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306 | class KSS:
"""
K-Subspaces (KSS) Clusering
Parameters
----------
n_clusters: int
Number of clusters.
subspaces_dims = int or sequence of int
Dimension(s) of each subspace. If an int is provided, all subspaces
will have the same dimension.
max_iter = int, default=100
Maximum number of iterations.
n_int = int, default=10
Number of random initializations. The best run (Highest cost) is kept
verbose = int, default=0
Verbosity level. 0=Silent, 1=per-run messsages, 2=per-iter bar.
random_state = int, default=None
Random seed for reproducibility.
"""
def __init__(
self,
n_clusters:int,
subspaces_dims:Union[int, Iterable[int]],
max_iter:int=100,
n_init:int=10,
verbose:int=0,
random_state:Optional[int]=None,
) -> None:
self.n_clusters = int(n_clusters)
self.subspaces_dims = subspaces_dims
self.max_iter = int(max_iter)
self.n_init = int(n_init)
self.verbose = int(verbose)
self.random_state = random_state
# attributes filled by fit()
self.labels_:Optional[np.ndarray] = None
self.subspaces_:Optional[List[Array]] = None
self.cost_:Optional[float] = None
def _check_susbpace_dims(self) -> List[int]:
if isinstance(self.subspaces_dims, int):
d = [int(self.subspaces_dims)] * self.n_clusters
return d
else:
d = [int(di) for di in self.subspaces_dims]
if len(d) != self.n_clusters:
raise ValueError(
"Length of subspaces_dims must match n_clusters"
f"({len(d)} != {self.n_clusters})."
)
return d
@staticmethod
def _to_mlx_column_major(X) -> Tuple[Array, int, int]:
"""
Convert input X to MLX array:
Accepts:
- Numpy Array of shape(n_features, n_samples)
- MLX Array of shape (n_features, n_samples)
"""
if isinstance(X, mx.array):
D, N = X.shape
return X, D, N
X_np = np.asarray(X, dtype=np.float64)
if X_np.ndim != 2:
raise ValueError("Input data X must be 2D (n_features, n_samples).")
X_mlx = mx.array(X_np.T, dtype=mx.float64)
return X_mlx
@staticmethod
def _cost(U: Sequence[Array], X:Array, labels: np.ndarray) -> float:
"""
Compute cost: sum over i of ||U_k^T x_i||^2 for assigned cluster k.
"""
K = len(U)
scores = mx.stack(
[mx.sum(mx.matmul(Uk.T, X, stream=mx.gpu) ** 2, axis=0) for Uk in U],
axis=0,
)
scores_np = np.array(scores)
c0 = labels
return float(scores_np[c0, np.arange(scores_np.shape[1])].sum())
def _kss_single(
self,
X: Array,
d: Sequence[int],
seed: Optional[int] = None,
) -> Tuple[List[Array], np.ndarray, float]:
"""
Single run of KSS clustering.
Parameters
----------
X : (D, N) mx.array
Data matrix with N points in R^D (columns are points).
d : sequence of int, length K
Subspace dimensions for each cluster.
seed : int, optional
Random seed for initialization.
Returns
-------
U : list of (D, d_k) mx.array
Learned subspace bases.
c: (N,) np.ndarray of ints in 0...K-1
Cluster labels.
cost: float
Cost of each run.
"""
if seed is not None:
mx.random.seed(seed)
K = len(d)
D, N = X.shape
# Initialize subspaces
U: List[Array] = [
polar(mx.random.normal(shape=(D, dk)))
for dk in d
]
# Initial cluster assignment
scores = mx.stack(
[mx.sum(mx.matmul(Uk.T, X, stream=mx.gpu) ** 2, axis=0) for Uk in U],
axis=0,
)
labels = np.argmax(np.array(scores), axis=0).astype(np.int32)
labels_prev = labels.copy()
# Iterations
if self.verbose >= 2:
iter_range = trange(self.max_iter, desc="KSS", leave=False)
else:
iter_range = range(self.max_iter)
for t in iter_range:
# Update subspaces
for k in range(K):
ilist = np.nonzero(labels == k)[0]
if ilist.size == 0:
# Empty cluster: reinitialize its subspace
U[k] = polar(mx.random.normal(shape=(D, d[k])))
continue
idx = mx.array(ilist)
X_k = mx.take(X, idx, axis=1)
A = mx.matmul(X_k, X_k.T, stream=mx.gpu)
w, V = mx.linalg.eigh(A, stream=mx.cpu)
U[k] = V[:, -d[k]:]
# Update clusters
scores = mx.stack(
[mx.sum(mx.matmul(Uk.T, X, stream=mx.gpu) ** 2, axis=0) for Uk in U],
axis=0,
)
labels = np.argmax(np.array(scores), axis=0).astype(np.int32)
# Break if clusters did not change, update otherwise
if np.array_equal(labels, labels_prev):
if self.verbose >= 2:
print(f"KSS terminated early at iteration {t + 1}")
break
labels_prev = labels.copy()
# Compute final cost
cost = self._cost(U, X, labels)
return U, labels, cost
# Public API
def fit(self, X) -> "KSS":
"""
Compute K-Subspaces clustering.
Parameters
----------
X : array-like of shape (n_features, n_samples) or MLX array (D, N)
Returns
-------
self : KSS
Fitted estimator.
"""
X_mx, D, N = self._to_mlx_column_major(X)
d = self._check_susbpace_dims()
if self.verbose >= 1:
print(
f"Running KSS with n_clusters={self.n_clusters}"
f", subspaces_dims={d}, max_iter={self.max_iter}, n_init={self.n_init}"
)
best_cost = -np.inf
best_labels = None
best_U: Optional[List[Array]] = None
for run in range(self.n_init):
if self.verbose >= 1:
print(f" KSS run {run + 1}/{self.n_init}")
seed = None if self.random_state is None else self.random_state + run
U_run, labels_run, cost_run = self._kss_single(X_mx, d, seed=seed)
if self.verbose >= 1:
print(f" Run cost: {cost_run:.4e}")
if cost_run > best_cost:
best_cost = cost_run
best_labels = labels_run.copy()
best_U = [Uk for Uk in U_run]
assert best_U is not None and best_labels is not None
self.subspaces_ = best_U
self.labels_ = best_labels.astype(np.int32) + 1
self.cost_ = best_cost
return self
def fit_predict(self, X, y=None) -> np.ndarray:
"""
Fit KSS and return labels.
Parameters
----------
X : array-like of shape (n_features, n_samples) or MLX array (D, N)
Returns
-------
labels: (n_samples, )
Labels in {1, ..., n_clusters}.
"""
self.fit(X, y=y)
return self.labels_
def predict(self, X) -> np.ndarray:
"""
Predict the closest cluster each sample in X belongs to.
Parameters
----------
X : array-like of shape (n_features, n_samples) or MLX array (D, N)
Returns
-------
labels: (n_samples, )
Labels in {1, ..., n_clusters}.
"""
if self.subspaces_ is None:
raise ValueError("KSS instance is not fitted yet. Call 'fit' first.")
X_mx, D, N = self._to_mlx_column_major(X)
K = len(self.subspaces_)
U = self.subspaces_
scores = mx.stack(
[
mx.sum(mx.matmul(Uk.T, X_mx, stream=mx.gpu) ** 2, axis=0)
for Uk in U
],
axis=0,
)
labels = np.argmax(np.array(scores), axis=0).astype(np.int32) + 1
return labels
|