"""
Matrix SVQ-OCC (SVQ-OCC-M).
Extends SVQ-OCC with a global Omega matrix (GMLVQ-style metric adaptation).
The distance becomes:
.. math::
d_{\\Omega}(x, w_k) = \\|\\Omega(x - w_k)\\|^2
where :math:`\\Omega` is a learned :math:`(d \\times l)` projection matrix.
The implicit metric :math:`\\Lambda = \\Omega^T \\Omega` captures feature
correlations for one-class classification.
References
----------
.. [1] Staps et al. (2022). Prototype-based One-Class-Classification
Learning Using Local Representations. IEEE WSOM+ 2022.
.. [2] Schneider, Biehl, Hammer (2009). Adaptive Relevance Matrices
in Learning Vector Quantization. Neural Computation, 21(12).
"""
import jax
import jax.numpy as jnp
import numpy as np
from prosemble.models.svq_occ import SVQOCC
from prosemble.core.initializers import identity_omega_init
[docs]
class SVQOCC_M(SVQOCC):
"""Matrix SVQ-OCC with global Omega projection.
Learns a global linear projection :math:`\\Omega` that captures feature
correlations for one-class classification.
Parameters
----------
latent_dim : int, optional
Dimensionality of the projected space. Default: n_features.
n_prototypes : int
Number of prototypes for the target class.
target_label : int, optional
Which label is the target (normal) class. Default: auto-detect
as the most frequent class.
alpha : float
Balance between representation (R) and classification (C) cost.
E = alpha * R + (1 - alpha) * C. Default: 0.5.
cost_function : str
Classification cost variant: 'contrastive', 'brier', 'cross_entropy'.
Default: 'contrastive'.
response_type : str
Response probability model: 'gaussian', 'student_t', 'uniform'.
Default: 'gaussian'.
sigma : float
Sigmoid sharpness for differentiable Heaviside approximation.
Smaller = sharper boundary. Default: 0.1.
gamma_resp : float
Response bandwidth for Gaussian probabilistic assignment. Default: 1.0.
nu : float
Degrees of freedom for Student-t response. Default: 1.0.
lambda_init : float, optional
Initial NG neighborhood range. Default: n_prototypes / 2.
lambda_final : float
Final NG neighborhood range. Default: 0.01.
lambda_decay : float, optional
Per-step multiplicative decay for lambda. Default: computed from
max_iter.
max_iter : int
Maximum training iterations.
lr : float
Learning rate.
epsilon : float
Convergence threshold on loss change.
random_seed : int
Random seed for reproducibility.
distance_fn : callable, optional
Distance function (default: squared Euclidean).
optimizer : str or optax optimizer, optional
Optimizer name ('adam', 'sgd') or optax GradientTransformation.
Default: 'adam'.
transfer_fn : callable, optional
Transfer function for loss shaping (default: identity).
margin : float
Margin for loss computation.
callbacks : list, optional
List of Callback objects.
use_scan : bool
If True (default), use jax.lax.scan for training (faster,
JIT-compiled, but runs all max_iter iterations even after
convergence). If False, use a Python for-loop with true early
stopping (no wasted compute after convergence, but slower per
iteration).
batch_size : int, optional
Mini-batch size. If None (default), use full-batch training.
When set, each epoch iterates over shuffled mini-batches of this
size.
lr_scheduler : str or optax.Schedule, optional
Learning rate schedule. Supported strings: 'exponential_decay',
'cosine_decay', 'warmup_cosine_decay', 'warmup_exponential_decay',
'warmup_constant', 'polynomial', 'linear', 'piecewise_constant',
'sgdr'. Or pass a custom optax.Schedule. Default: None.
lr_scheduler_kwargs : dict, optional
Keyword arguments passed to the learning rate scheduler
(e.g. ``decay_rate``, ``transition_steps``). Default: None.
prototypes_initializer : str or callable, optional
How to initialize prototypes. Supported strings:
'stratified_random' (default), 'class_mean',
'class_conditional_mean', 'stratified_noise', 'random_normal',
'uniform', 'zeros', 'ones', 'fill_value'. Or pass a callable
``(X, y, n_per_class, key) -> (protos, labels)``.
patience : int, optional
Number of consecutive epochs with no improvement before stopping.
If None (default), stops after a single non-improving step
(epsilon check). Requires use_scan=False for true early stopping.
restore_best : bool
If True, restore the parameters that achieved the lowest loss
(or validation loss if validation data is provided). Default:
False.
class_weight : dict or 'balanced', optional
Weights for each class. Dict maps class label to weight, e.g.
