import numpy as np
import matplotlib.pyplot as mplt
import os
from sklearn.base import BaseEstimator
from sklearn.model_selection import train_test_split
from sklearn.decomposition import PCA
from sklearn.neighbors import NearestNeighbors
from sklearn.neighbors import KNeighborsClassifier
import nlopt
import random
from scipy.spatial.distance import euclidean, squareform, pdist
from utils import minimum_spanning_tree, polar_to_cartesian
from sklearn.model_selection import GridSearchCV
from sklearn.svm import SVC
from sklearn.metrics import accuracy_score, f1_score
class DBPlot(BaseEstimator):
"""
Heuristic approach to estimate and visualize high-dimensional decision
boundaries for trained binary classifiers by using black-box optimization
to find regions in which the classifier is maximally uncertain (0.5 prediction
probability). The total number of keypoints representing the decision boundary
will depend on n_connecting_keypoints and n_interpolated_keypoints. Reduce
either or both to reduce runtime.
Parameters
----------
estimator : BaseEstimator instance, optional (default=`KNeighborsClassifier(n_neighbors=10)`).
Classifier for which the decision boundary should be plotted. Can be trained
or untrained (in which case the fit method will train it). Must have
probability estimates enabled (i.e. `estimator.predict_proba` must work).
Make sure it is possible for probability estimates to get close to 0.5
(more specifically, as close as specified by acceptance_threshold) - this usally
requires setting an even number of neighbors, estimators etc.
dimensionality_reduction : BaseEstimator instance, optional (default=`PCA(n_components=2)`).
Dimensionality reduction method to help plot the decision boundary in 2D. Can be trained
or untrained (in which case the fit method will train it). Must have n_components=2.
Must be able to project new points into the 2D space after fitting
(i.e. `dimensionality_reduction.transform` must work).
acceptance_threshold : float, optional (default=0.03)
Maximum allowed deviation from decision boundary (defined as the region
with 0.5 prediction probability) when accepting decision boundary keypoints
n_decision_boundary_keypoints : int, optional (default=60)
Total number of decision boundary keypoints added, including both connecting
and interpolated keypoints.
n_connecting_keypoints : int, optional (default=None)
Number of decision boundary keypoints estimated along lines connecting
instances from two different classes (each such line must cross the
decision boundary at least once). If None (default), it is set to 1/3
of n_decision_boundary_keypoints
n_interpolated_keypoints : int, optional (default=None)
Number of decision boundary keypoints interpolated between connecting
keypoints to increase keypoint density. If None (default), it is set to
2/3 of n_decision_boundary_keypoints
n_generated_testpoints_per_keypoint : int, optional (default=15)
Number of demo points generated around decision boundary keypoints, and
labeled according to the specified classifier, in order to enrich and
validate the decision boundary plot
linear_iteration_budget : int, optional (default=100)
Maximum number of iterations the optimizer is allowed to run for each
keypoint estimation while looking along linear trajectories
hypersphere_iteration_budget : int, optional (default=300)
Maximum number of iterations the optimizer is allowed to run for each
keypoint estimation while looking along hypersphere surfaces
verbose: bool, optional (default=True)
Verbose output
"""
def __init__(
self,
estimator=KNeighborsClassifier(n_neighbors=10),
dimensionality_reduction=PCA(n_components=2),
acceptance_threshold=0.03,
n_decision_boundary_keypoints=60,
n_connecting_keypoints=None,
n_interpolated_keypoints=None,
n_generated_testpoints_per_keypoint=15,
linear_iteration_budget=100,
hypersphere_iteration_budget=300,
verbose=True,
):
if acceptance_threshold == 0:
raise Warning(
"A nonzero acceptance threshold is strongly recommended so the optimizer can finish in finite time"
)
if linear_iteration_budget < 2 or hypersphere_iteration_budget < 2:
raise Exception("Invalid iteration budget")
self.classifier = estimator
self.dimensionality_reduction = dimensionality_reduction
self.acceptance_threshold = acceptance_threshold
if (
n_decision_boundary_keypoints
and n_connecting_keypoints
and n_interpolated_keypoints
and n_connecting_keypoints + n_interpolated_keypoints
!= n_decision_boundary_keypoints
):
raise Exception(
"n_connecting_keypoints and n_interpolated_keypoints must sum to n_decision_boundary_keypoints (set them to None to use calculated suggestions)"
)
self.n_connecting_keypoints = (
n_connecting_keypoints
if n_connecting_keypoints != None
else n_decision_boundary_keypoints / 3
)
self.n_interpolated_keypoints = (
n_interpolated_keypoints
if n_interpolated_keypoints != None
else n_decision_boundary_keypoints * 2 / 3
)
self.linear_iteration_budget = linear_iteration_budget
self.n_generated_testpoints_per_keypoint = n_generated_testpoints_per_keypoint
self.hypersphere_iteration_budget = hypersphere_iteration_budget
self.verbose = verbose
self.decision_boundary_points = []
self.decision_boundary_points_2d = []
self.X_testpoints = []
self.y_testpoints = []
self.background = []
self.steps = 3
self.hypersphere_max_retry_budget = 20
self.penalties_enabled = True
self.random_gap_selection = False
def setclassifier(self, estimator=KNeighborsClassifier(n_neighbors=10)):
"""Assign classifier for which decision boundary should be plotted.
