def create_dic():
all_names = open((FILE_ADDRESSES + 'all_names.txt'), 'a')
# clear the file if it is has values from previous tests
all_names.truncate()
# for each year read names and write them to a file
for num in range(2000, 2013):
file_name = FILE_ADDRESSES + 'Popular Baby Names ' + str(num) + '.htm'
text = read_file(file_name, 'rU')
# no number and a word: name
names = re.findall('<td>[^\d*]\w*</td>', text)
# just a number: rank
ranks = re.findall('<td>\d*</td>', text)
# create a dictionary object from values
names_with_ranks = {}
# there are both girls and boys names in one file, so for every two name we increase the rank number
i = 0
for index in range(len(names)):
names_with_ranks[re.search('[^<td>]\w+',
names[index]).group()] = re.search(
'[^<td>]\d*', ranks[i]).group()
if (index % 2 == 1):
i += 1
fill_dic(names_with_ranks, all_names)
all_names.close()
def part_1():
data = read_file('takens_1.txt')
time = np.arange(0, data.shape[0], 1)
x0 = data[:, 0]
# Plotting the data
fig, ax = plt.subplots(1, 1)
ax.plot(x0, data[:, 1], c='dodgerblue', linewidth=0.5)
ax.set_xlabel('$x$')
ax.set_ylabel('$y$')
plt.show()
# Plotting the first coordinate against the line number in the dataset (the “time”)
fig, ax = plt.subplots(1, 1)
ax.plot(time, x0, c='dodgerblue', linewidth=0.5)
ax.set_xlabel('time')
ax.set_ylabel('$x$')
plt.show()
# Plotting the coordinate against its delayed version , 2 dimensional
n_delay = 50
#delayed = np.hstack((x0[-n_delay:], x0[:data.shape[0]-n_delay]))
x = x0[:x0.shape[0] - n_delay]
delayed = x0[n_delay:]
fig, ax = plt.subplots(1, 1)
ax.plot(x, delayed, c='dodgerblue', linewidth=0.5) # x0
ax.set_xlabel('$x(t)$')
ax.set_ylabel('$x(t+ \Delta n)$')
ax.set_title('$\Delta n = {}$'.format(n_delay))
plt.show()
# Plotting the coordinate against its delayed version , 3 dimensional
n_delay_2 = 2 * n_delay
x_2 = x0[:x0.shape[0] - n_delay_2]
delayed_1 = x0[n_delay:x0.shape[0] - n_delay]
delayed_2 = x0[n_delay_2:]
fig = plt.figure()
ax0 = fig.gca(projection='3d')
ax0.plot(x_2,
delayed_1,
delayed_2,
c='dodgerblue',
linestyle=':',
antialiased=True)
ax0.set_xlabel('$x(t)$')
ax0.set_ylabel('$x(t+ \Delta n)$')
ax0.set_zlabel('$x(t+ 2 \Delta n)$')
ax0.set_title('$\Delta n = {}$'.format(n_delay))
plt.show()
def count_names(name):
text = read_file(FILE_ADDRESSES + 'all_names.txt', 'rU')
ranks = []
m = re.findall('(' + name + ')\t(\d+)', text, re.IGNORECASE)
# print m
for name in m:
ranks.append(name[1])
# print ranks
names_with_count = (str(len(m)), ranks)
# counted_names.append(name)
return names_with_count
def main():
## Part 1
N = 1000
L = 5
X, tk = generate_points(N)
plot_generated_points(X)
tk = np.array(tk)
S, lambda_l = diffusion_map_algorithm(X, L)
plot_5_eigenfunctions(tk, S)
## Part 2
N = 1000
L = 10
X, t = make_swiss_roll(N, noise=0.0, random_state=None)
plot_swiss_roll(X,t)
S, lambda_l = diffusion_map_algorithm(X,L)
plot_eigenfunctions(S,t)
# PCA
X = X - X.mean(axis=0, keepdims=True)
U, sigma, V = np.linalg.svd(X, 0)
S = np.diag(sigma)
trace = S.trace()
print("Sigma values of Swiss Roll: ", sigma)
# Reconstruction with 3 principal components
energy_3 = 0
S_3 = np.zeros(S.shape)
for i in range(3):
S_3[i][i] = sigma[i]
energy_3 += sigma[i] / trace
reconstructed_3 = np.dot(U, np.dot(S_3, V))
# Reconstruction with 2 principal components
energy_2 = 0
S_2 = np.zeros(S.shape)
for i in range(2):
S_2[i][i] = sigma[i]
energy_2 += sigma[i] / trace
