from typing import Optional, Union
from sklearn.base import BaseEstimator
from sklearn.utils import check_random_state
import numpy as np
from scipy.optimize import minimize
from scipy.spatial import distance
from cblearn import utils
from cblearn.embedding._base import TripletEmbeddingMixin
from cblearn.embedding import _torch_utils
[docs]
class CKL(BaseEstimator, TripletEmbeddingMixin):
""" Crowd Kernel Learning (CKL) embedding kernel for triplet data.
CKL [1]_ searches for an Euclidean representation of objects.
The model is regularized through the rank of the embedding's kernel matrix.
This estimator supports multiple implementations which can be selected by the `backend` parameter.
The *torch* backend uses the ADAM optimizer and backpropagation [2]_.
It can executed on CPU, but also CUDA GPUs.
.. note::
The *torch* backend requires the *pytorch* python package (see :ref:`extras_install`).
Attributes:
embedding_: Final embedding, shape (n_objects, n_components)
stress_: Final value of the SOE stress corresponding to the embedding.
n_iter_: Final number of optimization steps.
Examples:
>>> from cblearn import datasets
>>> np.random.seed(42)
>>> true_embedding = np.random.rand(15, 2)
>>> triplets = datasets.make_random_triplets(true_embedding, result_format='list-order', size=1000)
>>> triplets.shape, np.unique(triplets).shape
((1000, 3), (15,))
>>> estimator = CKL(n_components=2)
>>> embedding = estimator.fit_transform(triplets)
>>> embedding.shape
(15, 2)
>>> round(estimator.score(triplets), 1) > 0.6
True
>>> estimator = CKL(n_components=2, backend='torch', kernel=True)
>>> embedding = estimator.fit_transform(triplets)
>>> embedding.shape
(15, 2)
References
----------
.. [1] Tamuz, O., & Liu, mu., & Belognie, S., & Shamir, O., & Kalai, A.T. (2011).
Adaptively Learning the Crowd Kernel. International Conference on Machine Learning.
.. [2] Vankadara, L. C., Haghiri, S., Lohaus, M., Wahab, F. U., & von Luxburg, U. (2020).
Insights into Ordinal Embedding Algorithms: A Systematic Evaluation. ArXiv:1912.01666 [Cs, Stat].
"""
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def __init__(self, n_components=2, mu=0.0, verbose=False,
random_state: Union[None, int, np.random.RandomState] = None, max_iter=2000,
backend: str = 'scipy', kernel: bool = False, learning_rate=None, batch_size=50000,
device: str = "auto"):
""" Initialize the estimator.
Args:
n_components: The dimension of the embedding.
mu: Regularization parameter >= 0. Increased mu serves as increasing a margin constraint.
verbose: Enable verbose output.
random_state: The seed of the pseudo random number generator used to initialize the optimization.
max_iter: Maximum number of optimization iterations.
backend: The optimization backend for fitting. {"torch"}
kernel: Whether to optimize the kernel or the embedding (default).
learning_rate: Learning rate of the gradient-based optimizer.
If None, then 100 is used, or 1 if kernel=True.
Only used with *torch* backend, else ignored.
batch_size: Batch size of stochastic optimization. Only used with the *torch* backend, else ignored.
device: The device on which pytorch computes. {"auto", "cpu", "cuda"}
"auto" chooses cuda (GPU) if available, but falls back on cpu if not.
Only used with the *torch* backend, else ignored.
"""
self.n_components = n_components
self.max_iter = max_iter
self.mu = mu
self.learning_rate = learning_rate
self.batch_size = batch_size
self.kernel = kernel
self.verbose = verbose
self.random_state = random_state
self.backend = backend
self.device = device
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def fit(self, X: utils.Query, y: np.ndarray = None, init: np.ndarray = None,
n_objects: Optional[int] = None) -> 'CKL':
"""Computes the embedding.
Args:
X: The training input samples, shape (n_samples, 3)
y: Ignored
init: Initial embedding for optimization
Returns:
self.
