"""
Riemannian Differentiating Kernel GRLVQ (RiemannianDKGRLVQ).
Combines Riemannian manifold geometry with relevance-weighted Gaussian
kernel distance in tangent space:
.. math::
d_\\kappa^2(x, w_k) = 2\\left(1 - \\exp\\left(
-\\frac{\\sum_j \\lambda_j v_j^2}{2\\sigma_k^2}
\\right)\\right)
where :math:`v = \\text{Log}_{w_k}(x)_{\\text{flat}}` is the tangent vector,
:math:`\\lambda = \\text{softmax}(\\text{relevances})`, and :math:`\\sigma_k`
is a per-prototype bandwidth.
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_srng import RiemannianSRNG
from prosemble.models.prototype_base import SupervisedState
from prosemble.core.activations import sigmoid_beta
from prosemble.core.competitions import wtac
from prosemble.core.manifolds import SO, SPD, Grassmannian, HyperbolicPoincare
from prosemble.models.riemannian_srng import (
_so_log_map_diff, _spd_log_map_diff, _grassmannian_log_map_diff,
_hyperbolic_log_map_diff,
)
[docs]
class RiemannianDKGRLVQ(RiemannianSRNG):
"""Riemannian Differentiating Kernel GRLVQ.
Extends RiemannianSRNG with relevance-weighted Gaussian kernel
distance in tangent space. Each prototype :math:`w_k` has a learnable
bandwidth :math:`\\sigma_k`, and a shared relevance vector
:math:`\\lambda` weights the tangent space features.
.. math::
d_\\kappa^2(x, w_k) = 2\\left(1 - \\exp\\left(
-\\frac{\\sum_j \\lambda_j v_j^2}{2\\sigma_k^2}
\\right)\\right)
where :math:`v = \\text{Log}_{w_k}(x)_{\\text{flat}}`.
Parameters
----------
manifold : SO, SPD, or Grassmannian
Riemannian manifold instance defining the geometry.
sigma_init : str or float
Initialization strategy for per-prototype bandwidths.
'median' (default): per-class median geodesic distance.
'mean': per-class mean geodesic distance.
float: fixed value for all prototypes.
sigma_min : float
Lower bound for sigma to prevent bandwidth collapse. Default: 1e-3.
beta : float
Transfer function steepness parameter.
gamma_init : float, optional
Initial neighborhood range for NG cooperation.
gamma_final : float
Final neighborhood range. Default: 0.01.
gamma_decay : float, optional
Per-step multiplicative decay factor for gamma.
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 on loss change.
random_seed : int
Random seed for reproducibility.
optimizer : str or optax optimizer, optional
Default: 'adam'.
transfer_fn : callable, optional
Transfer function for loss shaping.
margin : float
Margin for loss computation.
callbacks : list, optional
List of Callback objects.
use_scan : bool
If True, use jax.lax.scan. Default: False.
batch_size : int, optional
Mini-batch size.
lr_scheduler : str or optax.Schedule, optional
Learning rate schedule.
lr_scheduler_kwargs : dict, optional
Keyword arguments for the learning rate scheduler.
prototypes_initializer : str or callable, optional
How to initialize prototypes.
patience : int, optional
Epochs with no improvement before stopping.
restore_best : bool
Restore best parameters. Default: False.
class_weight : dict or 'balanced', optional
Class weights.
gradient_accumulation_steps : int, optional
Gradient accumulation steps.
ema_decay : float, optional
EMA decay for parameters.
freeze_params : list of str, optional
Parameter groups to freeze.
lookahead : dict, optional
Lookahead optimizer 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
--------
RiemannianSRNG : Base Riemannian supervised Neural Gas.
RiemannianDKGLVQ : Gaussian kernel variant without relevance weighting.
"""
def __init__(self, manifold, sigma_init='median', sigma_min=1e-3,
beta=10.0, gamma_init=None, gamma_final=0.01,
gamma_decay=None, tau=0.95, lr_ratio=0.5,
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, beta=beta,
gamma_init=gamma_init, gamma_final=gamma_final,
gamma_decay=gamma_decay, tau=tau, lr_ratio=lr_ratio,
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.sigma_init = sigma_init
self.sigma_min = sigma_min
self.sigmas_ = None
self.relevances_ = None
def _diff_log_map(self, w, x):
"""Differentiable log map for a single (base, target) pair."""
if isinstance(self.manifold, SO):
return _so_log_map_diff(w, x)
elif isinstance(self.manifold, SPD):
return _spd_log_map_diff(w, x)
elif isinstance(self.manifold, Grassmannian):
return _grassmannian_log_map_diff(w, x)
elif isinstance(self.manifold, HyperbolicPoincare):
return _hyperbolic_log_map_diff(w, x, eps=self.manifold.eps)
else:
return self.manifold.log_map(w, x)
def _compute_tangent_vectors(self, X_manifold, W_manifold):
"""Compute tangent vectors from prototypes to data via log map.
