"""
One-Class Matrix RSLVQ (OC-MRSLVQ) and One-Class Local Matrix RSLVQ (OC-LMRSLVQ).
Extends OC-GLVQ with:
- Omega metric adaptation (global or per-prototype)
- Probabilistic soft-weighting of all prototypes via Gaussian mixture
Instead of using only the nearest prototype (hard argmin like OC-GMLVQ),
all prototypes contribute to the loss via Gaussian proximity weights:
.. math::
p(k|x) = \\frac{\\exp(-d_k / 2\\sigma^2)}{\\sum_j \\exp(-d_j / 2\\sigma^2)}
.. math::
\\mu_k = s \\cdot \\frac{d_k - \\theta_k}{d_k + \\theta_k}
.. math::
\\text{loss} = \\text{mean}\\left(\\sum_k p(k|x) \\cdot \\text{sigmoid}(\\mu_k + \\text{margin}, \\beta)\\right)
References
----------
.. [1] Schneider, P., Biehl, M., & Hammer, B. (2009). Adaptive
Relevance Matrices in Learning Vector Quantization. Neural
Computation.
.. [2] Seo, S., & Obermayer, K. (2007). Soft Nearest Prototype
Classification. IEEE Trans. Neural Networks.
.. [3] Staps et al. (2022). Prototype-based One-Class-Classification
Learning Using Local Representations. IEEE WSOM+ 2022.
"""
import jax
import jax.numpy as jnp
import numpy as np
from prosemble.models.oc_glvq import OCGLVQ
from prosemble.core.initializers import identity_omega_init
from prosemble.core.activations import sigmoid_beta
[docs]
class OCMRSLVQ(OCGLVQ):
"""One-Class Matrix Robust Soft LVQ.
Combines one-class threshold detection with a learned global Omega
projection matrix and probabilistic soft-weighting of all prototypes.
All prototypes contribute to the one-class decision via Gaussian
proximity weights, with distances computed in the Omega-projected space.
Parameters
----------
sigma : float
Bandwidth of Gaussian mixture for prototype weighting.
latent_dim : int, optional
Dimensionality of the projected space. Default: n_features.
n_prototypes : int
Number of prototypes for the target class. Default: 3.
target_label : int, optional
Target (normal) class label. Default: auto-detect.
beta : float
Sigmoid steepness. Default: 10.0.
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.
thetas_ : array of shape (n_prototypes,)
Learned per-prototype visibility thresholds.
"""
def __init__(self, sigma=1.0, latent_dim=None, n_prototypes=3,
target_label=None, beta=10.0, 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,
beta=beta, 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.sigma = sigma
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 thetas using omega-projected distances
target_mask = (y == self._target_label)
X_target = X[target_mask]
prototypes = params['prototypes']
omega = params['omega']
diff = X_target[:, None, :] - prototypes[None, :, :]
projected = jnp.einsum('nkd,dl->nkl', diff, omega)
dists = jnp.sum(projected ** 2, axis=2)
params['thetas'] = jnp.sqrt(jnp.mean(dists, axis=0) + 1e-10)
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']
omega = params['omega']
# Omega-projected squared distances: (n, K)
diff = X[:, None, :] - prototypes[None, :, :]
projected = jnp.einsum('nkd,dl->nkl', diff, omega)
distances = jnp.sum(projected ** 2, axis=2)
# Gaussian weights: p(k|x) for all prototypes
log_probs = -distances / (2.0 * self.sigma ** 2)
log_norm = jnp.max(log_probs, axis=1, keepdims=True)
weights = jnp.exp(log_probs - log_norm)
weights = weights / jnp.sum(weights, axis=1, keepdims=True)
# Per-prototype OC mu
s = jnp.where(y == self._target_label, 1.0, -1.0)
mu = s[:, None] * (distances - thetas[None, :]) / (
distances + thetas[None, :] + 1e-10
)
# Weighted sigmoid loss
transfer = self.transfer_fn or sigmoid_beta
cost = transfer(mu + self.margin, self.beta)
return jnp.mean(jnp.sum(weights * cost, axis=1))
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 target-likeness scores using soft-weighted Omega distances.
Scores near 1.0 indicate target class, near 0.0 indicate outlier.
Parameters
----------
X : array-like of shape (n_samples, n_features)
Returns
-------
scores : array of shape (n_samples,)
"""
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_)
distances = jnp.sum(projected ** 2, axis=2)
# Gaussian weights
log_probs = -distances / (2.0 * self.sigma ** 2)
log_norm = jnp.max(log_probs, axis=1, keepdims=True)
weights = jnp.exp(log_probs - log_norm)
weights = weights / jnp.sum(weights, axis=1, keepdims=True)
# Per-prototype mu (from target perspective, no sign flip)
mu = (distances - self.thetas_[None, :]) / (
distances + self.thetas_[None, :] + 1e-10
)
# Weighted score
weighted_mu = jnp.sum(weights * mu, axis=1)
return 1.0 - jax.nn.sigmoid(self.beta * weighted_mu)
@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['sigma'] = self.sigma
hp['latent_dim'] = self.latent_dim
return hp
[docs]
class OCLMRSLVQ(OCGLVQ):
"""One-Class Localized Matrix Robust Soft LVQ.
