# -*- coding: utf-8 -*-
"""Copyright 2019 DScribe developers
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
"""
from abc import ABC, abstractmethod
import numpy as np
from sklearn.metrics.pairwise import pairwise_kernels
[docs]class LocalSimilarityKernel(ABC):
"""An abstract base class for all kernels that use the similarity of local
atomic environments to compute a global similarity measure.
"""
def __init__(self, metric, gamma=None, degree=3, coef0=1, kernel_params=None, normalize_kernel=True):
"""
Args:
metric(string or callable): The pairwise metric used for
calculating the local similarity. Accepts any of the sklearn
pairwise metric strings (e.g. "linear", "rbf", "laplacian",
"polynomial") or a custom callable. A callable should accept
two arguments and the keyword arguments passed to this object
as kernel_params, and should return a floating point number.
gamma(float): Gamma parameter for the RBF, laplacian, polynomial,
exponential chi2 and sigmoid kernels. Interpretation of the
default value is left to the kernel; see the documentation for
sklearn.metrics.pairwise. Ignored by other kernels.
degree(float): Degree of the polynomial kernel. Ignored by other
kernels.
coef0(float): Zero coefficient for polynomial and sigmoid kernels.
Ignored by other kernels.
kernel_params(mapping of string to any): Additional parameters
(keyword arguments) for kernel function passed as callable
object.
normalize_kernel(boolean): Whether to normalize the final global
similarity kernel. The normalization is achieved by dividing each
kernel element :math:`K_{ij}` with the factor
:math:`\sqrt{K_{ii}K_{jj}}`
"""
self.metric = metric
self.gamma = gamma
self.degree = degree
self.coef0 = coef0
self.kernel_params = kernel_params
self.normalize_kernel = normalize_kernel
[docs] def create(self, x, y=None):
"""Creates the kernel matrix based on the given lists of local
features x and y.
Args:
x(iterable): A list of local feature arrays for each structure.
y(iterable): An optional second list of features. If not specified
it is assumed that y=x.
Returns:
The pairwise global similarity kernel K[i,j] between the given
structures, in the same order as given in the input, i.e. the
similarity of structures i and j is given by K[i,j], where features
for structure i and j were in features[i] and features[j]
respectively.
"""
symmetric = False
if y is None:
y = x
symmetric = True
# First calculate the "raw" pairwise similarity of atomic environments
n_x = len(x)
n_y = len(y)
C_ij_dict = {}
for i in range(n_x):
for j in range(n_y):
# Skip lower triangular part for symmetric matrices
if symmetric and j < i:
continue
x_i = x[i]
# Save time on symmetry
if symmetric and j == i:
y_j = None
else:
y_j = y[j]
C_ij = self.get_pairwise_matrix(x_i, y_j)
C_ij_dict[i, j] = C_ij
# Calculate the global pairwise similarity between the entire
# structures
K_ij = np.zeros((n_x, n_y))
for i in range(n_x):
for j in range(n_y):
# Skip lower triangular part for symmetric matrices
if symmetric and j < i:
continue
C_ij = C_ij_dict[i, j]
k_ij = self.get_global_similarity(C_ij)
K_ij[i, j] = k_ij
# Save data also on lower triangular part for symmetric matrices
if symmetric and j != i:
K_ij[j, i] = k_ij
# Enforce kernel normalization if requested.
if self.normalize_kernel:
if symmetric:
k_ii = np.diagonal(K_ij)
x_k_ii_sqrt = np.sqrt(k_ii)
y_k_ii_sqrt = x_k_ii_sqrt
else:
# Calculate self-similarity for X
x_k_ii = np.empty(n_x)
for i in range(n_x):
x_i = x[i]
C_ii = self.get_pairwise_matrix(x_i)
k_ii = self.get_global_similarity(C_ii)
x_k_ii[i] = k_ii
x_k_ii_sqrt = np.sqrt(x_k_ii)
# Calculate self-similarity for Y
y_k_ii = np.empty(n_y)
for i in range(n_y):
y_i = y[i]
C_ii = self.get_pairwise_matrix(y_i)
k_ii = self.get_global_similarity(C_ii)
y_k_ii[i] = k_ii
y_k_ii_sqrt = np.sqrt(y_k_ii)
K_ij /= np.outer(x_k_ii_sqrt, y_k_ii_sqrt)
return K_ij
[docs] def get_pairwise_matrix(self, X, Y=None):
"""Calculates the pairwise similarity of atomic environments with
scikit-learn, and the pairwise metric configured in the constructor.
Args:
X(np.ndarray): Feature vector for the atoms in structure A
Y(np.ndarray): Feature vector for the atoms in structure B
Returns:
np.ndarray: NxM matrix of local similarities between structures A
and B, with N and M atoms respectively.
"""
if callable(self.metric):
params = self.kernel_params or {}
else:
params = {"gamma": self.gamma,
"degree": self.degree,
"coef0": self.coef0}
return pairwise_kernels(X, Y, metric=self.metric,
filter_params=True, **params)
[docs] @abstractmethod
def get_global_similarity(self, localkernel):
"""
Computes the global similarity between two structures A and B.
Args:
localkernel(np.ndarray): NxM matrix of local similarities between
structures A and B, with N and M atoms respectively.
Returns:
float: Global similarity between the structures A and B.
"""