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plot_roc_curves.py
plot_roc_curves.py 7.99 KiB
"""Methods for plotting ROC (receiver operating characteristic) curve."""
import numpy
import matplotlib.colors
import matplotlib.pyplot as pyplot
import util.performance_diagrams as performance_diagrams
DEFAULT_LINE_COLOUR = numpy.array([228, 26, 28], dtype=float) / 255
DEFAULT_LINE_WIDTH = 3
DEFAULT_RANDOM_LINE_COLOUR = numpy.full(3, 152. / 255)
DEFAULT_RANDOM_LINE_WIDTH = 2
LEVELS_FOR_PEIRCE_CONTOURS = numpy.linspace(0, 1, num=11, dtype=float)
FIGURE_WIDTH_INCHES = 10
FIGURE_HEIGHT_INCHES = 10
FONT_SIZE = 20
pyplot.rc('font', size=FONT_SIZE)
pyplot.rc('axes', titlesize=FONT_SIZE)
pyplot.rc('axes', labelsize=FONT_SIZE)
pyplot.rc('xtick', labelsize=FONT_SIZE)
pyplot.rc('ytick', labelsize=FONT_SIZE)
pyplot.rc('legend', fontsize=FONT_SIZE)
pyplot.rc('figure', titlesize=FONT_SIZE)
def _get_pofd_pod_grid(pofd_spacing=0.01, pod_spacing=0.01):
"""Creates grid in POFD-POD space.
M = number of rows (unique POD values) in grid
N = number of columns (unique POFD values) in grid
:param pofd_spacing: Spacing between grid cells in adjacent columns.
:param pod_spacing: Spacing between grid cells in adjacent rows.
:return: pofd_matrix: M-by-N numpy array of POFD values.
:return: pod_matrix: M-by-N numpy array of POD values.
"""
num_pofd_values = 1 + int(numpy.ceil(1. / pofd_spacing))
num_pod_values = 1 + int(numpy.ceil(1. / pod_spacing))
unique_pofd_values = numpy.linspace(0., 1., num=num_pofd_values)
unique_pod_values = numpy.linspace(0., 1., num=num_pod_values)[::-1]
return numpy.meshgrid(unique_pofd_values, unique_pod_values)
def _get_peirce_colour_scheme():
"""Returns colour scheme for Peirce score.
:return: colour_map_object: Colour scheme (instance of
`matplotlib.colors.ListedColormap`).
:return: colour_norm_object: Instance of `matplotlib.colors.BoundaryNorm`,
defining the scale of the colour map.
"""
this_colour_map_object = pyplot.cm.Blues
this_colour_norm_object = matplotlib.colors.BoundaryNorm(
LEVELS_FOR_PEIRCE_CONTOURS, this_colour_map_object.N)
rgba_matrix = this_colour_map_object(this_colour_norm_object(
LEVELS_FOR_PEIRCE_CONTOURS
))
colour_list = [
rgba_matrix[i, ..., :-1] for i in range(rgba_matrix.shape[0])
]
colour_map_object = matplotlib.colors.ListedColormap(colour_list)
colour_map_object.set_under(numpy.array([1, 1, 1]))
colour_norm_object = matplotlib.colors.BoundaryNorm(
LEVELS_FOR_PEIRCE_CONTOURS, colour_map_object.N)
return colour_map_object, colour_norm_object
def get_points_in_roc_curve(observed_labels, forecast_probabilities):
"""Creates points for ROC curve.
E = number of examples
T = number of binarization thresholds
:param observed_labels: length-E numpy array of class labels (integers in
0...1).
:param forecast_probabilities: length-E numpy array with forecast
probabilities of label = 1.
:return: pofd_by_threshold: length-T numpy array of POFD (probability of
false detection) values.
:return: pod_by_threshold: length-T numpy array of POD (probability of
detection) values.
