 0
assert isinstance(G2, graphtools.graphs.kNNGraph)
K2 = G2.build_kernel_to_data(G2.data_nu, knn=k)
K2 = (K2 + K2.T) / 2
assert (G2.K - K2).nnz == 0
assert (G2.build_kernel_to_data(
G2.data_nu, knn=data.shape[0]).nnz == data.shape[0] * data.shape[0])
with assert_warns_message(
UserWarning,
"Cannot set knn ({}) to be greater than "
"n_samples ({}). Setting knn={}".format(data.shape[0] + 1,
data.shape[0],
data.shape[0]),
):
G2.build_kernel_to_data(
Y=G2.data_nu,
knn=data.shape[0] + 1,
)
def test_exact_graph_anisotropy():
k = 3
a = 13
n_pca = 20
anisotropy = 0.9
data_small = data[np.random.choice(len(data),
len(data) // 2,
replace=False)]
pca = PCA(n_pca, svd_solver="randomized", random_state=42).fit(data_small)
data_small_nu = pca.transform(data_small)
pdx = squareform(pdist(data_small_nu, metric="euclidean"))
knn_dist = np.partition(pdx, k, axis=1)[:, :k]
epsilon = np.max(knn_dist, axis=1)
weighted_pdx = (pdx.T / epsilon).T
K = np.exp(-1 * weighted_pdx**a)
K = K + K.T
K = np.divide(K, 2)
d = K.sum(1)
W = K / (np.outer(d, d)**anisotropy)
np.fill_diagonal(W, 0)
G = pygsp.graphs.Graph(W)
G2 = build_graph(
data_small,
thresh=0,
n_pca=n_pca,
decay=a,
knn=k - 1,
random_state=42,
use_pygsp=True,
anisotropy=anisotropy,
)
assert isinstance(G2, graphtools.graphs.TraditionalGraph)
assert G.N == G2.N
np.testing.assert_equal(G.dw, G2.dw)
assert (G2.W != G.W).sum() == 0
assert (G.W != G2.W).nnz == 0
with assert_raises_message(ValueError,
"Expected 0 <= anisotropy <= 1. Got -1"):
build_graph(
data_small,
thresh=0,
n_pca=n_pca,
decay=a,
knn=k - 1,
random_state=42,
use_pygsp=True,
anisotropy=-1,
)
with assert_raises_message(ValueError,
"Expected 0 <= anisotropy <= 1. Got 2"):
build_graph(
data_small,
thresh=0,
n_pca=n_pca,
decay=a,
knn=k - 1,
random_state=42,
use_pygsp=True,
anisotropy=2,
)
with assert_raises_message(ValueError,
"Expected 0 <= anisotropy <= 1. Got invalid"):
build_graph(
data_small,
thresh=0,
n_pca=n_pca,
decay=a,
knn=k - 1,
random_state=42,
use_pygsp=True,
anisotropy="invalid",
)
def test_exact_graph():
k = 3
a = 13
n_pca = 20
bandwidth_scale = 1.3
data_small = data[np.random.choice(len(data),
len(data) // 2,
replace=False)]
pca = PCA(n_pca, svd_solver="randomized", random_state=42).fit(data_small)
data_small_nu = pca.transform(data_small)
pdx = squareform(pdist(data_small_nu, metric="euclidean"))
knn_dist = np.partition(pdx, k, axis=1)[:, :k]
epsilon = np.max(knn_dist, axis=1) * bandwidth_scale
weighted_pdx = (pdx.T / epsilon).T
K = np.exp(-1 * weighted_pdx**a)
W = K + K.T
W = np.divide(W, 2)
np.fill_diagonal(W, 0)
G = pygsp.graphs.Graph(W)
G2 = build_graph(
data_small,
thresh=0,
n_pca=n_pca,
decay=a,
knn=k - 1,
random_state=42,
bandwidth_scale=bandwidth_scale,
use_pygsp=True,
)
assert G.N == G2.N
np.testing.assert_equal(G.dw, G2.dw)
assert (G.W != G2.W).nnz == 0
assert (G2.W != G.W).sum() == 0
assert isinstance(G2, graphtools.graphs.TraditionalGraph)
G2 = build_graph(
pdx,
n_pca=None,
precomputed="distance",
bandwidth_scale=bandwidth_scale,
decay=a,
knn=k - 1,
random_state=42,
use_pygsp=True,
)
assert G.N == G2.N
np.testing.assert_equal(G.dw, G2.dw)