Parameters
----------
estimator : BaseEstimator instance, optional (default=KNeighborsClassifier(n_neighbors=10)).
Classifier for which the decision boundary should be plotted. Must have
probability estimates enabled (i.e. estimator.predict_proba must work).
Make sure it is possible for probability estimates to get close to 0.5
(more specifically, as close as specified by acceptance_threshold).
"""
self.classifier = estimator
def fit(self, X, y, training_indices=None):
"""Specify data to be plotted, and fit classifier only if required (the
specified clasifier is only trained if it has not been trained yet).
All the input data is provided in the matrix X, and corresponding
binary labels (values taking 0 or 1) in the vector y
Parameters
----------
X : array-like, shape = [n_samples, n_features]
A {n_samples by n_samples} size matrix containing data
y : array-like, shape = [n_samples]
Labels
training_indices : array-like or float, optional (default=None)
Indices on which the classifier has been trained / should be trained.
If float, it is converted to a random sample with the specified proportion
of the full dataset.
Returns
-------
self : returns an instance of self.
"""
if set(np.array(y, dtype=int).tolist()) != set([0, 1]):
raise Exception(
"Currently only implemented for binary classification. Make sure you pass in two classes (0 and 1)"
)
if training_indices == None:
train_idx = range(len(y))
elif type(training_indices) == float:
train_idx, test_idx = train_test_split(range(len(y)), test_size=0.2)
else:
train_idx = training_indices
self.X = X
self.y = y
self.train_idx = train_idx
# self.test_idx = np.setdiff1d(np.arange(len(y)), self.train_idx, assume_unique=False)
self.test_idx = list(set(range(len(y))).difference(set(self.train_idx)))
# fit classifier if necessary
try:
self.classifier.predict([X[0]])
except:
self.classifier.fit(X[train_idx, :], y[train_idx])
self.y_pred = self.classifier.predict(self.X)
# fit DR method if necessary
try:
self.dimensionality_reduction.transform([X[0]])
except:
self.dimensionality_reduction.fit(X, y)
try:
self.dimensionality_reduction.transform([X[0]])
except:
raise Exception(
"Please make sure your dimensionality reduction method has an exposed transform() method! If in doubt, use PCA or Isomap"
)
# transform data
self.X2d = self.dimensionality_reduction.transform(self.X)
self.mean_2d_dist = np.mean(pdist(self.X2d))
self.X2d_xmin, self.X2d_xmax = np.min(self.X2d[:, 0]), np.max(self.X2d[:, 0])
self.X2d_ymin, self.X2d_ymax = np.min(self.X2d[:, 1]), np.max(self.X2d[:, 1])
self.majorityclass = 0 if list(y).count(0) > list(y).count(1) else 1
self.minorityclass = 1 - self.majorityclass
minority_idx, majority_idx = (
np.where(y == self.minorityclass)[0],
np.where(y == self.majorityclass)[0],
)
self.Xminor, self.Xmajor = X[minority_idx], X[majority_idx]
self.Xminor2d, self.Xmajor2d = self.X2d[minority_idx], self.X2d[majority_idx]
# set up efficient nearest neighbor models for later use
self.nn_model_2d_majorityclass = NearestNeighbors(n_neighbors=2)
self.nn_model_2d_majorityclass.fit(self.X2d[majority_idx, :])
self.nn_model_2d_minorityclass = NearestNeighbors(n_neighbors=2)
self.nn_model_2d_minorityclass.fit(self.X2d[minority_idx, :])
# step 1. look for decision boundary points between corners of majority &
# minority class distribution
minority_corner_idx, majority_corner_idx = [], []
for extremum1 in [np.min, np.max]:
for extremum2 in [np.min, np.max]:
_, idx = self.nn_model_2d_minorityclass.kneighbors(
[[extremum1(self.Xminor2d[:, 0]), extremum2(self.Xminor2d[:, 1])]]
)
minority_corner_idx.append(idx[0][0])
_, idx = self.nn_model_2d_majorityclass.kneighbors(
