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408 | class TSC:
"""
Thresholded Subspace Clustering (TSC)
Parameters
----------
n_clusters : int or None, default=None
Number of clusters. If None, estimate using eigengap heuristic.
max_nz : int, default=15
Number of retained neighbors per point in the affinity graph.
max_chunksize : int, default=1024
Number of query columns processed per chunk during affinity construction.
n_eig : int or None, default=None
Number of leading eigenvectors/eigenvalues to compute. If None, a sensible
value is chosen automatically.
n_init : int, default=20
Number of k-means initializations.
max_iter : int, default=100
Maximum number of k-means iterations.
symmetrize : bool, default=True
If True, use A + A.T after directed neighbor selection.
normalize_embedding : bool, default=True
If True, row-normalize the spectral embedding before k-means.
verbose : int, default=0
Verbosity level. 0=silent, 1=summary messages, 2=progress during affinity.
random_state : int or None, default=None
Random seed for reproducibility.
dtype : numpy dtype, default=np.float64
Floating-point dtype used for the NumPy pipeline.
"""
def __init__(
self,
n_clusters: Optional[int] = None,
max_nz: int = 15,
max_chunksize: int = 1024,
n_eig: Optional[int] = None,
n_init: int = 20,
max_iter: int = 100,
symmetrize: bool = True,
normalize_embedding: bool = True,
verbose: int = 0,
random_state: Optional[int] = None,
dtype=np.float64,
) -> None:
self.n_clusters = None if n_clusters is None else int(n_clusters)
self.max_nz = int(max_nz)
self.max_chunksize = int(max_chunksize)
self.n_eig = None if n_eig is None else int(n_eig)
self.n_init = int(n_init)
self.max_iter = int(max_iter)
self.symmetrize = bool(symmetrize)
self.normalize_embedding = bool(normalize_embedding)
self.verbose = int(verbose)
self.random_state = random_state
self.dtype = dtype
# attributes filled by fit()
self.labels_: Optional[np.ndarray] = None
self.affinity_: Optional[sp.csr_matrix] = None
self.embedding_: Optional[np.ndarray] = None
self.eigenvalues_: Optional[np.ndarray] = None
self.kmeans_ = None
self.n_clusters_: Optional[int] = None
self.result_: Optional[TSCResult] = None
def _to_numpy_column_major(self, X) -> Tuple[np.ndarray, int, int]:
"""
Convert input X to NumPy array of shape (D, N).
Accepts
-------
- NumPy array of shape (n_features, n_samples)
- array-like of shape (n_features, n_samples)
"""
X_np = np.asarray(X, dtype=self.dtype)
if X_np.ndim != 2:
raise ValueError("Input data X must be 2D with shape (n_features, n_samples).")
if self.verbose >= 2:
print(f"[TSC] Converting input to NumPy array with dtype={X_np.dtype}, shape={X_np.shape}")
D, N = X_np.shape
return X_np, D, N
@staticmethod
def _normalize_columns(X: np.ndarray, eps: float = 1e-12) -> np.ndarray:
"""
Normalize columns of X to unit l2 norm.
"""
norms = np.linalg.norm(X, axis=0) + eps
return X / norms
@staticmethod
def _estimate_k_eigengap(
eigenvalues: np.ndarray,
kmax: Optional[int] = None,
min_k: int = 2,
) -> int:
"""
Estimate number of clusters from descending eigenvalues.
"""
vals = np.asarray(eigenvalues).ravel()
if vals.size < 2:
raise ValueError("Need at least two eigenvalues for eigengap estimation.")
upper = vals.size - 1 if kmax is None else min(int(kmax), vals.size - 1)
lower = max(1, int(min_k) - 1)
if lower > upper:
lower = 1
gaps = vals[:-1] - vals[1:]
idx = np.argmax(gaps[lower - 1:upper]) + (lower - 1)
return int(idx + 1)
def _build_affinity(self, X: np.ndarray) -> sp.csr_matrix:
"""
Build sparse TSC affinity matrix.
"""
_, N = X.shape
if self.max_nz < 1:
raise ValueError(f"max_nz must be >= 1, got {self.max_nz}.")
q = min(self.max_nz, max(N - 1, 1))
chunksize = min(self.max_chunksize, N)
n_chunks = (N + chunksize - 1) // chunksize
Y = self._normalize_columns(X)
nnz_est = N * q
rows = np.empty(nnz_est, dtype=np.int32)
cols = np.empty(nnz_est, dtype=np.int32)
data = np.empty(nnz_est, dtype=self.dtype)
write_ptr = 0
if self.verbose >= 1:
print(
f"[TSC] Building affinity matrix | "
f"N={N}, q={q}, chunksize={chunksize}, n_chunks={n_chunks}, backend=CPU"
)
if self.verbose >= 2:
chunk_iter = trange(n_chunks, desc="TSC affinity", leave=False)
else:
chunk_iter = range(n_chunks)
for chunk_idx in chunk_iter:
j0 = chunk_idx * chunksize
j1 = min(N, (chunk_idx + 1) * chunksize)
m = j1 - j0
Y_chunk = Y[:, j0:j1]
C = np.abs(Y.T @ Y_chunk)
# zero self-similarities for current chunk columns
local_cols = np.arange(m, dtype=np.int64)
global_rows = np.arange(j0, j1, dtype=np.int64)
C[global_rows, local_cols] = 0.0
inds = np.argpartition(-C, q - 1, axis=0)[:q, :]
sims = np.take_along_axis(C, inds, axis=0)
order = np.argsort(-sims, axis=0)
inds = np.take_along_axis(inds, order, axis=0)
sims = np.take_along_axis(sims, order, axis=0)
block_nnz = q * m
rows[write_ptr:write_ptr + block_nnz] = inds.reshape(-1, order="F")
cols[write_ptr:write_ptr + block_nnz] = np.repeat(
np.arange(j0, j1, dtype=np.int32), q
)
data[write_ptr:write_ptr + block_nnz] = sims.reshape(-1, order="F")
write_ptr += block_nnz
A = sp.csr_matrix(
(data[:write_ptr], (rows[:write_ptr], cols[:write_ptr])),
shape=(N, N),
)
A.setdiag(0)
A.eliminate_zeros()
if self.symmetrize:
A = A + A.T
A.setdiag(0)
A.eliminate_zeros()
if self.verbose >= 1:
print(f"[TSC] Affinity construction finished | nnz={A.nnz}")
return A.tocsr()
def _spectral_embedding(self, A: sp.csr_matrix):
"""
Compute spectral embedding from sparse affinity matrix.