assert (G.W != G2.W).nnz == 0
assert (G2.W != G.W).sum() == 0
assert isinstance(G2, graphtools.graphs.TraditionalGraph)
G2 = build_graph(
sp.coo_matrix(K),
n_pca=None,
precomputed="affinity",
random_state=42,
use_pygsp=True,
)
assert G.N == G2.N
np.testing.assert_equal(G.dw, G2.dw)
assert (G.W != G2.W).nnz == 0
assert (G2.W != G.W).sum() == 0
assert isinstance(G2, graphtools.graphs.TraditionalGraph)
G2 = build_graph(K,
n_pca=None,
precomputed="affinity",
random_state=42,
use_pygsp=True)
assert G.N == G2.N
np.testing.assert_equal(G.dw, G2.dw)
assert (G.W != G2.W).nnz == 0
assert (G2.W != G.W).sum() == 0
assert isinstance(G2, graphtools.graphs.TraditionalGraph)
G2 = build_graph(W,
n_pca=None,
precomputed="adjacency",
random_state=42,
use_pygsp=True)
assert G.N == G2.N
np.testing.assert_equal(G.dw, G2.dw)
assert (G.W != G2.W).nnz == 0
assert (G2.W != G.W).sum() == 0
assert isinstance(G2, graphtools.graphs.TraditionalGraph)
def test_truncated_exact_graph_sparse():
k = 3
a = 13
n_pca = 20
thresh = 1e-4
data_small = data[np.random.choice(len(data),
len(data) // 2,
replace=False)]
pca = TruncatedSVD(n_pca, random_state=42).fit(data_small)
data_small_nu = pca.transform(data_small)
pdx = squareform(pdist(data_small_nu, metric="euclidean"))
knn_dist = np.partition(pdx, k, axis=1)[:, :k]
epsilon = np.max(knn_dist, axis=1)
weighted_pdx = (pdx.T / epsilon).T
K = np.exp(-1 * weighted_pdx**a)
K[K < thresh] = 0
W = K + K.T
W = np.divide(W, 2)
np.fill_diagonal(W, 0)
G = pygsp.graphs.Graph(W)
G2 = build_graph(
sp.coo_matrix(data_small),
thresh=thresh,
graphtype="exact",
n_pca=n_pca,
decay=a,
knn=k - 1,
random_state=42,
use_pygsp=True,
)
assert G.N == G2.N
np.testing.assert_allclose(G2.W.toarray(), G.W.toarray())
assert isinstance(G2, graphtools.graphs.TraditionalGraph)
G2 = build_graph(
sp.bsr_matrix(pdx),
n_pca=None,
precomputed="distance",
thresh=thresh,
decay=a,
knn=k - 1,
random_state=42,
use_pygsp=True,
)
assert G.N == G2.N
np.testing.assert_equal(G.dw, G2.dw)
assert (G.W != G2.W).nnz == 0
assert (G2.W != G.W).sum() == 0
assert isinstance(G2, graphtools.graphs.TraditionalGraph)
G2 = build_graph(
sp.lil_matrix(K),
n_pca=None,
precomputed="affinity",
thresh=thresh,
random_state=42,
use_pygsp=True,
)
assert G.N == G2.N
np.testing.assert_equal(G.dw, G2.dw)
assert (G.W != G2.W).nnz == 0
assert (G2.W != G.W).sum() == 0
assert isinstance(G2, graphtools.graphs.TraditionalGraph)
G2 = build_graph(
sp.dok_matrix(W),
n_pca=None,
precomputed="adjacency",
random_state=42,
use_pygsp=True,
)
assert G.N == G2.N
np.testing.assert_equal(G.dw, G2.dw)
assert (G.W != G2.W).nnz == 0
assert (G2.W != G.W).sum() == 0
assert isinstance(G2, graphtools.graphs.TraditionalGraph)
def test_mnn_graph_decay():
X, sample_idx = generate_swiss_roll()
theta = 0.9
k = 10
a = 20
metric = "euclidean"
beta = 0.2
samples = np.unique(sample_idx)
K = np.zeros((len(X), len(X)))
K[:] = np.nan
K = pd.DataFrame(K)
for si in samples:
X_i = X[sample_idx == si] # get observations in sample i
for sj in samples:
batch_k = k if si == sj else k - 1
X_j = X[sample_idx == sj] # get observation in sample j
pdx_ij = cdist(X_i, X_j, metric=metric) # pairwise distances