[[extremum1(self.Xmajor2d[:, 0]), extremum2(self.Xmajor2d[:, 1])]]
)
majority_corner_idx.append(idx[0][0])
# optimize to find new db keypoints between corners
self._linear_decision_boundary_optimization(
minority_corner_idx, majority_corner_idx, all_combinations=True, step=1
)
# step 2. look for decision boundary points on lines connecting randomly
# sampled points of majority & minority class
n_samples = int(self.n_connecting_keypoints)
from_idx = list(random.sample(list(np.arange(len(self.Xminor))), n_samples))
to_idx = list(random.sample(list(np.arange(len(self.Xmajor))), n_samples))
# optimize to find new db keypoints between minority and majority class
self._linear_decision_boundary_optimization(
from_idx, to_idx, all_combinations=False, step=2
)
if len(self.decision_boundary_points_2d) < 2:
print(
"Failed to find initial decision boundary. Retrying... If this keeps happening, increasing the acceptance threshold might help. Also, make sure the classifier is able to find a point with 0.5 prediction probability (usually requires an even number of estimators/neighbors/etc)."
)
return self.fit(X, y, training_indices)
# step 3. look for decision boundary points between already known db
# points that are too distant (search on connecting line first, then on
# surrounding hypersphere surfaces)
edges, gap_distances, gap_probability_scores = (
self._get_sorted_db_keypoint_distances()
) # find gaps
self.nn_model_decision_boundary_points = NearestNeighbors(n_neighbors=2)
self.nn_model_decision_boundary_points.fit(self.decision_boundary_points)
i = 0
retries = 0
while i < self.n_interpolated_keypoints:
if self.verbose:
print(
"Step 3/{}:{}/".format(self.steps, i, self.n_interpolated_keypoints)
)
if self.random_gap_selection:
# randomly sample from sorted DB keypoint gaps?
gap_idx = np.random.choice(
len(gap_probability_scores), 1, p=gap_probability_scores
)[0]
else:
# get largest gap
gap_idx = 0
from_point = self.decision_boundary_points[edges[gap_idx][0]]
to_point = self.decision_boundary_points[edges[gap_idx][1]]
# optimize to find new db keypoint along line connecting two db keypoints
# with large gap
db_point = self._find_decision_boundary_along_line(
from_point, to_point, penalize_tangent_distance=self.penalties_enabled
)
if self.decision_boundary_distance(db_point) > self.acceptance_threshold:
if self.verbose:
print(
"No good solution along straight line - trying to find decision boundary on hypersphere surface around known decision boundary point"
)
# hypersphere radius half the distance between from and to db keypoints
R = euclidean(from_point, to_point) / 2.0
# search around either source or target keypoint, with 0.5 probability,
# hoping to find decision boundary in between
if random.random() > 0.5:
from_point = to_point
# optimize to find new db keypoint on hypersphere surphase around known keypoint
db_point = self._find_decision_boundary_on_hypersphere(from_point, R)
if (
self.decision_boundary_distance(db_point)
<= self.acceptance_threshold
):
db_point2d = self.dimensionality_reduction.transform([db_point])[0]
self.decision_boundary_points.append(db_point)
self.decision_boundary_points_2d.append(db_point2d)
i += 1
retries = 0
else:
retries += 1
if retries > self.hypersphere_max_retry_budget:
i += 1
dist = self.decision_boundary_distance(db_point)
msg = "Found point is too distant from decision boundary ({}), but retry budget exceeded ({})"
print(msg.format(dist, self.hypersphere_max_retry_budget))
elif self.verbose:
dist = self.decision_boundary_distance(db_point)
print(
"Found point is too distant from decision boundary ({}) retrying...".format(
dist
)
)
else:
db_point2d = self.dimensionality_reduction.transform([db_point])[0]
