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Experiments_GraphicalRepresentation.py
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Experiments_GraphicalRepresentation.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
# 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=(6, 6))
ax1 = fig.add_subplot(111)
fig_table = plt.figure(figsize=(15, 5))
ax2 = fig_table.add_subplot(111)
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
# Plotting the points.
ax1.plot(X_points, Y_points, marker='o', markersize=5, color='gray', linestyle='None', label="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)
# Plotting the points.
ax1.plot(X_points, Y_points, marker='o', markersize=5, color='gray', linestyle='None', label="points")
ax1.plot([X_points[random_index_1]], [Y_points[random_index_1]], marker='o', markersize=10, color='magenta', linestyle='None', label="outliers")
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])
# Plotting the points
ax1.plot(X_points, Y_points, marker='o', markersize=5, color='gray', linestyle='None', label="points")
ax1.plot([X_points[random_index_1], X_points[random_index_2]], [Y_points[random_index_1], Y_points[random_index_2]], marker='o', markersize=10, color='magenta', linestyle='None', label="outliers")
# Making the table.
data = []
data.append(["Initial", [round(x, 2) for x in coefficients]])
# Solving with Least Squares and removed outliers.
RP = RegressionProblem_LeastSquare(X_points_without_outliers,Y_points_without_outliers)
RegressionPolynomial, RegressionCoefficients = RP.solve(n,1000)
data.append(["Least Squares (rem. out.)", [round(x, 2) for x in RegressionCoefficients]])
Y = RegressionPolynomial(X)
ax1.plot(X,Y, label="Least Squares (rem. out.)")
# Solving with Huber and different gammas.
for gamma in [2,1,0.5]:
RP = RegressionProblem_Huber(X_points,Y_points)
RegressionPolynomial, RegressionCoefficients = RP.solve(n,1000,gamma)
data.append([r'Huber ($\gamma$ = %1.1f)' % gamma, [round(x, 2) for x in RegressionCoefficients]])
Y = RegressionPolynomial(X)
ax1.plot(X, Y, label=r'Huber ($\gamma$ = %1.1f)' % gamma)
# Solving with Least Squares.
RP = RegressionProblem_LeastSquare(X_points,Y_points)
RegressionPolynomial, RegressionCoefficients = RP.solve(n,1000)
data.append(["Least Squares (stand.)", [round(x, 2) for x in RegressionCoefficients]])
Y = RegressionPolynomial(X)
ax1.plot(X,Y, label="Least Squares (stand.)")
# Setting options for the table.
ax2.axis('off')
table = ax2.table(cellText=data, colLabels=['Label', 'Coefficients'], loc='center')
plt.tight_layout()
# Setting options for the graph.
ax1.set_xlabel('x', fontsize=25)
ax1.set_ylabel('RegressionPolynomial(x)', fontsize=25)
ax1.tick_params(axis='x', labelsize=20)
ax1.tick_params(axis='y', labelsize=20)
ax1.yaxis.set_label_coords(-0.135, 0.5)
ax1.grid(True)
# Setting options for the figure and saving it.
plt.tight_layout()
table_filename = "n=%i,outliers:%s,noise_percentage=%f" % (n, number_of_outliers, noise_percentage) + "_table.png"
graph_filename = "n=%i,outliers:%s,noise_percentage=%f" % (n, number_of_outliers, noise_percentage) + "_graph.png"
fig.savefig(graph_filename, bbox_inches='tight')
fig_table.savefig(table_filename, bbox_inches='tight')
# Closing the figures to free memory.
plt.close(fig)
plt.close(fig_table)
# Making random points and plotting them (2nd experiment)
fig = plt.figure(figsize=(6, 6))
ax1 = fig.add_subplot(111)
fig_table = plt.figure(figsize=(15, 5))
ax2 = fig_table.add_subplot(111)
plt.rc('text', usetex=True)
for i in range(len(X_points)):
Y_points[i] = random.uniform(0, 5)
ax1.plot(X_points, Y_points, marker='o', markersize=5, color='gray', linestyle='None', label="points")
# Making the table.
data = []
# Solving with Huber and different gammas.
for gamma in [0.5, 1.0, 2.0]:
RP = RegressionProblem_Huber(X_points,Y_points)
RegressionPolynomial, RegressionCoefficients = RP.solve(n,1000,gamma)
data.append([r'Huber ($\gamma$ = %1.1f)' % gamma, [round(x, 2) for x in RegressionCoefficients]])
Y = RegressionPolynomial(X)
ax1.plot(X, Y, label=r'Huber ($\gamma$ = %1.1f)' % gamma)
# Solving with Least Squares.
RP = RegressionProblem_LeastSquare(X_points,Y_points)
RegressionPolynomial, RegressionCoefficients = RP.solve(n,1000)
data.append(["Least Squares (stand.)", [round(x, 2) for x in RegressionCoefficients]])
Y = RegressionPolynomial(X)
ax1.plot(X,Y, label="Least Squares (stand.)")
# Setting options for the table.
ax2.axis('off')
table = ax2.table(cellText=data, colLabels=['Label', 'Coefficients'], loc='center')
plt.tight_layout()
# Setting options for the graph.
ax1.set_xlabel('x', fontsize=25)
ax1.set_ylabel('RegressionPolynomial(x)', fontsize=25)
ax1.tick_params(axis='x', labelsize=20)
ax1.tick_params(axis='y', labelsize=20)
ax1.yaxis.set_label_coords(-0.135, 0.5)
ax1.grid(True)
# Setting options for the figure and saving it.
plt.tight_layout()
table_filename = "random,n=%i" % n + "_table.png"
graph_filename = "random,n=%i" % n + "_graph.png"
fig.savefig(graph_filename, bbox_inches='tight')
fig_table.savefig(table_filename, bbox_inches='tight')
# Closing the figures to free memory.
plt.close(fig)
plt.close(fig_table)