Each prototype :math:`k` has its own :math:`\\Omega_k` matrix for local metric
adaptation, combined with probabilistic soft-weighting and
one-class threshold detection.
Parameters
----------
sigma : float
Bandwidth of Gaussian mixture for prototype weighting.
latent_dim : int, optional
Latent space dimensionality per prototype. Default: n_features.
n_prototypes : int
Number of prototypes for the target class. Default: 3.
target_label : int, optional
Target (normal) class label. Default: auto-detect.
beta : float
Sigmoid steepness. Default: 10.0.
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
----------
omegas_ : array of shape (n_prototypes, n_features, latent_dim)
Learned per-prototype projection matrices.
thetas_ : array of shape (n_prototypes,)
Learned per-prototype visibility thresholds.
"""
def __init__(self, sigma=1.0, latent_dim=None, n_prototypes=3,
target_label=None, beta=10.0, 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,
beta=beta, 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.sigma = sigma
self.latent_dim = latent_dim
self.omegas_ = None
def _get_resume_params(self, params):
params = super()._get_resume_params(params)
params['omegas'] = self.omegas_
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
n_protos = params['prototypes'].shape[0]
omega_single = identity_omega_init(n_features, latent_dim)
params['omegas'] = jnp.tile(omega_single[None, :, :], (n_protos, 1, 1))
# Reinitialize thetas using local-omega-projected distances
target_mask = (y == self._target_label)
X_target = X[target_mask]
prototypes = params['prototypes']
omegas = params['omegas']
diff = X_target[:, None, :] - prototypes[None, :, :]
projected = jnp.einsum('nkd,kdl->nkl', diff, omegas)
dists = jnp.sum(projected ** 2, axis=2)
params['thetas'] = jnp.sqrt(jnp.mean(dists, axis=0) + 1e-10)
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']
omegas = params['omegas'] # (K, d, l)
# Local omega-projected squared distances: (n, K)
diff = X[:, None, :] - prototypes[None, :, :]
projected = jnp.einsum('nkd,kdl->nkl', diff, omegas)
distances = jnp.sum(projected ** 2, axis=2)
# Gaussian weights
log_probs = -distances / (2.0 * self.sigma ** 2)
log_norm = jnp.max(log_probs, axis=1, keepdims=True)
weights = jnp.exp(log_probs - log_norm)
weights = weights / jnp.sum(weights, axis=1, keepdims=True)
# Per-prototype OC mu
s = jnp.where(y == self._target_label, 1.0, -1.0)
mu = s[:, None] * (distances - thetas[None, :]) / (
distances + thetas[None, :] + 1e-10
)
transfer = self.transfer_fn or sigmoid_beta
cost = transfer(mu + self.margin, self.beta)
return jnp.mean(jnp.sum(weights * cost, axis=1))
def _extract_results(self, params, proto_labels, loss_history, n_iter,
**kwargs):
super()._extract_results(
params, proto_labels, loss_history, n_iter, **kwargs
)
self.omegas_ = params['omegas']
[docs]
def decision_function(self, X):
"""Compute target-likeness scores using local Omega distances.
Parameters
----------
X : array-like of shape (n_samples, n_features)
Returns
-------
scores : array of shape (n_samples,)
"""
self._check_fitted()
X = jnp.asarray(X, dtype=jnp.float32)
diff = X[:, None, :] - self.prototypes_[None, :, :]
projected = jnp.einsum('nkd,kdl->nkl', diff, self.omegas_)
distances = jnp.sum(projected ** 2, axis=2)
# Gaussian weights
log_probs = -distances / (2.0 * self.sigma ** 2)
log_norm = jnp.max(log_probs, axis=1, keepdims=True)
weights = jnp.exp(log_probs - log_norm)
weights = weights / jnp.sum(weights, axis=1, keepdims=True)
mu = (distances - self.thetas_[None, :]) / (
distances + self.thetas_[None, :] + 1e-10
)
weighted_mu = jnp.sum(weights * mu, axis=1)
return 1.0 - jax.nn.sigmoid(self.beta * weighted_mu)
def _get_quantizable_attrs(self):
attrs = super()._get_quantizable_attrs()
if self.omegas_ is not None:
attrs.append('omegas_')
return attrs
def _get_fitted_arrays(self):
arrays = super()._get_fitted_arrays()
if self.omegas_ is not None:
arrays['omegas_'] = np.asarray(self.omegas_)
return arrays
def _set_fitted_arrays(self, arrays):
super()._set_fitted_arrays(arrays)
if 'omegas_' in arrays:
self.omegas_ = jnp.asarray(arrays['omegas_'])
def _get_hyperparams(self):
hp = super()._get_hyperparams()
hp['sigma'] = self.sigma
hp['latent_dim'] = self.latent_dim
return hp