reconstructed_2 = np.dot(U, np.dot(S_2, V))
fig = plt.figure()
ax1 = fig.gca(projection='3d')
ax1.scatter(reconstructed_3[:, 0], reconstructed_3[:, 1], reconstructed_3[:, 2], c=t, cmap="Spectral", s=2)
ax1.set_title("Swiss Roll \n Reconstructed with 3 principal components \n Energy: {:.2f}%".format(energy_3 * 100))
ax1.set_xlabel('x')
ax1.set_ylabel('y')
ax1.set_zlabel('z')
plt.tight_layout()
plt.show()
fig = plt.figure()
ax2 = fig.gca(projection='3d')
ax2.scatter(reconstructed_2[:, 0], reconstructed_2[:, 1], reconstructed_2[:, 2], c=t, cmap="Spectral", s=2)
ax2.set_title("Swiss Roll \n Reconstructed with 2 principal components \n Energy: {:.2f}%".format(energy_2 * 100))
ax2.set_xlabel('x')
ax2.set_ylabel('y')
ax2.set_zlabel('z')
plt.tight_layout()
plt.show()
bonus()
## Part 3
X = read_file('data_DMAP_PCA_vadere.txt')
L = 10
time = np.arange(X.shape[0])
s, lambda_l = diffusion_map_algorithm(X, L)
plot_eigenfunctions(s,time)
# plotting lambda values
plt.plot(lambda_l, 'o')
plt.show()
plot_5_eigenfunctions(time, s)
def part_1():
# Read data
X = read_file('pca_dataset.txt')
# Find center of data set
mean_d1, mean_d2 = X.mean(0)
mean = X.mean(axis=0, keepdims=True)
X_centered = X - mean
mean_centered_d1, mean_centered_d2 = X_centered.mean(0)
# Make PCA analysis via SVD
U, sigma, VT = np.linalg.svd(X_centered, 0)
V = VT.T
S = np.diag(sigma)
trace = S.trace()
S_one_dimension = np.zeros(S.shape)
S_one_dimension[0][0] = S[0][0]
X_one_dimension = U.dot(S_one_dimension).dot(VT)
MSE_one = (X_centered - X_one_dimension)**2
MSE_one = np.sum(MSE_one)
print("MSE One Dimension: {:.4f}".format(MSE_one**2))
# Approximates one-dimensional linear subspace
X_1D = U.dot(S).dot(VT[0])
print("X 1D: " + str(X_1D))
fig = plt.figure(figsize=(6, 3))
ax = fig.add_subplot(1, 1, 1)
ax.set_title('1-Dimensional Projection')
ax.scatter(X_1D,
np.zeros(X_1D.shape),
label='Projected Data',
c="red",
s=3)
plt.xlabel("z")
plt.legend(loc='upper left')
plt.tight_layout()
plt.show()
print("X_head: " + str(X_one_dimension))
print("U: " + str(U))
print("V: " + str(V))
print("Sigma: " + str(S))
print("Trace: " + str(trace))
print("Energy of " + str(sigma[0]) + ": " + str(sigma[0] / trace))
print("Energy of " + str(sigma[1]) + ": " + str(sigma[1] / trace))
# Plot data set
fig = plt.figure(figsize=(7, 7))
ax = fig.add_subplot(1, 1, 1)
ax.set_title('PCA')
ax.scatter(X[:, 0], X[:, 1], label='Data', c="mediumseagreen", s=3)
ax.scatter(X_centered[:, 0],
X_centered[:, 1],
label='Centered Data',
c="lightskyblue",
s=3)
ax.scatter(X_one_dimension[:, 0],
X_one_dimension[:, 1],
label='Projected Data',
c="red",
s=1)
plt.xlabel("x")
plt.ylabel("f(x)")
plt.grid(True)
plt.legend(loc='upper left')
# Mark the center of data set
ax.plot(mean_d1,
mean_d2,
'o',
markersize=5,
color='olivedrab',
label='Center of data')
ax.plot(mean_centered_d1,
mean_centered_d2,
'o',
markersize=5,
color='darkblue',
label='Center of centralized data')
# Draw the direction of two principal components
plt.arrow(mean_d1,
mean_d2,
V[0, 0],
V[1, 0],
width=0.01,
color='darkred',
alpha=0.5)
plt.arrow(mean_d1,
mean_d2,
V[0, 1],
V[1, 1],
width=0.01,
color='darkblue',
alpha=0.5)
# Show eigenvalues of Sigma
plt.text(V[0, 0] - 0.6,
V[1, 0] + 0.1,
"{:.4f}".format(sigma[0]),
fontsize=12,
color='darkred')
plt.text(V[0, 1],
V[1, 1] - 0.1,
"{:.4f}".format(sigma[1]),
fontsize=12,
color='darkblue')
plt.show()
def part_3():
# Read data
X = read_file('data_DMAP_PCA_vadere.txt')
