def _spectral_embedding(self, X):
"""
Helper function to embed the dataset X into the eigenvectors of the graph Laplacian matrix
Returns
-------
ht.DNDarray, shape=(m_lanczos):
Eigenvalues of the graph's Laplacian matrix.
ht.DNDarray, shape=(n, m_lanczos):
Eigenvectors of the graph's Laplacian matrix.
"""
L = self._laplacian.construct(X)
# 3. Eigenvalue and -vector calculation via Lanczos Algorithm
v0 = ht.full(
(L.shape[0], ),
fill_value=1.0 / math.sqrt(L.shape[0]),
dtype=L.dtype,
split=0,
device=L.device,
)
V, T = ht.lanczos(L, self.n_lanczos, v0)
# 4. Calculate and Sort Eigenvalues and Eigenvectors of tridiagonal matrix T
eval, evec = torch.eig(T._DNDarray__array, eigenvectors=True)
# If x is an Eigenvector of T, then y = V@x is the corresponding Eigenvector of L
eval, idx = torch.sort(eval[:, 0], dim=0)
eigenvalues = ht.array(eval)
eigenvectors = ht.matmul(V, ht.array(evec))[:, idx]
return eigenvalues, eigenvectors
def _spectral_embedding(self, x: DNDarray) -> Tuple[DNDarray, DNDarray]:
"""
Helper function for dataset x embedding.
Returns Tupel(Eigenvalues, Eigenvectors) of the graph's Laplacian matrix.
Parameters
----------
x : DNDarray
Sample Matrix for which the embedding should be calculated
"""
L = self._laplacian.construct(x)
# 3. Eigenvalue and -vector calculation via Lanczos Algorithm
v0 = ht.full(
(L.shape[0],),
fill_value=1.0 / math.sqrt(L.shape[0]),
dtype=L.dtype,
split=0,
device=L.device,
)
V, T = ht.lanczos(L, self.n_lanczos, v0)
# 4. Calculate and Sort Eigenvalues and Eigenvectors of tridiagonal matrix T
eval, evec = torch.eig(T.larray, eigenvectors=True)
# If x is an Eigenvector of T, then y = V@x is the corresponding Eigenvector of L
eval, idx = torch.sort(eval[:, 0], dim=0)
eigenvalues = ht.array(eval)
eigenvectors = ht.matmul(V, ht.array(evec))[:, idx]
return eigenvalues, eigenvectors
def _spectral_embedding(self, x: DNDarray) -> Tuple[DNDarray, DNDarray]:
"""
Helper function for dataset x embedding.
Returns Tupel(Eigenvalues, Eigenvectors) of the graph's Laplacian matrix.
Parameters
----------
x : DNDarray
Sample Matrix for which the embedding should be calculated
Notes
-----
This will throw out the complex side of the eigenvalues found during this.
"""
L = self._laplacian.construct(x)
# 3. Eigenvalue and -vector calculation via Lanczos Algorithm
v0 = ht.full(
(L.shape[0], ),
fill_value=1.0 / math.sqrt(L.shape[0]),
dtype=L.dtype,
split=0,
device=L.device,
)
V, T = ht.lanczos(L, self.n_lanczos, v0)
# if int(torch.__version__.split(".")[1]) >= 9:
try:
# 4. Calculate and Sort Eigenvalues and Eigenvectors of tridiagonal matrix T
eval, evec = torch.linalg.eig(T.larray)
# If x is an Eigenvector of T, then y = V@x is the corresponding Eigenvector of L
eval, idx = torch.sort(eval.real, dim=0)
eigenvalues = ht.array(eval)
eigenvectors = ht.matmul(V, ht.array(evec))[:, idx]
return eigenvalues.real, eigenvectors.real
except AttributeError: # torch version is less than 1.9.0
# 4. Calculate and Sort Eigenvalues and Eigenvectors of tridiagonal matrix T
eval, evec = torch.eig(T.larray, eigenvectors=True)
# If x is an Eigenvector of T, then y = V@x is the corresponding Eigenvector of L
eval, idx = torch.sort(eval[:, 0], dim=0)
eigenvalues = ht.array(eval)
eigenvectors = ht.matmul(V, ht.array(evec))[:, idx]
return eigenvalues, eigenvectors