"""
Riemannian Differentiating Kernel Matrix SMNG (RiemannianDKMSMNG).
Combines RiemannianSMNG (global omega metric in tangent space) with an
exponential kernel using a learned transformation matrix in the projected space:
.. math::
d_\\kappa^2(x, w_k) = \\exp\\left(
(\\Omega \\cdot v)^T \\hat\\Lambda (\\Omega \\cdot v)
\\right) - 1
where :math:`v = \\text{Log}_{w_k}(x)_{\\text{flat}}`,
:math:`\\Omega` is the global metric matrix projecting from d_flat to latent_dim,
and :math:`\\hat\\Lambda = \\hat\\Omega \\hat\\Omega^T` is a learned PSD matrix
operating in the projected (latent) space.
References
----------
.. [1] Villmann, T., Haase, S., & Kaden, M. (2015). Kernelized vector
quantization in gradient-descent learning. Neurocomputing.
"""
import jax
import jax.numpy as jnp
import numpy as np
from prosemble.models.riemannian_smng import RiemannianSMNG
from prosemble.models.prototype_base import SupervisedState
from prosemble.core.activations import sigmoid_beta
from prosemble.core.initializers import identity_omega_init
from prosemble.core.competitions import wtac
[docs]
class RiemannianDKMSMNG(RiemannianSMNG):
"""Riemannian Differentiating Kernel Matrix SMNG.
Extends RiemannianSMNG with an exponential kernel in the omega-projected
tangent space. The global omega :math:`\\Omega` projects tangent vectors
from d_flat to latent_dim, then a learned matrix
:math:`\\hat\\Lambda = \\hat\\Omega \\hat\\Omega^T` provides further
metric adaptation in the projected space:
.. math::
d_\\kappa^2(x, w_k) = \\exp\\left(
(\\Omega \\cdot v)^T \\hat\\Lambda (\\Omega \\cdot v)
\\right) - 1
Parameters
----------
manifold : SO, SPD, or Grassmannian
Riemannian manifold instance.
latent_dim : int, optional
Projection dimensionality for global omega. Default: d_flat.
kernel_latent_dim : int, optional
Dimensionality for the kernel's omega_hat. Default: same as
omega's output dimension (latent_dim).
omega_hat_scale : float
Scale for omega_hat initialization. Default: 0.1.
beta : float
Transfer function steepness.
gamma_init : float, optional
Initial neighborhood range.
gamma_final : float
Final neighborhood range. Default: 0.01.
gamma_decay : float, optional
Per-step decay factor.
tau : float
Injectivity radius safety factor. Default: 0.95.
n_prototypes_per_class : int
Number of prototypes per class.
max_iter : int
Maximum training iterations.
lr : float
Learning rate.
epsilon : float
Convergence threshold.
random_seed : int
Random seed.
optimizer : str or optax optimizer, optional
Default: 'adam'.
transfer_fn : callable, optional
Transfer function.
margin : float
Margin for loss.
callbacks : list, optional
Callback objects.
use_scan : bool
Default: False.
batch_size : int, optional
Mini-batch size.
lr_scheduler : str or optax.Schedule, optional
Learning rate schedule.
lr_scheduler_kwargs : dict, optional
LR scheduler kwargs.
prototypes_initializer : str or callable, optional
Prototype initialization.
patience : int, optional
Early stopping patience.
restore_best : bool
Restore best parameters. Default: False.
class_weight : dict or 'balanced', optional
Class weights.
gradient_accumulation_steps : int, optional
Gradient accumulation.
ema_decay : float, optional
EMA decay.
freeze_params : list of str, optional
Frozen parameters.
lookahead : dict, optional
Lookahead config.
mixed_precision : str or None, optional
Mixed precision dtype.
References
----------
.. [1] Villmann, T., Haase, S., & Kaden, M. (2015). Kernelized vector
quantization in gradient-descent learning. Neurocomputing.
See Also
--------
RiemannianSMNG : Base Riemannian matrix Neural Gas.
RiemannianDKSMNG : Gaussian kernel variant (no matrix kernel).
RiemannianDKRSMNG : Relevance kernel variant.