kdx_ij = np.sort(pdx_ij, axis=1) # get kNN
e_ij = kdx_ij[:, batch_k] # dist to kNN
pdxe_ij = pdx_ij / e_ij[:, np.newaxis] # normalize
k_ij = np.exp(-1 * (pdxe_ij ** a)) # apply alpha-decaying kernel
if si == sj:
K.iloc[sample_idx == si, sample_idx == sj] = (k_ij + k_ij.T) / 2
else:
# fill out values in K for NN on diagonal
K.iloc[sample_idx == si, sample_idx == sj] = k_ij
Kn = K.copy()
for i in samples:
curr_K = K.iloc[sample_idx == i, sample_idx == i]
i_norm = norm(curr_K, 1, axis=1)
for j in samples:
if i == j:
continue
else:
curr_K = K.iloc[sample_idx == i, sample_idx == j]
curr_norm = norm(curr_K, 1, axis=1)
scale = np.minimum(1, i_norm / curr_norm) * beta
Kn.iloc[sample_idx == i, sample_idx == j] = (
curr_K.values * scale[:, None]
)
K = Kn
W = np.array((theta * np.minimum(K, K.T)) + ((1 - theta) * np.maximum(K, K.T)))
np.fill_diagonal(W, 0)
G = pygsp.graphs.Graph(W)
G2 = graphtools.Graph(
X,
knn=k,
decay=a,
beta=beta,
kernel_symm="mnn",
theta=theta,
distance=metric,
sample_idx=sample_idx,
thresh=0,
use_pygsp=True,
)
assert G.N == G2.N
np.testing.assert_array_equal(G.dw, G2.dw)
np.testing.assert_array_equal((G.W - G2.W).data, 0)
assert isinstance(G2, graphtools.graphs.MNNGraph)
def test_exact_graph():
k = 3
a = 13
n_pca = 20
data_small = data[np.random.choice(len(data),
len(data) // 2,
replace=False)]
pca = PCA(n_pca, svd_solver='randomized', random_state=42).fit(data_small)
data_small_nu = pca.transform(data_small)
pdx = squareform(pdist(data_small_nu, metric='euclidean'))
knn_dist = np.partition(pdx, k, axis=1)[:, :k]
epsilon = np.max(knn_dist, axis=1)
weighted_pdx = (pdx.T / epsilon).T
K = np.exp(-1 * weighted_pdx**a)
W = K + K.T
W = np.divide(W, 2)
np.fill_diagonal(W, 0)
G = pygsp.graphs.Graph(W)
G2 = build_graph(data_small,
thresh=0,
n_pca=n_pca,
decay=a,
knn=k,
random_state=42,
use_pygsp=True)
assert (G.N == G2.N)
assert (np.all(G.d == G2.d))
assert ((G.W != G2.W).nnz == 0)
assert ((G2.W != G.W).sum() == 0)
assert (isinstance(G2, graphtools.graphs.TraditionalGraph))
G2 = build_graph(pdx,
n_pca=None,
precomputed='distance',
decay=a,
knn=k,
random_state=42,
use_pygsp=True)
assert (G.N == G2.N)
assert (np.all(G.d == G2.d))
assert ((G.W != G2.W).nnz == 0)
assert ((G2.W != G.W).sum() == 0)
assert (isinstance(G2, graphtools.graphs.TraditionalGraph))
G2 = build_graph(sp.coo_matrix(K),
n_pca=None,
precomputed='affinity',
random_state=42,
use_pygsp=True)
assert (G.N == G2.N)
assert (np.all(G.d == G2.d))
assert ((G.W != G2.W).nnz == 0)
assert ((G2.W != G.W).sum() == 0)
assert (isinstance(G2, graphtools.graphs.TraditionalGraph))
G2 = build_graph(K,
n_pca=None,
precomputed='affinity',
random_state=42,
use_pygsp=True)
assert (G.N == G2.N)
assert (np.all(G.d == G2.d))
assert ((G.W != G2.W).nnz == 0)
assert ((G2.W != G.W).sum() == 0)
assert (isinstance(G2, graphtools.graphs.TraditionalGraph))
G2 = build_graph(W,
n_pca=None,
precomputed='adjacency',
random_state=42,
use_pygsp=True)
assert (G.N == G2.N)
assert (np.all(G.d == G2.d))
assert ((G.W != G2.W).nnz == 0)
assert ((G2.W != G.W).sum() == 0)
assert (isinstance(G2, graphtools.graphs.TraditionalGraph))