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_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_precomputed_nonzero_diagonal():
with assert_warns_message(RuntimeWarning,
"K should have a non-zero diagonal"):
build_graph(np.zeros((10, 10)), precomputed="affinity", n_pca=None)