dscribe.kernels.rematchkernel module¶

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class dscribe.kernels.rematchkernel.REMatchKernel(alpha=0.1, threshold=1e-06, metric='linear', gamma=None, degree=3, coef0=1, kernel_params=None, normalize_kernel=True)[source]¶

Bases: dscribe.kernels.localsimilaritykernel.LocalSimilarityKernel

Used to compute a global similarity of structures based on the regularized-entropy match (REMatch) kernel of local atomic environments in the structure. More precisely, returns the similarity kernel K as:

\[ \begin{align}\begin{aligned}\DeclareMathOperator*{\argmax}{argmax} K(A, B) &= \mathrm{Tr} \mathbf{P}^\alpha \mathbf{C}(A, B)\\\mathbf{P}^\alpha &= \argmax_{\mathbf{P} \in \mathcal{U}(N, N)} \sum_{ij} P_{ij} (1-C_{ij} +\alpha \ln P_{ij})\end{aligned}\end{align} \]

where the similarity between local atomic environments \(C_{ij}\) has been calculated with the pairwise metric (e.g. linear, gaussian) defined by the parameters given in the constructor.

For reference, see:

“Comparing molecules and solids across structural and alchemical space”, Sandip De, Albert P. Bartók, Gábor Csányi and Michele Ceriotti, Phys. Chem. Chem. Phys. 18, 13754 (2016), https://doi.org/10.1039/c6cp00415f

Parameters

alpha (float) – Parameter controlling the entropic penalty. Values close to zero approach the best-match solution and values towards infinity approach the average kernel.
threshold (float) – Convergence threshold used in the Sinkhorn-algorithm.
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 \(K_{ij}\) with the factor \(\sqrt{K_{ii}K_{jj}}\)

get_global_similarity(localkernel)[source]¶

Computes the REMatch similarity between two structures A and B.

Parameters: localkernel (np.ndarray) – NxM matrix of local similarities between structures A and B, with N and M atoms respectively.
Returns: REMatch similarity between the structures A and B.
Return type: float