"""
self.fit_X_ = utils.check_query(X, result_format='list-order') # for data validation in .transform
triplets = utils.check_query_response(X, y, result_format='list-order')
self.n_features_in_ = 3
if not n_objects:
n_objects = triplets.max() + 1
random_state = check_random_state(self.random_state)
if init is None:
init = random_state.multivariate_normal(
np.zeros(self.n_components), np.eye(self.n_components), size=n_objects)
if self.backend == 'torch':
_torch_utils.assert_torch_is_available()
if self.kernel:
result = _torch_utils.torch_minimize_kernel(
'adam', _ckl_kernel_loss_torch, init, data=[triplets.astype(int)], args=(self.mu,),
device=self.device, max_iter=self.max_iter, batch_size=self.batch_size, lr=self.learning_rate or 100,
seed=random_state.randint(1))
else:
result = _torch_utils.torch_minimize(
'adam', _ckl_x_loss_torch, init, data=(triplets.astype(int),), args=(self.mu,),
device=self.device, max_iter=self.max_iter, lr=self.learning_rate or 1,
seed=random_state.randint(1))
elif self.backend == "scipy":
if self.kernel:
raise ValueError(f"Kernel objective is not available for backend {self.backend}.")
result = minimize(_ckl_x_loss, init.ravel(), args=(init.shape, triplets, self.mu), method='L-BFGS-B',
jac=True, options=dict(maxiter=self.max_iter, disp=self.verbose))
else:
raise ValueError(f"Unknown backend '{self.backend}'. Try 'scipy' or 'torch' instead.")
if self.verbose and not result.success:
print(f"CKL's optimization failed with reason: {result.message}.")
self.embedding_ = result.x.reshape(-1, self.n_components)
self.stress_, self.n_iter_ = result.fun, result.nit
return self
def _ckl_x_loss(x, x_shape, triplets, mu, float_min=np.finfo(float).tiny):
X = x.reshape(x_shape)
n_objects, n_dim = X.shape
D = distance.squareform(distance.pdist(X, 'sqeuclidean'))
I, J, K = tuple(triplets.T)
nom = mu + D[I, K]
den = 2 * mu + D[I, K] + D[I, J]
loss = -(np.log(np.maximum(nom, float_min)) - np.log(np.maximum(den, float_min))).sum()
loss_grad = np.empty_like(X)
for dim in range(n_dim):
triplet_grads = [
2 / nom * (X[I, dim] - X[K, dim]) - 2 / den * ((X[I, dim] - X[J, dim]) + (X[I, dim] - X[K, dim])),
2 / den * (X[I, dim] - X[J, dim]),
-2 / nom * (X[I, dim] - X[K, dim]) + 2 / den * (X[I, dim] - X[K, dim]),
]
loss_grad[:, dim] = -np.bincount(triplets[:, 0], triplet_grads[0], n_objects)
loss_grad[:, dim] -= np.bincount(triplets[:, 1], triplet_grads[1], n_objects)
loss_grad[:, dim] -= np.bincount(triplets[:, 2], triplet_grads[2], n_objects)
return loss, loss_grad.ravel()
def _ckl_x_loss_torch(embedding, triplets, mu):
X = embedding[triplets.long()]
x_i, x_j, x_k = X[:, 0, :], X[:, 1, :], X[:, 2, :]
nominator = (x_i - x_k).norm(p=2, dim=1) ** 2 + mu
denominator = (x_i - x_j).norm(p=2, dim=1) ** 2 + (x_i - x_k).norm(p=2, dim=1) ** 2 + 2 * mu
return -1 * (nominator.log() - denominator.log()).sum()
def _ckl_kernel_loss_torch(kernel_matrix, triplets, mu):
triplets = triplets.long()
diag = kernel_matrix.diag()[:, None]
dist = -2 * kernel_matrix + diag + diag.transpose(0, 1)
d_ij = dist[triplets[:, 0], triplets[:, 1]].squeeze()
d_ik = dist[triplets[:, 0], triplets[:, 2]].squeeze()
probability = (d_ik + mu).log() - (d_ij + d_ik + 2 * mu).log()
return -probability.sum()
