Functions related to Gaussian kernel model.

kernel_model.py

#!/usr/bin/python2

from __future__ import division

import numpy as np


def gaussian_kernel(p, q, h):
    """Compute Gaussian kernel function."""
    return np.exp(-(p-q)**2 / (2*h*h))


def kernel_matrix(train_data, bandwith=0.25):
    """Compute kernel matrix."""
    x = train_data
    n, = x.shape
    K = np.empty((n, n))
    for i, x1 in enumerate(x):
        for j, x2 in enumerate(x):
            K[i, j] = gaussian_kernel(x1, x2, bandwith)
    return K


def kernel_model(test_point, train_data, weights, bandwith=0.25,
        skip_zeros=False, tol=1e-7):
    """Compute the estimated value of a test point using kernel model."""
    if skip_zeros:
        tpl = [(a, xi) for a, xi in zip(weights, train_data) if abs(a) >= tol]
    else:
        tpl = [(a, xi) for a, xi in zip(weights, train_data)]
    return sum(a * gaussian_kernel(test_point, xi, bandwith) for a, xi in tpl)