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Experiments_Ratio.py
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Experiments_Ratio.py
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import numpy as np
import random
import matplotlib.pyplot as plt
from Solvers.Solvers_Interface import RegressionProblem_LeastSquare
from Solvers.Solvers_Interface import RegressionProblem_Huber
number_of_iterations = 1000000
# Maximum degree of regression polynomial.
for n in [1,2,3]:
# Points along a polynomial with a different amount of outliers (1st experiment).
# Random polynomial of given maximum degree.
coefficients = []
for i in range(n+1):
coefficients.append(random.random())
def Polynomial(x,coefficients):
y = 0
for i in range(len(coefficients)):
y += coefficients[i]*x**i
return y
# Different levels of noise.
for noise_percentage in [0.01,0.03,0.1]:
# Making the data points.
X_points = np.linspace(0, 5, 11)
X = np.linspace(np.min(X_points), np.max(X_points), 1000)
Y_points_initial = np.array(Polynomial(X_points, coefficients))
# Adding noise.
noise = np.random.normal(0, noise_percentage, len(Y_points_initial))
Y_points_noisy = Y_points_initial + noise
# Different amount of outliers and plotting the points.
for number_of_outliers in [0,1,2]:
fig = plt.figure(figsize=(10, 6))
plt.rc('text', usetex=True)
Y_points = Y_points_initial.copy()
if (number_of_outliers==0):
# "Removing" the outlier for one data set.
X_points_without_outliers = X_points
Y_points_without_outliers = Y_points
if (number_of_outliers==1):
# Adding an outlier.
random_index_1 = random.randint(0, len(X_points)-1)
Y_points[random_index_1] *= 3
# Removing the outlier for one data set.
X_points_without_outliers = np.delete(X_points, random_index_1)
Y_points_without_outliers = np.delete(Y_points, random_index_1)
if (number_of_outliers==2):
# Adding 2 outliers
random_index_1 = random.randint(0, len(X_points)-1)
Y_points[random_index_1] *= 3
random_index_2 = random.randint(0, len(X_points)-1)
while random_index_2 == random_index_1:
random_index_2 = random.randint(0, len(X_points)-1)
Y_points[random_index_2] *= 3
# Removing the outliers for one data set.
X_points_without_outliers = np.delete(X_points, [random_index_1, random_index_2])
Y_points_without_outliers = np.delete(Y_points, [random_index_1, random_index_2])
# Making the table.
data = []
# Solving with Least Squares and removed outliers.
data_temp = np.zeros(n+1)
for i in range(number_of_iterations):
RP = RegressionProblem_LeastSquare(X_points_without_outliers,Y_points_without_outliers)
RegressionPolynomial, RegressionCoefficients = RP.solve(n,1000)
data_temp += np.abs(coefficients/RegressionCoefficients)
data_temp = data_temp/number_of_iterations
data.append(["Least Squares (rem. out.)", [round(x, 2) for x in data_temp]])
# Solving with Huber and different gammas.
for gamma in [0.5, 1.0, 2.0]:
data_temp = np.zeros(n+1)
for i in range(number_of_iterations):
RP = RegressionProblem_Huber(X_points,Y_points)
RegressionPolynomial, RegressionCoefficients = RP.solve(n,1000,gamma)
data_temp += np.abs(coefficients/RegressionCoefficients)
data_temp = data_temp/number_of_iterations
data.append([r'Huber ($\gamma$ = %1.1f)' % gamma, [round(x, 2) for x in data_temp]])
# Solving with Least Squares.
data_temp = np.zeros(n+1)
for i in range(number_of_iterations):
RP = RegressionProblem_LeastSquare(X_points,Y_points)
RegressionPolynomial, RegressionCoefficients = RP.solve(n,1000)
data_temp += np.abs(coefficients/RegressionCoefficients)
data_temp = data_temp/number_of_iterations
data.append(["Least Squares (stand.)", [round(x, 2) for x in data_temp]])
# Setting options for the table.
table = plt.table(cellText=data, colLabels=["Method", "InitialCoefficients/NumericalCoefficients"], loc='center')
table.scale(2, 3.86)
table.auto_set_font_size(False)
table.set_fontsize(22)
table.auto_set_column_width([0, 1])
plt.axis('off')
# Setting options for the figure and saving it.
plt.tight_layout()
plt.savefig("InitialCoefficients_ratio_NumericalCoefficients_n=%i,outliers:%s,noise_percentage=%f" % (n, number_of_outliers, noise_percentage) + ".png", bbox_inches='tight')
plt.close(fig)