self.decision_boundary_points.append(db_point)
self.decision_boundary_points_2d.append(db_point2d)
i += 1
retries = 0
edges, gap_distances, gap_probability_scores = (
self._get_sorted_db_keypoint_distances()
) # reload gaps
self.decision_boundary_points = np.array(self.decision_boundary_points)
self.decision_boundary_points_2d = np.array(self.decision_boundary_points_2d)
if self.verbose:
print(
"Done fitting! Found {} decision boundary keypoints.".format(
len(self.decision_boundary_points)
)
)
return self
def plot(
self,
plt=None,
generate_testpoints=True,
generate_background=True,
tune_background_model=False,
background_resolution=100,
scatter_size_scale=1.0,
legend=True,
):
"""Plots the dataset and the identified decision boundary in 2D.
(If you wish to create custom plots, get the data using generate_plot() and plot it manually)
Parameters
----------
plt : matplotlib.pyplot or axis object (default=matplotlib.pyplot)
Object to be plotted on
generate_testpoints : boolean, optional (default=True)
Whether to generate demo points around the estimated decision boundary
as a sanity check
generate_background : boolean, optional (default=True)
Whether to generate faint background plot (using prediction probabilities
of a fitted suppor vector machine, trained on generated demo points)
to aid visualization
tune_background_model : boolean, optional (default=False)
Whether to tune the parameters of the support vector machine generating
the background
background_resolution : int, optional (default=100)
Desired resolution (height and width) of background to be generated
scatter_size_scale : float, optional (default=1.0)
Scaling factor for scatter plot marker size
legend : boolean, optional (default=False)
Whether to display a legend
Returns
-------
plt : The matplotlib.pyplot or axis object which has been passed in, after
plotting the data and decision boundary on it. (plt.show() is NOT called
and will be required)
"""
if plt == None:
plt = mplt
if len(self.X_testpoints) == 0:
self.generate_plot(
generate_testpoints=generate_testpoints,
generate_background=generate_background,
tune_background_model=tune_background_model,
background_resolution=background_resolution,
)
if generate_background and generate_testpoints:
try:
plt.imshow(
np.flipud(self.background),
extent=[self.X2d_xmin, self.X2d_xmax, self.X2d_ymin, self.X2d_ymax],
cmap="GnBu",
alpha=0.33,
)
except (Exception, ex):
print("Failed to render image background")
# decision boundary
plt.scatter(
self.decision_boundary_points_2d[:, 0],
self.decision_boundary_points_2d[:, 1],
600 * scatter_size_scale,
c="c",
marker="p",
)
# generated demo points
if generate_testpoints:
plt.scatter(
self.X_testpoints_2d[:, 0],
self.X_testpoints_2d[:, 1],
20 * scatter_size_scale,
c=["g" if i else "b" for i in self.y_testpoints],
alpha=0.6,
)
# training data
plt.scatter(
self.X2d[self.train_idx, 0],
self.X2d[self.train_idx, 1],
40 * scatter_size_scale,
facecolor=["g" if i else "b" for i in self.y[self.train_idx]],
edgecolor=[
"g"
if self.y_pred[self.train_idx[i]] == self.y[self.train_idx[i]] == 1
else (
"b"
if self.y_pred[self.train_idx[i]] == self.y[self.train_idx[i]] == 0
else "r"
)
for i in range(len(self.train_idx))
],
linewidths=5 * scatter_size_scale,
)
# testing data
plt.scatter(
self.X2d[self.test_idx, 0],
self.X2d[self.test_idx, 1],
150 * scatter_size_scale,
facecolor=["g" if i else "b" for i in self.y[self.test_idx]],
edgecolor=[
"g"
if self.y_pred[self.test_idx[i]] == self.y[self.test_idx[i]] == 1
else (
"b"
if self.y_pred[self.test_idx[i]] == self.y[self.test_idx[i]] == 0
else "r"
)
for i in range(len(self.test_idx))
],
linewidths=5 * scatter_size_scale,
