def compare(self, dist_1, dist_2):
dist_1_interval = TimeInterval(*self.bounds_of(dist_1))
dist_2_interval = TimeInterval(*self.bounds_of(dist_2))
dictionary_input_output = {}
for time_step in dist_1_interval + dist_2_interval:
dictionary_input_output[time_step] = sqrt(
dist_1.pdf(time_step) * dist_2.pdf(time_step))
geometric_mean = FunctionPiecewiseLinear(
dictionary_input_output, function_undefined=FUNCTION_ZERO)
same = integral(geometric_mean, NEGATIVE_INFINITY, POSITIVE_INFINITY)
dist_1_mean, dist_1_skewness, dist_1_kurtosis = dist_1.stats(
moments='msk')
dist_1_standard_deviation = dist_1.std()
dist_2_mean, dist_2_skewness, dist_2_kurtosis = dist_2.stats(
moments='msk')
dist_2_standard_deviation = dist_2.std()
distance = fabs(dist_1_standard_deviation -
dist_2_standard_deviation) + fabs(dist_1_skewness -
dist_2_skewness)
distance += fabs(dist_1_kurtosis - dist_2_kurtosis)
delta = dist_1_mean - dist_2_mean
non_same_portion = 1.0 - same
portion_after, portion_before = 1.0, 0.0
if almost_equals(distance, 0):
if delta < 0:
portion_after, portion_before = 0.0, 1.0
else:
dist_1_standardized_pdf = lambda x: dist_1.pdf(
dist_1_standard_deviation * x + dist_1_mean)
dist_2_standardized_pdf = lambda x: dist_2.pdf(
dist_2_standard_deviation * x + dist_2_mean)
geometric_mean = lambda t: sqrt(
dist_1_standardized_pdf(t) * dist_2_standardized_pdf(t))
geometric_mean_scaled = lambda p: geometric_mean(p / distance)
geometric_mean_scaled_length = max(self.duration_of(dist_1),
self.duration_of(dist_2))
dictionary_input_output = {}
for time_step in TimeInterval(-geometric_mean_scaled_length / 2.0,
geometric_mean_scaled_length / 2.0):
dictionary_input_output[time_step] = geometric_mean_scaled(
time_step)
geometric_mean_scaled = FunctionPiecewiseLinear(
dictionary_input_output, function_undefined=FUNCTION_ZERO)
portion_after = integral(geometric_mean_scaled, NEGATIVE_INFINITY,
delta)
portion_before = integral(geometric_mean_scaled, delta,
POSITIVE_INFINITY)
after = portion_after / (portion_after +
portion_before) * non_same_portion
return 1.0 - same - after, same, after
def compare(self, dist_1, dist_2):
convolution = self.function_convolution(dist_1, dist_2)
before = integral(convolution, NEGATIVE_INFINITY, 0)
after = integral(convolution, 0, POSITIVE_INFINITY)
similarity = self.calculate_similarity(dist_1, dist_2)
correlation = 1 - fabs(before - after)
same = similarity * correlation
return before, same, after
def compare(self, dist_1, dist_2):
convolution = self.function_convolution(dist_1, dist_2)
before = integral(convolution, NEGATIVE_INFINITY, 0)
after = integral(convolution, 0, POSITIVE_INFINITY)
similarity = self.calculate_similarity(dist_1, dist_2)
correlation = 1 - fabs(before - after)
same = similarity * correlation
return before, same, after
def compare(self, dist_1, dist_2):
dist_1_interval = TimeInterval(*self.bounds_of(dist_1))
dist_2_interval = TimeInterval(*self.bounds_of(dist_2))
dictionary_input_output = {}
for time_step in dist_1_interval + dist_2_interval:
dictionary_input_output[time_step] = sqrt(dist_1.pdf(time_step) * dist_2.pdf(time_step))
geometric_mean = FunctionPiecewiseLinear(dictionary_input_output, function_undefined=FUNCTION_ZERO)
same = integral(geometric_mean, NEGATIVE_INFINITY, POSITIVE_INFINITY)
dist_1_mean, dist_1_skewness, dist_1_kurtosis = dist_1.stats(moments='msk')
dist_1_standard_deviation = dist_1.std()
dist_2_mean, dist_2_skewness, dist_2_kurtosis = dist_2.stats(moments='msk')
dist_2_standard_deviation = dist_2.std()
distance = fabs(dist_1_standard_deviation - dist_2_standard_deviation) + fabs(dist_1_skewness - dist_2_skewness)
distance += fabs(dist_1_kurtosis - dist_2_kurtosis)
delta = dist_1_mean - dist_2_mean
non_same_portion = 1.0 - same
portion_after, portion_before = 1.0, 0.0
if almost_equals(distance, 0):
if delta < 0:
portion_after, portion_before = 0.0, 1.0
else:
dist_1_standardized_pdf = lambda x: dist_1.pdf(dist_1_standard_deviation * x + dist_1_mean)