Parameters
----------
X_manifold : array of shape (n_samples, *point_shape)
W_manifold : array of shape (n_prototypes, *point_shape)
Returns
-------
tangents_flat : array of shape (n_samples, n_prototypes, d_flat)
"""
log_to_all_x = jax.vmap(self._diff_log_map, in_axes=(None, 0))
log_matrix = jax.vmap(log_to_all_x, in_axes=(0, None))
tangents = log_matrix(W_manifold, X_manifold)
tangents = jnp.moveaxis(tangents, 0, 1)
n = X_manifold.shape[0]
p = W_manifold.shape[0]
return tangents.reshape(n, p, -1)
def _estimate_sigmas(self, X_flat, y, prototypes_flat, proto_labels):
"""Estimate per-prototype bandwidths from manifold distances."""
if isinstance(self.sigma_init, (int, float)):
return jnp.full(prototypes_flat.shape[0], float(self.sigma_init))
n_protos = prototypes_flat.shape[0]
n = X_flat.shape[0]
X_m = self._reshape_to_manifold(X_flat, n)
W_m = self._reshape_to_manifold(prototypes_flat, n_protos)
dist_matrix = self._geodesic_distances(X_m, W_m)
sigmas = []
for k in range(n_protos):
label_k = proto_labels[k]
class_mask = (y == label_k)
dists_k = jnp.sqrt(jnp.maximum(dist_matrix[class_mask, k], 0.0))
if self.sigma_init == 'median':
sigma_k = jnp.median(dists_k)
else:
sigma_k = jnp.mean(dists_k)
sigmas.append(jnp.maximum(sigma_k, self.sigma_min))
return jnp.array(sigmas)
def _get_resume_params(self, params):
base = super()._get_resume_params(params)
base['sigmas'] = self.sigmas_
base['relevances'] = self.relevances_
return base
def _init_state(self, X, y, key):
state, params, proto_labels = super()._init_state(X, y, key)
d_flat = X.shape[1]
sigmas = self._estimate_sigmas(X, y, params['prototypes'], proto_labels)
relevances = jnp.zeros(d_flat) # uniform under softmax
params = {**params, 'sigmas': sigmas, 'relevances': relevances}
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']
gamma = params['gamma']
sigmas = jnp.maximum(params['sigmas'], self.sigma_min)
lam = jax.nn.softmax(params['relevances'])
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. Tangent vectors via log map
tangent_flat = self._compute_tangent_vectors(X_m, W_m) # (n, p, d_flat)
# 2. Relevance-weighted squared norms
weighted_sq = jnp.sum(
lam[None, None, :] * tangent_flat ** 2, axis=2
) # (n, p)
# 3. Apply Gaussian kernel
K = jnp.exp(-weighted_sq / (2.0 * sigmas[None, :] ** 2))
distances = 2.0 * (1.0 - K)
# 4. Compute ranks within same-class prototypes
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)
# 5. Neighborhood function h = exp(-rank / gamma)
h = jnp.exp(-ranks / (gamma + 1e-10))
h = jnp.where(same_class, h, 0.0)
# 6. Normalize per sample
C = jnp.sum(h, axis=1, keepdims=True)
h_normalized = h / (C + 1e-10)
# 7. Closest different-class prototype distance
d_diff = jnp.where(~same_class, distances, INF)
dm = jnp.min(d_diff, axis=1)
# 8. GLVQ mu
mu = (distances - dm[:, None]) / (distances + dm[:, None] + 1e-10)
# 9. Transfer function
transfer = self.transfer_fn or sigmoid_beta
cost = transfer(mu + self.margin, self.beta)
# 10. Rank-weighted sum
weighted_cost = jnp.sum(h_normalized * cost, axis=1)
return jnp.mean(weighted_cost)
def _post_update(self, params):
params = super()._post_update(params)
params['sigmas'] = jnp.maximum(params['sigmas'], self.sigma_min)
return params
def _extract_results(self, params, proto_labels, loss_history, n_iter, **kwargs):
super()._extract_results(params, proto_labels, loss_history, n_iter, **kwargs)
self.sigmas_ = params['sigmas']
self.relevances_ = params['relevances']
@property
def kernel_bandwidths(self):
"""Return the learned per-prototype bandwidths."""
if self.sigmas_ is None:
raise ValueError("Model not fitted. Call fit() first.")
return self.sigmas_
@property
def relevance_profile(self):
"""Return the learned relevance weights (normalized via softmax)."""
if self.relevances_ is None:
raise ValueError("Model not fitted. Call fit() first.")
return jax.nn.softmax(self.relevances_)
[docs]
def predict(self, X):
"""Predict using relevance-weighted kernel distance in tangent 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)
lam = jax.nn.softmax(self.relevances_)
weighted_sq = jnp.sum(
lam[None, None, :] * tangent_flat ** 2, axis=2
)
sigmas = jnp.maximum(self.sigmas_, self.sigma_min)
K = jnp.exp(-weighted_sq / (2.0 * sigmas[None, :] ** 2))
distances = 2.0 * (1.0 - K)
return wtac(distances, self.prototype_labels_)
def _get_quantizable_attrs(self):
attrs = {'prototypes_': self.prototypes_}
if self.sigmas_ is not None:
attrs['sigmas_'] = self.sigmas_
if self.relevances_ is not None:
attrs['relevances_'] = self.relevances_
return attrs
def _get_fitted_arrays(self):
arrays = super()._get_fitted_arrays()
if self.sigmas_ is not None:
arrays['sigmas_'] = np.asarray(self.sigmas_)
if self.relevances_ is not None:
arrays['relevances_'] = np.asarray(self.relevances_)
return arrays
def _set_fitted_arrays(self, arrays):
super()._set_fitted_arrays(arrays)
if 'sigmas_' in arrays:
self.sigmas_ = jnp.asarray(arrays['sigmas_'])
if 'relevances_' in arrays:
self.relevances_ = jnp.asarray(arrays['relevances_'])
def _get_hyperparams(self):
hp = super()._get_hyperparams()
hp['sigma_init'] = self.sigma_init
hp['sigma_min'] = self.sigma_min
return hp