marker="s",
)
# label data points with their indices
for i in range(len(self.X2d)):
plt.text(
self.X2d[i, 0] + (self.X2d_xmax - self.X2d_xmin) * 0.5e-2,
self.X2d[i, 1] + (self.X2d_ymax - self.X2d_ymin) * 0.5e-2,
str(i),
size=8,
)
if legend:
plt.legend(
[
"Estimated decision boundary keypoints",
"Generated demo data around decision boundary",
"Actual data (training set)",
"Actual data (demo set)",
],
loc="lower right",
prop={"size": 9},
)
# decision boundary keypoints, in case not visible in background
plt.scatter(
self.decision_boundary_points_2d[:, 0],
self.decision_boundary_points_2d[:, 1],
600 * scatter_size_scale,
c="c",
marker="p",
alpha=0.1,
)
plt.scatter(
self.decision_boundary_points_2d[:, 0],
self.decision_boundary_points_2d[:, 1],
30 * scatter_size_scale,
c="c",
marker="p",
edgecolor="c",
alpha=0.8,
)
# minimum spanning tree through decision boundary keypoints
D = pdist(self.decision_boundary_points_2d)
edges = minimum_spanning_tree(squareform(D))
for e in edges:
plt.plot(
[
self.decision_boundary_points_2d[e[0], 0],
self.decision_boundary_points_2d[e[1], 0],
],
[
self.decision_boundary_points_2d[e[0], 1],
self.decision_boundary_points_2d[e[1], 1],
],
"--c",
linewidth=4 * scatter_size_scale,
)
plt.plot(
[
self.decision_boundary_points_2d[e[0], 0],
self.decision_boundary_points_2d[e[1], 0],
],
[
self.decision_boundary_points_2d[e[0], 1],
self.decision_boundary_points_2d[e[1], 1],
],
"--k",
linewidth=1,
)
if len(self.test_idx) == 0:
print("No demo performance calculated, as no testing data was specified")
else:
freq = np.array(
np.unique(self.y[self.test_idx], return_counts=True)
).T.astype(float)
imbalance = np.round(
np.max((freq[0, 1], freq[1, 1])) / len(self.test_idx), 3
)
acc_score = np.round(
accuracy_score(self.y[self.test_idx], self.y_pred[self.test_idx]), 3
)
f1 = np.round(
f1_score(self.y[self.test_idx], self.y_pred[self.test_idx]), 3
)
plt.title(
"Test accuracy: "
+ str(acc_score)
+ ", F1 score: "
+ str(f1)
+ ". Imbalance (max chance accuracy): "
+ str(imbalance)
)
if self.verbose:
print(
"Plot successfully generated! Don't forget to call the show() method to display it"
)
return plt
def generate_plot(
self,
generate_testpoints=True,
generate_background=True,
tune_background_model=False,
background_resolution=100,
):
"""Generates and returns arrays for visualizing the dataset and the
identified decision boundary in 2D.
Parameters
----------
generate_testpoints : boolean, optional (default=True)
Whether to generate demo points around the estimated decision boundary
as a sanity check
generate_background : boolean, optional (default=True)
Whether to generate faint background plot (using prediction probabilities
of a fitted suppor vector machine, trained on generated demo points)
to aid visualization
tune_background_model : boolean, optional (default=False)
Whether to tune the parameters of the support vector machine generating
the background
background_resolution : int, optional (default=100)
Desired resolution (height and width) of background to be generated
Returns
-------
decision_boundary_points_2d : array
Array containing points in the dimensionality-reduced 2D space which
are very close to the true decision boundary
X_testpoints_2d : array
Array containing generated demo points in the dimensionality-reduced
2D space which surround the decision boundary and can be used for
visual feedback to estimate which area would be assigned which class
y_testpoints : array
Classifier predictions for each of the generated demo points
background: array
Generated background image showing prediction probabilities of the
classifier in each region (only returned if generate_background is set
to True!)
