#!/usr/bin/env python
# -*- coding: utf-8 -*-
import numpy as np
import numba as nb
import numba.core.types as nbtypes
[docs]class DeterminantMaximizer:
'''Select a subset of a dataset such that the determinant of the kernel
matrix of the selected samples are as large as possible. In other words,
the objective here is to ensure that the samples are as linearly
independent as possible in a reproducible kernel Hilbert space (RKHS).
Parameters
----------
kernel: callable or 'precomputed'
A symmetric positive semidefinite function implemented via the
``__call__`` semantics. Alternatively, if the value is 'precomputed',
a square kernel matrix will be expected as an argument to
:py:`__call__`.
kernel_options: dict
Additional arguments to be passed into the kernel.
'''
def __init__(self, kernel, kernel_options=None):
assert kernel == 'precomputed' or callable(kernel)
self.kernel = kernel
self.kernel_options = kernel_options or {}
[docs] def __call__(self, X, n):
'''Find a n-sample subset of X that attempts to maximize the diversity
and return the indices of the samples.
Parameters
----------
X: feature matrix or list of objects
Input dataset.
n: int
Number of samples to be chosen.
Returns
-------
chosen: list
Indices of the samples that are chosen.
'''
assert len(X) >= n
if self.kernel == 'precomputed':
assert (
isinstance(X, np.ndarray) and
X.ndim == 2 and
X.shape[0] == X.shape[1]
), 'A precomputed kernel matrix must be square.'
K = X
else:
K = self.kernel(X, **self.kernel_options)
return _choose(K.astype(np.float32), n)
@nb.jit(
nbtypes.intc[:](
nbtypes.float32[:, :],
nbtypes.intc
),
forceobj=True
)
def _choose(K, n):
chosen = []
for _ in range(n):
L = np.sum(K**2, axis=1)
L[chosen] = -np.inf # ensure chosen points won't be selected again
i = np.argmax(L)
chosen.append(i)
v = K[i, :] / np.linalg.norm(K[i, :])
K -= np.outer(K @ v, v)
return chosen