{0: 1.0, 1: 2.0, 2: 1.5}. 'balanced' auto-computes weights
inversely proportional to class frequencies. Default: None
(uniform).
gradient_accumulation_steps : int, optional
Accumulate gradients over this many steps before applying an
update. Effective batch size = batch_size *
gradient_accumulation_steps. Default: None (no accumulation).
ema_decay : float, optional
Exponential moving average decay for parameters
(0 < ema_decay < 1). After training, model parameters are
replaced with EMA-smoothed values. Typical values: 0.999,
0.9999. Default: None (no EMA).
freeze_params : list of str, optional
List of parameter group names to freeze (zero gradients).
E.g. ['backbone'] to freeze the backbone and only train
prototypes. Default: None (all parameters trainable).
lookahead : dict, optional
Enable lookahead optimizer wrapper. Dict with keys:
- 'sync_period': int (default 6) -- sync every k steps
- 'slow_step_size': float (default 0.5) -- interpolation factor
Default: None (no lookahead).
mixed_precision : str or None, optional
Compute dtype for mixed precision training. 'float16' or
'bfloat16'. Master weights stay in float32; forward/backward
pass runs in lower precision for ~2x speed and ~half memory on
GPU. Float16 uses static loss scaling to prevent gradient
underflow. Default: None (disabled).
Attributes
----------
omega_ : array of shape (n_features, latent_dim)
Learned projection matrix.
See Also
--------
SVQOCC : Base SVQ-OCC model.
"""
def __init__(self, latent_dim=None, n_prototypes=3, target_label=None,
alpha=0.5, cost_function='contrastive',
response_type='gaussian', sigma=0.1, gamma_resp=1.0,
nu=1.0, lambda_init=None, lambda_final=0.01,
lambda_decay=None, max_iter=100, lr=0.01, epsilon=1e-6,
random_seed=42, distance_fn=None, optimizer='adam',
transfer_fn=None, margin=0.0, callbacks=None,
use_scan=True, batch_size=None, lr_scheduler=None,
lr_scheduler_kwargs=None, prototypes_initializer=None,
patience=None, restore_best=False, class_weight=None,
gradient_accumulation_steps=None, ema_decay=None,
freeze_params=None, lookahead=None, mixed_precision=None):
super().__init__(
n_prototypes=n_prototypes, target_label=target_label,
alpha=alpha, cost_function=cost_function,
response_type=response_type, sigma=sigma,
gamma_resp=gamma_resp, nu=nu, lambda_init=lambda_init,
lambda_final=lambda_final, lambda_decay=lambda_decay,
max_iter=max_iter, lr=lr, epsilon=epsilon,
random_seed=random_seed, distance_fn=distance_fn,
optimizer=optimizer, transfer_fn=transfer_fn, margin=margin,
callbacks=callbacks, use_scan=use_scan, batch_size=batch_size,
lr_scheduler=lr_scheduler,
lr_scheduler_kwargs=lr_scheduler_kwargs,
prototypes_initializer=prototypes_initializer,
patience=patience, restore_best=restore_best,
class_weight=class_weight,
gradient_accumulation_steps=gradient_accumulation_steps,
ema_decay=ema_decay, freeze_params=freeze_params,
lookahead=lookahead, mixed_precision=mixed_precision,
)
self.latent_dim = latent_dim
self.omega_ = None
def _get_resume_params(self, params):
params = super()._get_resume_params(params)
params['omega'] = self.omega_
return params
def _init_state(self, X, y, key):
state, params, proto_labels = super()._init_state(X, y, key)
n_features = X.shape[1]
latent_dim = self.latent_dim if self.latent_dim is not None else n_features
params['omega'] = identity_omega_init(n_features, latent_dim)
# Reinitialize optimizer with omega
opt_state = self._optimizer.init(params)
from prosemble.models.prototype_base import SupervisedState
state = SupervisedState(
prototypes=params['prototypes'],
opt_state=opt_state,
loss=jnp.array(float('inf')),
iteration=0,
converged=False,
)
return state, params, proto_labels
def _compute_loss(self, params, X, y, proto_labels):
