ThomasParistech

# Normalize the density by the disk/kernel convolution
density /= gaussian_blurred

ThomasParistech

import cv2

def ceil_odd(x: float) -> int:
    """Round float to nearest odd integer."""
    return 1 + 2*math.ceil(0.5*(x-1.0))

# Perform KDE and retrieve the bandwidth
kde = gaussian_kde(disk_xy.T)
sigma = np.sqrt(kde.covariance[0, 0])

ThomasParistech

from sklearn.neighbors import KernelDensity

kde = KernelDensity(kernel='linear', bandwidth="silverman")
kde.fit(input_xy)
density = np.exp(kde.score_samples(pred_xy))

ThomasParistech

...

# Change radius
new_radius = np.sqrt(2.0 - r**2)

...

ThomasParistech

... # Generate disk_xy

# Compute radius
r = np.linalg.norm(disk_xy, axis=-1)

# Change radius
new_radius = 2 - r
reflected_disk_xy = np.multiply((new_radius/r)[:, None],
                                disk_xy)
                                

ThomasParistech

  import numpy as np
  import matplotlib.pyplot as plt
  from scipy.stats import gaussian_kde

  # Generate a uniform grid of points in [-1, 1] x [-1, 1]
  n_rows = 100
  grid_xy = np.stack(np.meshgrid(np.linspace(-1, 1, n_rows),
                                 np.linspace(-1, 1, n_rows),
                                 indexing="xy"),
                     axis=-1).reshape(-1, 2)

ThomasParistech

import numpy as np
from scipy.stats import norm

def weighted_kde(x_data: np.ndarray, x_prediction: np.ndarray) -> np.ndarray:
    h = silverman_bandwidth(x_data)  # Required to evaluate CDF
    area_values = norm.cdf(1.0, x_prediction, h) - norm.cdf(0.0, x_prediction, h)
    basic_densities = basic_kde(x_data, x_prediction, h)
    return basic_densities / area_values

ThomasParistech

import numpy as np

def reflective_kde(x_data: np.ndarray, x_prediction: np.ndarray) -> np.ndarray:
    h = silverman_bandwidth(x_data)  # Compute before adding reflected data
    x_data_augmented = np.stack((-x_data, x_data, 2-x_data))
    reflective_densities = basic_kde(x_data_augmented, x_prediction, h)
    # Discard left and right reflected samples and normalize density by 1/3
    return 3 * reflective_densities 

ThomasParistech

import numpy as np
from scipy.special import logit

def transformed_kde(x_data: np.ndarray, x_prediction: np.ndarray) -> np.ndarray:
    x_data_logit = logit(x_data)
    x_prediction_logit = logit(x_prediction)
    densities_logit = basic_kde(x_data_logit, x_prediction_logit)
    return densities_logit / (x_prediction * (1.0-x_prediction))

ThomasParistech

import numpy as np
from scipy.stats import norm


def silverman_bandwidth(x_data: np.ndarray) -> float:
    return (4/(3*x_data.shape[0]))**0.2 * np.std(x_data)


def basic_kde(x_data: np.ndarray, x_prediction: np.ndarray) -> np.ndarray:
    """Perform Gaussian Kernel Density Estimation.