"""
from scipy.sparse.linalg import eigsh
N = A.shape[0]
if A.shape[0] != A.shape[1]:
raise ValueError(f"Affinity matrix must be square, got {A.shape}.")
degrees = np.asarray(A.sum(axis=1)).ravel()
inv_sqrt_deg = 1.0 / np.sqrt(np.maximum(degrees, 1e-12))
D_inv_sqrt = sp.diags(inv_sqrt_deg)
L = D_inv_sqrt @ A @ D_inv_sqrt
if self.n_clusters is None:
nev = self.n_eig
if nev is None:
nev = min(max(10, 2), N - 1)
else:
nev = self.n_eig if self.n_eig is not None else max(self.n_clusters, 2)
nev = min(nev, N - 1)
if self.verbose >= 1:
mode = "eigengap" if self.n_clusters is None else f"fixed K={self.n_clusters}"
print(f"[TSC] Computing spectral embedding | nev={nev}, mode={mode}")
if N == 1:
vals = np.array([1.0], dtype=self.dtype)
vecs = np.ones((1, 1), dtype=self.dtype)
elif nev >= N - 1:
if self.verbose >= 2:
print("[TSC] Using dense eigendecomposition")
dense = L.toarray()
vals, vecs = np.linalg.eigh(dense)
order = np.argsort(vals)[::-1]
vals = vals[order]
vecs = vecs[:, order]
else:
if self.verbose >= 2:
print("[TSC] Using sparse eigsh")
vals, vecs = eigsh(L, k=nev, which="LA")
order = np.argsort(vals)[::-1]
vals = vals[order]
vecs = vecs[:, order]
if self.n_clusters is None:
if self.verbose >= 1:
print("[TSC] Estimating number of clusters using eigengap heuristic")
K = self._estimate_k_eigengap(vals)
if self.verbose >= 1:
print(f"[TSC] Selected n_clusters={K}")
else:
K = self.n_clusters
embedding = np.asarray(vecs[:, :K], dtype=self.dtype)
if self.normalize_embedding:
embedding = _row_normalize(embedding)
return embedding, np.asarray(vals), int(K)
def _cluster_embedding(self, embedding: np.ndarray):
"""
Run k-means on spectral embedding.
"""
try:
from sklearn.cluster import KMeans
except Exception as e:
raise ImportError(
"scikit-learn is required for k-means. "
"Install it with: pip install scikit-learn"
) from e
if self.verbose >= 1:
print(
f"[TSC] Running k-means on embedding with shape={embedding.shape}, "
f"n_clusters={self.n_clusters_}, n_init={self.n_init}, max_iter={self.max_iter}"
)
km = KMeans(
n_clusters=self.n_clusters_,
n_init=self.n_init,
max_iter=self.max_iter,
random_state=self.random_state,
)
labels = km.fit_predict(embedding).astype(np.int32)
return labels, km
# Public API
def fit(self, X) -> "TSC":
"""
Compute Thresholded Subspace Clustering.
Parameters
----------
X : array-like of shape (n_features, n_samples)
Returns
-------
self : TSC
Fitted estimator.
"""
X_np, _, N = self._to_numpy_column_major(X)
if self.n_clusters is not None and not (1 <= self.n_clusters <= N):
raise ValueError(
f"n_clusters must satisfy 1 <= n_clusters <= N, got {self.n_clusters}."
)
if self.verbose >= 1:
print(
f"Running TSC with n_clusters={self.n_clusters}, "
f"max_nz={self.max_nz}, max_chunksize={self.max_chunksize}, "
f"n_init={self.n_init}, max_iter={self.max_iter}"
)
A = self._build_affinity(X_np)
embedding, eigenvalues, K_used = self._spectral_embedding(A)
self.n_clusters_ = K_used
labels, km = self._cluster_embedding(embedding)
labels = labels + 1
self.affinity_ = A
self.embedding_ = embedding
self.eigenvalues_ = eigenvalues
self.kmeans_ = km
self.labels_ = labels
self.result_ = TSCResult(
affinity=A,
embedding=embedding,
eigenvalues=eigenvalues,
labels=labels,
kmeans_model=km,
n_clusters=K_used,
)
if self.verbose >= 1:
print(f"Finished TSC with n_clusters_={self.n_clusters_}")
return self
def fit_predict(self, X, y=None) -> np.ndarray:
"""
Fit TSC and return labels.
Parameters
----------
X : array-like of shape (n_features, n_samples)
Returns
-------
labels : ndarray of shape (n_samples,)
Labels in {1, ..., n_clusters}.
"""
self.fit(X)
return self.labels_
|