"""
if len(self.decision_boundary_points) == 0:
raise Exception("Please call the fit method first!")
if not generate_testpoints and generate_background:
print("Warning: cannot generate a background without testpoints")
if len(self.X_testpoints) == 0 and generate_testpoints:
if self.verbose:
print("Generating demo points around decision boundary...")
self._generate_testpoints()
if generate_background and generate_testpoints:
if tune_background_model:
params = {
"C": np.power(10, np.linspace(0, 2, 2)),
"gamma": np.power(10, np.linspace(-2, 0, 2)),
}
grid = GridSearchCV(
SVC(), params, n_jobs=-1 if os.name != "nt" else 1
)
grid.fit(
np.vstack((self.X2d[self.train_idx], self.X_testpoints_2d)),
np.hstack((self.y[self.train_idx], self.y_testpoints)),
)
bestparams = grid.best_params_
else:
bestparams = {"C": 1, "gamma": 1}
self.background_model = SVC(
probability=True, C=bestparams["C"], gamma=bestparams["gamma"]
).fit(
np.vstack((self.X2d[self.train_idx], self.X_testpoints_2d)),
np.hstack((self.y[self.train_idx], self.y_testpoints)),
)
xx, yy = np.meshgrid(
np.linspace(self.X2d_xmin, self.X2d_xmax, background_resolution),
np.linspace(self.X2d_ymin, self.X2d_ymax, background_resolution),
)
Z = self.background_model.predict_proba(np.c_[xx.ravel(), yy.ravel()])[
:, 0
]
Z = Z.reshape((background_resolution, background_resolution))
self.background = Z
if generate_background and generate_testpoints:
return (
self.decision_boundary_points_2d,
self.X_testpoints_2d,
self.y_testpoints,
Z,
)
elif generate_testpoints:
return (
self.decision_boundary_points_2d,
self.X_testpoints_2d,
self.y_testpoints,
)
else:
return self.decision_boundary_points_2d
def _generate_testpoints(self, tries=100):
"""Generate random demo points around decision boundary keypoints
"""
nn_model = NearestNeighbors(n_neighbors=3)
nn_model.fit(self.decision_boundary_points)
nn_model_2d = NearestNeighbors(n_neighbors=2)
nn_model_2d.fit(self.decision_boundary_points_2d)
# max_radius = 2*np.max([nn_model_2d.kneighbors([self.decision_boundary_points_2d[i]])[0][0][1] for i in range(len(self.decision_boundary_points_2d))])
self.X_testpoints = np.zeros((0, self.X.shape[1]))
self.y_testpoints = []
for i in range(len(self.decision_boundary_points)):
if self.verbose:
msg = "Generating testpoint for plotting {}/{}"
print(msg.format(i, len(self.decision_boundary_points)))
testpoints = np.zeros((0, self.X.shape[1]))
# generate Np points in Gaussian around decision_boundary_points[i] with
# radius depending on the distance to the next point
d, idx = nn_model.kneighbors([self.decision_boundary_points[i]])
radius = d[0][1] if d[0][1] != 0 else d[0][2]
if radius == 0:
radius = np.mean(pdist(self.decision_boundary_points_2d))
max_radius = radius * 2
radius /= 5.0
# add demo points, keeping some balance
max_imbalance = 5.0
y_testpoints = []
for j in range(self.n_generated_testpoints_per_keypoint - 2):
c_radius = radius
freq = np.array(np.unique(y_testpoints, return_counts=True)).T.astype(
float
)
imbalanced = freq.shape[0] != 0
if freq.shape[0] == 2 and (
freq[0, 1] / freq[1, 1] < 1.0 / max_imbalance
or freq[0, 1] / freq[1, 1] > max_imbalance
):
imbalanced = True
for try_i in range(tries):
testpoint = np.random.normal(
self.decision_boundary_points[i], radius, (1, self.X.shape[1])
)
try:
testpoint2d = self.dimensionality_reduction.transform(
testpoint
)[0]
except: # DR can fail e.g. if NMF gets negative values
testpoint = []
continue
# demo point needs to be close to current key point
if (
euclidean(testpoint2d, self.decision_boundary_points_2d[i])
<= max_radius
):
if not imbalanced: # needs to be not imbalanced
break
y_pred = self.classifier.predict(testpoint)[0]
# imbalanced but this would actually improve things
if freq.shape[0] == 2 and freq[y_pred, 1] < freq[1 - y_pred, 1]:
break
c_radius /= 2.0
if len(testpoint) != 0:
testpoints = np.vstack((testpoints, testpoint))
y_testpoints.append(self.classifier.predict(testpoint)[0])
self.X_testpoints = np.vstack((self.X_testpoints, testpoints))