# Visualize the path of the first two pedestrians in the two-dimensional space.
fig = plt.figure(figsize=(10, 7))
ax = fig.add_subplot()
ax.set_title('Pedestrian Paths')
ax.plot(X[:, 0],
X[:, 1],
color='dodgerblue',
linewidth=0.5,
label='First Pedestrian')
ax.scatter(X[0, 0],
X[0, 1],
c='lightskyblue',
s=5,
label='Starting Point of the First Pedestrian')
ax.scatter(X[-1, 0],
X[-1, 1],
c='darkblue',
s=5,
label='Ending Point of the First Pedestrian')
ax.plot(X[:, 2],
X[:, 3],
color='firebrick',
linewidth=0.5,
label='Second Pedestrian')
ax.scatter(X[0, 2],
X[0, 3],
c='lightcoral',
s=5,
label='Starting Point of the Second Pedestrian')
ax.scatter(X[-1, 2],
X[-1, 3],
c='darkred',
s=5,
label='Ending Point of the Second Pedestrian')
plt.xlabel("x")
plt.ylabel("y")
plt.legend(loc='upper right')
plt.show()
# Make PCA analysis via SVD
U, sigma, V = np.linalg.svd(X, 0)
S = np.diag(sigma)
trace = S.trace()
# Reconstruction with 2 principal components
energy_2 = 0
S_2 = np.zeros(S.shape)
for i in range(2):
S_2[i][i] = sigma[i]
energy_2 += sigma[i] / trace
reconstructed_2 = np.dot(U, np.dot(S_2, V))
# Reconstruction with 3 principal components
energy_3 = 0
S_3 = np.zeros(S.shape)
for i in range(3):
S_3[i][i] = sigma[i]
energy_3 += sigma[i] / trace
reconstructed_3 = np.dot(U, np.dot(S_3, V))
# Reconstruction with 4 principal components
energy_4 = 0
S_4 = np.zeros(S.shape)
for i in range(4):
S_4[i][i] = sigma[i]
energy_4 += sigma[i] / trace
reconstructed_4 = np.dot(U, np.dot(S_4, V))
# Reconstruction with 5 principal components
energy_5 = 0
S_5 = np.zeros(S.shape)
for i in range(5):
S_5[i][i] = sigma[i]
energy_5 += sigma[i] / trace
reconstructed_5 = np.dot(U, np.dot(S_5, V))
fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2, 2, figsize=(10, 10))
ax1.plot(reconstructed_2[:, 0],
reconstructed_2[:, 1],
color='dodgerblue',
linewidth=0.5,
label='First Pedestrian')
ax1.plot(reconstructed_2[:, 2],
reconstructed_2[:, 3],
color='firebrick',
linewidth=0.5,
label='Second Pedestrian')
ax1.set_title(
"Reconstructed with 2 principal components \n Energy: {:.2f}%".format(
energy_2 * 100))
ax1.legend(loc="upper right")
ax2.plot(reconstructed_3[:, 0],
reconstructed_3[:, 1],
color='dodgerblue',
linewidth=0.5,
label='First Pedestrian')
ax2.plot(reconstructed_3[:, 2],
reconstructed_3[:, 3],
color='firebrick',
linewidth=0.5,
label='Second Pedestrian')
ax2.set_title(
"Reconstructed with 3 principal components\n Energy: {:.2f}%".format(
energy_3 * 100))
ax2.legend(loc="upper right")
ax3.plot(reconstructed_4[:, 0],
reconstructed_4[:, 1],
color='dodgerblue',
linewidth=0.5,
label='First Pedestrian')
ax3.plot(reconstructed_4[:, 2],
reconstructed_4[:, 3],
color='firebrick',
linewidth=0.5,
label='Second Pedestrian')
ax3.set_title(
"Reconstructed with 4 principal components \n Energy: {:.2f}%".format(
energy_4 * 100))
ax3.legend(loc="upper right")
ax4.plot(reconstructed_5[:, 0],
reconstructed_5[:, 1],
color='dodgerblue',
linewidth=0.5,
label='First Pedestrian')
ax4.plot(reconstructed_5[:, 2],
reconstructed_5[:, 3],
color='firebrick',
linewidth=0.5,
label='Second Pedestrian')
ax4.set_title(
"Reconstructed with 5 principal components \n Energy: {:.2f}%".format(
energy_5 * 100))
ax4.legend(loc="upper right")
fig.text(0.5, 0.01, 'x', ha='center')
fig.text(0.01, 0.5, 'y', va='center', rotation='vertical')
plt.tight_layout()
plt.savefig('part_3_reconstructed_paths.png')
plt.show()