dist_2_standardized_pdf = lambda x: dist_2.pdf(dist_2_standard_deviation * x + dist_2_mean)
geometric_mean = lambda t: sqrt(dist_1_standardized_pdf(t) * dist_2_standardized_pdf(t))
geometric_mean_scaled = lambda p: geometric_mean(p / distance)
geometric_mean_scaled_length = max(self.duration_of(dist_1), self.duration_of(dist_2))
dictionary_input_output = {}
for time_step in TimeInterval(-geometric_mean_scaled_length / 2.0, geometric_mean_scaled_length / 2.0):
dictionary_input_output[time_step] = geometric_mean_scaled(time_step)
geometric_mean_scaled = FunctionPiecewiseLinear(dictionary_input_output, function_undefined=FUNCTION_ZERO)
portion_after = integral(geometric_mean_scaled, NEGATIVE_INFINITY, delta)
portion_before = integral(geometric_mean_scaled, delta, POSITIVE_INFINITY)
after = portion_after / (portion_after + portion_before) * non_same_portion
return 1.0 - same - after, same, after
def calculate_similarity(self, dist_1, dist_2):
if (type(dist_1.dist), type(dist_2.dist)) == (uniform_gen, uniform_gen):
length_dist_1 = self.duration_of(dist_1)
length_dist_2 = self.duration_of(dist_2)
return min(length_dist_1, length_dist_2) / sqrt(length_dist_1 * length_dist_2)
dist_1_mean, dist_2_mean = dist_1.mean(), dist_2.mean()
dist_1_transformed = lambda t: dist_1.pdf(t + dist_1_mean)
dist_2_transformed = lambda t: dist_2.pdf(t + dist_2_mean)
geometric_mean = lambda t: sqrt(dist_1_transformed(t) * dist_2_transformed(t))
return integral(geometric_mean, NEGATIVE_INFINITY, POSITIVE_INFINITY)
def degree(self, time_step=None, a=None, b=None, interval=None):
"""
usage: provide 'time_step' or 'a' and 'b' or 'interval'
"""
if time_step is not None:
return self.membership_function(time_step)
if interval is None:
if (a, b) == (None, None):
interval = self
else:
interval = TimeInterval(a, b)
else:
check_is_time_interval(interval)
return integral(self.membership_function, interval.a, interval.b)
def calculate_similarity(self, dist_1, dist_2):
if (type(dist_1.dist), type(dist_2.dist)) == (uniform_gen,
uniform_gen):
length_dist_1 = self.duration_of(dist_1)
length_dist_2 = self.duration_of(dist_2)
return min(length_dist_1, length_dist_2) / sqrt(
length_dist_1 * length_dist_2)
dist_1_mean, dist_2_mean = dist_1.mean(), dist_2.mean()
dist_1_transformed = lambda t: dist_1.pdf(t + dist_1_mean)
dist_2_transformed = lambda t: dist_2.pdf(t + dist_2_mean)
geometric_mean = lambda t: sqrt(
dist_1_transformed(t) * dist_2_transformed(t))
return integral(geometric_mean, NEGATIVE_INFINITY, POSITIVE_INFINITY)
def after(self, dist_1, dist_2):
return integral(lambda x: self.after_point(dist_1.pdf(x), dist_2.pdf(x)),
*self.after_integral_bounds(dist_1, dist_2))
def same(self, dist_1, dist_2):
return integral(lambda x: self.same_point(dist_1.pdf(x), dist_2.pdf(x)),
*self.same_integral_bounds(dist_1, dist_2))
def after(self, dist_1, dist_2):
return integral(
lambda x: self.after_point(dist_1.pdf(x), dist_2.pdf(x)),
*self.after_integral_bounds(dist_1, dist_2))
def same(self, dist_1, dist_2):
return integral(
lambda x: self.same_point(dist_1.pdf(x), dist_2.pdf(x)),
*self.same_integral_bounds(dist_1, dist_2))
if __name__ == '__main__':
from utility.functions import integral
from scipy.stats import norm
import matplotlib.pyplot as plt
#event = TemporalInstance(datetime(2010, 1, 1), datetime(2011, 2, 1))
#plt = event.plot()
#plt.show()
events = [
# TemporalEvent(norm(loc=10, scale=2), norm(loc=30, scale=2), 100),
# TemporalEvent(norm(loc=5, scale=2), norm(loc=15, scale=4), 100),
TemporalEventPiecewiseLinear({1: 0, 2: 0.1, 3: 0.3, 4: 0.7, 5: 1}, {6: 1, 7: 0.9, 8: 0.6, 9: 0.1, 10: 0}),
TemporalEventPiecewiseLinear({1: 0, 2: 0.1, 3: 0.3, 4: 0.7, 5: 1}, {3.5: 1, 4.5: 0.9, 8: 0.6, 9: 0.1, 10: 0})
]
print type(events[0])
print events[0] * events[1]
for event in events:
plt = event.plot()
print integral(event.distribution_beginning.pdf, event.a, event.beginning)
print event.distribution_beginning.rvs(10)
plt.ylim(ymax=1.1)
#plt.figure()
plt.show()