self.y_testpoints = np.hstack((self.y_testpoints, y_testpoints))
self.X_testpoints_2d = self.dimensionality_reduction.transform(
self.X_testpoints
)
idx_within_bounds = np.where(
(self.X_testpoints_2d[:, 0] >= self.X2d_xmin)
& (self.X_testpoints_2d[:, 0] <= self.X2d_xmax)
& (self.X_testpoints_2d[:, 1] >= self.X2d_ymin)
& (self.X_testpoints_2d[:, 1] <= self.X2d_ymax)
)[0]
self.X_testpoints = self.X_testpoints[idx_within_bounds]
self.y_testpoints = self.y_testpoints[idx_within_bounds]
self.X_testpoints_2d = self.X_testpoints_2d[idx_within_bounds]
def decision_boundary_distance(self, x, grad=0):
"""Returns the distance of the given point from the decision boundary,
i.e. the distance from the region with maximal uncertainty (0.5
prediction probability)"""
return np.abs(0.5 - self.classifier.predict_proba([x])[0][1])
def get_decision_boundary_keypoints(self):
"""Returns the arrays of located decision boundary keypoints (both in the
original feature space, and in the dimensionality-reduced 2D space)
Returns
-------
decision_boundary_points : array
Array containing points in the original feature space which are very
close to the true decision boundary (closer than acceptance_threshold)
decision_boundary_points_2d : array
Array containing points in the dimensionality-reduced 2D space which
are very close to the true decision boundary
"""
if len(self.decision_boundary_points) == 0:
raise Exception("Please call the fit method first!")
return self.decision_boundary_points, self.decision_boundary_points_2d
def _get_sorted_db_keypoint_distances(self, N=None):
"""Use a minimum spanning tree heuristic to find the N largest gaps in the
line constituted by the current decision boundary keypoints.
"""
if N == None:
N = self.n_interpolated_keypoints
edges = minimum_spanning_tree(
squareform(pdist(self.decision_boundary_points_2d))
)
edged = np.array(
[
euclidean(
self.decision_boundary_points_2d[u],
self.decision_boundary_points_2d[v],
)
for u, v in edges
]
)
gap_edge_idx = np.argsort(edged)[::-1][: int(N)]
edges = edges[gap_edge_idx]
gap_distances = np.square(edged[gap_edge_idx])
gap_probability_scores = gap_distances / np.sum(gap_distances)
return edges, gap_distances, gap_probability_scores
def _linear_decision_boundary_optimization(
self,
from_idx,
to_idx,
all_combinations=True,
retry_neighbor_if_failed=True,
step=None,
suppress_output=False,
):
"""Use global optimization to locate the decision boundary along lines
defined by instances from_idx and to_idx in the dataset (from_idx and to_idx
have to contain indices from distinct classes to guarantee the existence of
a decision boundary between them!)
"""
step_str = (
("Step " + str(step) + "/" + str(self.steps) + ":") if step != None else ""
)
retries = 4 if retry_neighbor_if_failed else 1
for i in range(len(from_idx)):
n = len(to_idx) if all_combinations else 1
for j in range(n):
from_i = from_idx[i]
to_i = to_idx[j] if all_combinations else to_idx[i]
for k in range(retries):
if k == 0:
from_point = self.Xminor[from_i]
to_point = self.Xmajor[to_i]
else:
# first attempt failed, try nearest neighbors of source and destination
# point instead
_, idx = self.nn_model_2d_minorityclass.kneighbors(
[self.Xminor2d[from_i]]
)
from_point = self.Xminor[idx[0][k // 2]]
_, idx = self.nn_model_2d_minorityclass.kneighbors(
[self.Xmajor2d[to_i]]
)
to_point = self.Xmajor[idx[0][k % 2]]
if euclidean(from_point, to_point) == 0:
break # no decision boundary between equivalent points
db_point = self._find_decision_boundary_along_line(
from_point,
to_point,
penalize_tangent_distance=self.penalties_enabled,
penalize_extremes=self.penalties_enabled,
)
if (
self.decision_boundary_distance(db_point)
<= self.acceptance_threshold
):
db_point2d = self.dimensionality_reduction.transform(
[db_point]
)[0]
if (
db_point2d[0] >= self.X2d_xmin
and db_point2d[0] <= self.X2d_xmax
and db_point2d[1] >= self.X2d_ymin
and db_point2d[1] <= self.X2d_ymax
):
self.decision_boundary_points.append(db_point)
self.decision_boundary_points_2d.append(db_point2d)
if self.verbose and not suppress_output:
