Farthest Point Sampling (FPS)

Farthest Point Sampling determine a data subset that maximizes the variance in the distribution of the features or samples.
In FPS, the selection of the first point is made at random or by a separate metric. Each subsequent selection is made to maximize the Haussdorf distance, i.e. the minimum distance between a point and all previous selections.
\[*_{m+1} = argmax_{j} \left\{ min_{i \in *_{m}} [d(i, j)] \right\}\]
where ∗m contains the previous selections, ∗m+1 is the next selected sample or feature, and d(i, j) indicates the distance between the ith and jth column or row.
For machine learning potentials, FPS can be used to select the initial training set from a pool of data points. Also, FPS can be used for feature selection in case of Behler-Parrinello based machine learning potentials.

For more information, see the following references: Feature and Sample selection methods

Note

The FPS algorithm works on atomic environments of a system. So, to perform FPS on a pool of data points, one needs to convert atomic coordinates into atomic environments e.g. SOAP, ACSF, etc.

How to perfrom FPS on a pool of data points?

1. Install librascal which is used to convert atomic positions into SOAP descriptors.

Note

How to compile librascal?

1. conda create -n rascal
2. conda install python==3.9 (!! cation: do not use python version above 3.10, you wont be able to compile it because in newer versions The PyFrameObject structure members have been removed from the public C API).
3. mkdir build
2. Install scikit-matter which have the FPS API.

Diving into the code

  1. Reading the atomic coordinated using ASE.

frames = read(structure_file, index=':', format='extxyz')

  1. Initilizing the SOAP hyperparameters.

SOAP_HYPERS = {
    "interaction_cutoff": 3.5,
    "max_radial": 6,
    "max_angular": 6,
    "gaussian_sigma_constant": 0.4,
    "cutoff_smooth_width": 0.5,
    "gaussian_sigma_type": "Constant",
}

  1. Transforming atomic coordinates into SOAP descriptors.

x = soap.transform(frame).get_features(soap).mean(axis=0)

  1. Perform FPS on the samples.

struct_idx = FPS(n_to_select=n_FPS, initialize = 123).fit(X.T).selected_idx_

  1. Visualize the FPS selected samples by performing PCA on SOAP descriptors. (Here one can use any dimensionality reduction technique)

X_full = StandardFlexibleScaler(column_wise=False).fit_transform(X_full)
T = PCA(n_components=2).fit_transform(X_full)
fps