prototypes = params['prototypes']
thetas = params['thetas']
lambda_ng = params['lambda_ng']
omega = params['omega']
n_protos = prototypes.shape[0]
# Omega-projected squared distances
diff = X[:, None, :] - prototypes[None, :, :] # (n, K, d)
projected = jnp.einsum('nkd,dl->nkl', diff, omega) # (n, K, l)
sq_distances = jnp.sum(projected ** 2, axis=2) # (n, K)
target_mask = (y == self._target_label)
# Representation cost R (target only)
order = jnp.argsort(sq_distances, axis=1)
ranks = jnp.argsort(order, axis=1).astype(jnp.float32)
h_ng = jnp.exp(-ranks / (lambda_ng + 1e-10))
R_per_sample = jnp.sum(h_ng * sq_distances, axis=1)
R_per_sample = jnp.where(target_mask, R_per_sample, 0.0)
R = jnp.sum(R_per_sample) / (jnp.sum(target_mask) + 1e-10)
# Classification cost C
if self.response_type == 'gaussian':
p_k = jax.nn.softmax(-self.gamma_resp * sq_distances, axis=1)
elif self.response_type == 'student_t':
p_unnorm = (1.0 + sq_distances / self.nu) ** (-(self.nu + 1) / 2)
p_k = p_unnorm / (jnp.sum(p_unnorm, axis=1, keepdims=True) + 1e-10)
else:
p_k = jnp.ones_like(sq_distances) / n_protos
thetas_pos = jnp.maximum(thetas, 1e-6)
heaviside = jax.nn.sigmoid(
(thetas_pos[None, :] - sq_distances) / (self.sigma + 1e-10)
)
total_resp = jnp.clip(
jnp.sum(p_k * heaviside, axis=1), 1e-10, 1.0 - 1e-10
)
y_binary = target_mask.astype(jnp.float32)
if self.cost_function == 'contrastive':
TP = jnp.sum(y_binary * total_resp)
FP = jnp.sum((1.0 - y_binary) * total_resp)
FN = jnp.sum(y_binary) - TP
TN = jnp.sum(1.0 - y_binary) - FP
C = 1.0 - (TP * TN - FP * FN) / (
(TP + FP + 1e-10) * (TN + FN + 1e-10)
)
elif self.cost_function == 'brier':
C = jnp.mean((y_binary - total_resp) ** 2)
else:
C = -jnp.mean(
y_binary * jnp.log(total_resp) +
(1.0 - y_binary) * jnp.log(1.0 - total_resp)
)
return self.alpha * R + (1.0 - self.alpha) * C
def _extract_results(self, params, proto_labels, loss_history, n_iter,
**kwargs):
super()._extract_results(
params, proto_labels, loss_history, n_iter, **kwargs
)
self.omega_ = params['omega']
[docs]
def decision_function(self, X):
"""Compute scores using Omega-projected distances."""
self._check_fitted()
X = jnp.asarray(X, dtype=jnp.float32)
diff = X[:, None, :] - self.prototypes_[None, :, :]
projected = jnp.einsum('nkd,dl->nkl', diff, self.omega_)
sq_distances = jnp.sum(projected ** 2, axis=2)
n_protos = self.prototypes_.shape[0]
if self.response_type == 'gaussian':
p_k = jax.nn.softmax(-self.gamma_resp * sq_distances, axis=1)
elif self.response_type == 'student_t':
p_unnorm = (
(1.0 + sq_distances / self.nu) ** (-(self.nu + 1) / 2)
)
p_k = p_unnorm / (
jnp.sum(p_unnorm, axis=1, keepdims=True) + 1e-10
)
else:
p_k = jnp.ones_like(sq_distances) / n_protos
heaviside = jax.nn.sigmoid(
(self.thetas_[None, :] - sq_distances) / (self.sigma + 1e-10)
)
return jnp.clip(jnp.sum(p_k * heaviside, axis=1), 0.0, 1.0)
@property
def omega_matrix(self):
"""Return the learned projection matrix :math:`\\Omega`."""
if self.omega_ is None:
raise ValueError("Model not fitted. Call fit() first.")
return self.omega_
@property
def lambda_matrix(self):
"""Return the implicit metric :math:`\\Lambda = \\Omega^T \\Omega`."""
return self.omega_matrix.T @ self.omega_matrix
def _get_quantizable_attrs(self):
attrs = super()._get_quantizable_attrs()
if self.omega_ is not None:
attrs.append('omega_')
return attrs
def _get_fitted_arrays(self):
arrays = super()._get_fitted_arrays()
if self.omega_ is not None:
arrays['omega_'] = np.asarray(self.omega_)
return arrays
def _set_fitted_arrays(self, arrays):
super()._set_fitted_arrays(arrays)
if 'omega_' in arrays:
self.omega_ = jnp.asarray(arrays['omega_'])
def _get_hyperparams(self):
hp = super()._get_hyperparams()
hp['latent_dim'] = self.latent_dim
return hp