"""
assert numpy.all(numpy.logical_or(
observed_labels == 0, observed_labels == 1
))
assert numpy.all(numpy.logical_and(
forecast_probabilities >= 0, forecast_probabilities <= 1
))
observed_labels = observed_labels.astype(int)
binarization_thresholds = numpy.linspace(0, 1, num=1001, dtype=float)
num_thresholds = len(binarization_thresholds)
pofd_by_threshold = numpy.full(num_thresholds, numpy.nan)
pod_by_threshold = numpy.full(num_thresholds, numpy.nan)
for k in range(num_thresholds):
these_forecast_labels = (
forecast_probabilities >= binarization_thresholds[k]
).astype(int)
this_num_hits = numpy.sum(numpy.logical_and(
these_forecast_labels == 1, observed_labels == 1
))
this_num_false_alarms = numpy.sum(numpy.logical_and(
these_forecast_labels == 1, observed_labels == 0
))
this_num_misses = numpy.sum(numpy.logical_and(
these_forecast_labels == 0, observed_labels == 1
))
this_num_correct_nulls = numpy.sum(numpy.logical_and(
these_forecast_labels == 0, observed_labels == 0
))
try:
pofd_by_threshold[k] = (
float(this_num_false_alarms) /
(this_num_false_alarms + this_num_correct_nulls)
)
except ZeroDivisionError:
pass
try:
pod_by_threshold[k] = (
float(this_num_hits) / (this_num_hits + this_num_misses)
)
except ZeroDivisionError:
pass
pod_by_threshold = numpy.array([1.] + pod_by_threshold.tolist() + [0.])
pofd_by_threshold = numpy.array([1.] + pofd_by_threshold.tolist() + [0.])
return pofd_by_threshold, pod_by_threshold
def plot_roc_curve(
observed_labels, forecast_probabilities,
line_colour=DEFAULT_LINE_COLOUR, line_width=DEFAULT_LINE_WIDTH,
random_line_colour=DEFAULT_RANDOM_LINE_COLOUR,
random_line_width=DEFAULT_RANDOM_LINE_WIDTH, axes_object=None):
"""Plots ROC curve.
E = number of examples
:param observed_labels: length-E numpy array of class labels (integers in
0...1).
:param forecast_probabilities: length-E numpy array with forecast
probabilities of label = 1.
:param line_colour: Colour (in any format accepted by `matplotlib.colors`).
:param line_width: Line width (real positive number).
:param random_line_colour: Colour of reference line (ROC curve for random
predictor).
:param random_line_width: Width of reference line (ROC curve for random
predictor).
:param axes_object: Will plot on these axes (instance of
`matplotlib.axes._subplots.AxesSubplot`). If `axes_object is None`,
will create new axes.
:return: pofd_by_threshold: See doc for `get_points_in_roc_curve`.
:return: pod_by_threshold: Same.
"""
pofd_by_threshold, pod_by_threshold = get_points_in_roc_curve(
observed_labels=observed_labels,
forecast_probabilities=forecast_probabilities)
if axes_object is None:
_, axes_object = pyplot.subplots(
1, 1, figsize=(FIGURE_WIDTH_INCHES, FIGURE_HEIGHT_INCHES)
)
pofd_matrix, pod_matrix = _get_pofd_pod_grid()
peirce_score_matrix = pod_matrix - pofd_matrix
colour_map_object, colour_norm_object = _get_peirce_colour_scheme()
pyplot.contourf(
pofd_matrix, pod_matrix, peirce_score_matrix,
LEVELS_FOR_PEIRCE_CONTOURS, cmap=colour_map_object,
norm=colour_norm_object, vmin=0., vmax=1., axes=axes_object)
# TODO(thunderhoser): Calling private method is a HACK.
colour_bar_object = performance_diagrams._add_colour_bar(
axes_object=axes_object, colour_map_object=colour_map_object,
colour_norm_object=colour_norm_object,
values_to_colour=peirce_score_matrix, min_colour_value=0.,
max_colour_value=1., orientation_string='vertical',
extend_min=False, extend_max=False)
print(colour_bar_object)
colour_bar_object.set_label('Peirce score')
random_x_coords = numpy.array([0., 1.])
random_y_coords = numpy.array([0., 1.])
axes_object.plot(
random_x_coords, random_y_coords, color=random_line_colour,
linestyle='dashed', linewidth=random_line_width)
nan_flags = numpy.logical_or(
numpy.isnan(pofd_by_threshold), numpy.isnan(pod_by_threshold)
)
if not numpy.all(nan_flags):
real_indices = numpy.where(numpy.invert(nan_flags))[0]
axes_object.plot(
pofd_by_threshold[real_indices], pod_by_threshold[real_indices],
color=line_colour, linestyle='solid', linewidth=line_width)
axes_object.set_xlabel('POFD (probability of false detection)')
axes_object.set_ylabel('POD (probability of detection)')
axes_object.set_xlim(0., 1.)
axes_object.set_ylim(0., 1.)
return pofd_by_threshold, pod_by_threshold