# , ": New decision boundary keypoint found using linear optimization!"
print(
"{} {}/{}".format(
step_str, i * n + j, len(from_idx) * n
)
)
break
else:
if self.verbose and not suppress_output:
msg = "{} {}/{}: Rejected decision boundary keypoint (outside of plot area)"
print(
msg.format(step_str, i * n + j, len(from_idx) * n)
)
def _find_decision_boundary_along_line(
self,
from_point,
to_point,
penalize_extremes=False,
penalize_tangent_distance=False,
):
def objective(l, grad=0):
# interpolate between source and destionation; calculate distance from
# decision boundary
X = from_point + l[0] * (to_point - from_point)
error = self.decision_boundary_distance(X)
if penalize_tangent_distance:
# distance from tangent between class1 and class0 point in 2d space
x0, y0 = self.dimensionality_reduction.transform([X])[0]
x1, y1 = self.dimensionality_reduction.transform([from_point])[0]
x2, y2 = self.dimensionality_reduction.transform([to_point])[0]
error += (
1e-12
* np.abs((y2 - y1) * x0 - (x2 - x1) * y0 + x2 * y1 - y2 * x1)
/ np.sqrt((y2 - y1) ** 2 + (x2 - x1) ** 2)
)
if penalize_extremes:
error += 1e-8 * np.abs(0.5 - l[0])
return error
optimizer = self._get_optimizer()
optimizer.set_min_objective(objective)
cl = optimizer.optimize([random.random()])
db_point = from_point + cl[0] * (to_point - from_point)
return db_point
def _find_decision_boundary_on_hypersphere(self, centroid, R, penalize_known=False):
def objective(phi, grad=0):
# search on hypersphere surface in polar coordinates - map back to cartesian
cx = centroid + polar_to_cartesian(phi, R)
try:
cx2d = self.dimensionality_reduction.transform([cx])[0]
error = self.decision_boundary_distance(cx)
if penalize_known:
# slight penalty for being too close to already known decision boundary
# keypoints
db_distances = [
euclidean(cx2d, self.decision_boundary_points_2d[k])
for k in range(len(self.decision_boundary_points_2d))
]
error += (
1e-8
* (
(self.mean_2d_dist - np.min(db_distances))
/ self.mean_2d_dist
)
** 2
)
return error
except (Exception, ex):
print("Error in objective function:", ex)
return np.infty
optimizer = self._get_optimizer(
D=self.X.shape[1] - 1,
upper_bound=2 * np.pi,
iteration_budget=self.hypersphere_iteration_budget,
)
optimizer.set_min_objective(objective)
db_phi = optimizer.optimize(
[random.random() * 2 * np.pi for k in range(self.X.shape[1] - 1)]
)
db_point = centroid + polar_to_cartesian(db_phi, R)
return db_point
def _get_optimizer(self, D=1, upper_bound=1, iteration_budget=None):
"""Utility function creating an NLOPT optimizer with default
parameters depending on this objects parameters
"""
if iteration_budget == None:
iteration_budget = self.linear_iteration_budget
opt = nlopt.opt(nlopt.GN_DIRECT_L_RAND, D)
# opt.set_stopval(self.acceptance_threshold/10.0)
opt.set_ftol_rel(1e-5)
opt.set_maxeval(iteration_budget)
opt.set_lower_bounds(0)
opt.set_upper_bounds(upper_bound)
return opt