"""
def __init__(self, manifold, latent_dim=None, kernel_latent_dim=None,
omega_hat_scale=0.1, beta=10.0, gamma_init=None,
gamma_final=0.01, gamma_decay=None, lr_ratio=0.5,
tau=0.95,
n_prototypes_per_class=1, max_iter=100, lr=0.01,
epsilon=1e-6, random_seed=42, optimizer='adam',
transfer_fn=None, margin=0.0, callbacks=None,
use_scan=False, 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__(
manifold=manifold, latent_dim=latent_dim, beta=beta,
gamma_init=gamma_init, gamma_final=gamma_final,
gamma_decay=gamma_decay, tau=tau,
n_prototypes_per_class=n_prototypes_per_class,
max_iter=max_iter, lr=lr, epsilon=epsilon,
random_seed=random_seed, 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.kernel_latent_dim = kernel_latent_dim
self.omega_hat_scale = omega_hat_scale
self.lr_ratio = lr_ratio
self.omega_hat_ = None
def _get_resume_params(self, params):
base = super()._get_resume_params(params)
base['omega_hat'] = self.omega_hat_
return base
def _init_state(self, X, y, key):
state, params, proto_labels = super()._init_state(X, y, key)
# omega_hat operates in the projected space (latent_dim)
proj_dim = params['omega'].shape[1]
kld = self.kernel_latent_dim if self.kernel_latent_dim is not None else proj_dim
omega_hat = self.omega_hat_scale * identity_omega_init(proj_dim, kld)
params = {**params, 'omega_hat': omega_hat}
opt_state = self._optimizer.init(params)
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']
omega = params['omega']
gamma = params['gamma']
omega_hat = params['omega_hat']
lambda_hat = jnp.dot(omega_hat, omega_hat.T) # (proj_dim, proj_dim)
n = X.shape[0]
p = prototypes.shape[0]
X_m = self._reshape_to_manifold(X, n)
W_m = self._reshape_to_manifold(prototypes, p)
# 1. Omega-projected tangent vectors
tangent_flat = self._compute_tangent_vectors(X_m, W_m)
projected = jnp.einsum('npd,dl->npl', tangent_flat, omega) # (n, p, L)
# 2. Exponential kernel: exp(proj^T Lambda_hat proj) - 1
Lp = jnp.einsum('npl,lm->npm', projected, lambda_hat) # (n, p, L)
pLp = jnp.sum(projected * Lp, axis=2) # (n, p)
pLp = jnp.clip(pLp, None, 20.0) # prevent exp overflow
distances = jnp.maximum(jnp.exp(pLp) - 1.0, 0.0)
# 3. NG ranking + GLVQ loss
same_class = (y[:, None] == proto_labels[None, :])
INF = jnp.finfo(distances.dtype).max
d_same = jnp.where(same_class, distances, INF)
order = jnp.argsort(d_same, axis=1)
ranks = jnp.argsort(order, axis=1).astype(jnp.float32)
h = jnp.exp(-ranks / (gamma + 1e-10))
h = jnp.where(same_class, h, 0.0)
C = jnp.sum(h, axis=1, keepdims=True)
h_normalized = h / (C + 1e-10)
d_diff = jnp.where(~same_class, distances, INF)
dm = jnp.min(d_diff, axis=1)
# Separate learning rates (Hammer et al. 2003: epsilon^- = lr_ratio * epsilon^+)
# Scale gradient through dm by lr_ratio; forward pass unchanged.
dm = jax.lax.stop_gradient(dm) + self.lr_ratio * (
dm - jax.lax.stop_gradient(dm))
mu = (distances - dm[:, None]) / (distances + dm[:, None] + 1e-10)
transfer = self.transfer_fn or sigmoid_beta
cost = transfer(mu + self.margin, self.beta)
weighted_cost = jnp.sum(h_normalized * cost, axis=1)
return jnp.mean(weighted_cost)
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_hat_ = params['omega_hat']
@property
def omega_hat_matrix(self):
"""Return the learned kernel :math:`\\hat\\Omega` matrix."""
if self.omega_hat_ is None:
raise ValueError("Model not fitted. Call fit() first.")
return self.omega_hat_
@property
def lambda_hat_matrix(self):
"""Return :math:`\\hat\\Lambda = \\hat\\Omega \\hat\\Omega^T`."""
if self.omega_hat_ is None:
raise ValueError("Model not fitted. Call fit() first.")
return self.omega_hat_ @ self.omega_hat_.T
[docs]
def predict(self, X):
"""Predict using exponential kernel in omega-projected space.
Parameters
----------
X : array-like of shape (n_samples, n_features_flat)
Returns
-------
labels : array of shape (n_samples,)
"""
self._check_fitted()
X = jnp.asarray(X, dtype=jnp.float32)
n = X.shape[0]
p = self.prototypes_.shape[0]
X_m = self._reshape_to_manifold(X, n)
W_m = self._reshape_to_manifold(self.prototypes_, p)
tangent_flat = self._compute_tangent_vectors(X_m, W_m)
projected = jnp.einsum('npd,dl->npl', tangent_flat, self.omega_)
lambda_hat = jnp.dot(self.omega_hat_, self.omega_hat_.T)
Lp = jnp.einsum('npl,lm->npm', projected, lambda_hat)
pLp = jnp.sum(projected * Lp, axis=2)
pLp = jnp.clip(pLp, None, 20.0)
distances = jnp.maximum(jnp.exp(pLp) - 1.0, 0.0)
return wtac(distances, self.prototype_labels_)
def _get_quantizable_attrs(self):
attrs = super()._get_quantizable_attrs()
if isinstance(attrs, dict):
if self.omega_hat_ is not None:
attrs['omega_hat_'] = self.omega_hat_
return attrs
def _get_fitted_arrays(self):
arrays = super()._get_fitted_arrays()
if self.omega_hat_ is not None:
arrays['omega_hat_'] = np.asarray(self.omega_hat_)
return arrays
def _set_fitted_arrays(self, arrays):
super()._set_fitted_arrays(arrays)
if 'omega_hat_' in arrays:
self.omega_hat_ = jnp.asarray(arrays['omega_hat_'])
def _get_hyperparams(self):
hp = super()._get_hyperparams()
hp['omega_hat_scale'] = self.omega_hat_scale
if self.kernel_latent_dim is not None:
hp['kernel_latent_dim'] = self.kernel_latent_dim
hp['lr_ratio'] = self.lr_ratio
return hp