def test_PCA_for_Visualization(self):
plt.close()
# Re-load the image from the previous exercise and run K-Means on it
# For this to work, you need to complete the K-Means assignment first
# A = double(imread('bird_small.png'));
# If imread does not work for you, you can try instead
mat = scipy.io.loadmat('resource/bird_small.mat')
A = mat["A"]
A = A / 255
image_size = np.shape(A)
X = A.reshape(image_size[0] * image_size[1], 3)
K = 16
max_iters = 10
from ex7_K_means_Clustering_and_Principal_Component_Analysis.kMeansInitCentroids import kMeansInitCentroids
initial_centroids = kMeansInitCentroids(X, K)
from ex7_K_means_Clustering_and_Principal_Component_Analysis.runkMeans import runkMeans
centorids, idx = runkMeans(X, initial_centroids, max_iters, True)
# Sample 1000 random indexes(since working with all the data is
# too expensive.If you have a fast computer, you may increase this.
sel = np.floor(np.random.rand(1000, 1) *
X.shape[0]).astype(int).flatten()
# Setup Color Palette
from utils.hsv import hsv
palette = hsv(K)
colors = np.array([palette[int(i)] for i in idx[sel]])
# fig = plt.figure()
# ax = fig.add_subplot(111, projection='3d')
# ax.scatter(X[sel, 0], X[sel, 1], X[sel, 2], s=100, c=colors)
# plt.title('Pixel dataset plotted in 3D. Color shows centroid memberships')
# plt.show(block=False)
# === Part 8(b): Optional (ungraded) Exercise: PCA for Visualization ===
# Use PCA to project this cloud to 2D for visualization
from ex5_regularized_linear_regressionand_bias_vs_variance.featureNormalize import featureNormalize
# Subtract the mean to use PCA
X_norm, _, _ = featureNormalize(X)
# PCA and project the data to 2D
from ex7_K_means_Clustering_and_Principal_Component_Analysis.pca import pca
U, S = pca(X_norm)
from ex7_K_means_Clustering_and_Principal_Component_Analysis.projectData import projectData
Z = projectData(X_norm, U, 2)
# Plot in 2D
plt.figure(2)
from ex7_K_means_Clustering_and_Principal_Component_Analysis.plotDataPoints import plotDataPoints
plotDataPoints(Z[sel, :], idx[sel], K)
plt.title(
'Pixel dataset plotted in 2D, using PCA for dimensionality reduction'
)
plt.show(block=False)
def test_PCA_on_Face_Data_Eignfaces(self):
print("Running PCA on face dataset.")
print("this mght take a minute or two ...")
# Load Face dataset
mat = scipy.io.loadmat('resource/ex7faces.mat')
X = np.array(mat["X"])
# Before running PCA, it is important to first normalize X by subtracting
# the mean value from each feature
from utils.featureNormalize import featureNormalize
X_norm, _, _ = featureNormalize(X)
# Run PCA
from ex7_K_means_Clustering_and_Principal_Component_Analysis.pca import pca
U, S = pca(X_norm)
# Visualize the top 36 eigenvectors found
from utils.displayData import displayData
displayData(U[:, :36].T)
# ============= Part 6: Dimension Reduction for Faces =================
# Project images to the eigen space using the top k eigenvectors
# If you are applying a machine learning algorithm
print("Dimension reduction for face dataset.")
K = 100
from ex7_K_means_Clustering_and_Principal_Component_Analysis.projectData import projectData
Z = projectData(X_norm, U, K)
print("The projected data Z has a size of: {z}".format(z=np.shape(Z)))
# ==== Part 7: Visualization of Faces after PCA Dimension Reduction ====
# Project images to the eigen space using the top K eigen vectors and
# visualize only using those K dimensions
# Compare to the original input, which is also displayed
print("Visualizing the projected (reduced dimension) faces.")
K = 100
from ex7_K_means_Clustering_and_Principal_Component_Analysis.recoverData import recoverData
X_rec = recoverData(Z, U, K)
# Display normalized data
plt.close()
plt.subplot(1, 2, 1)
displayData(X_norm[:100, :])
plt.title('Original faces')
plt.gca().set_aspect('equal', adjustable='box')
# Display reconstructed data from only k eigenfaces
plt.subplot(1, 2, 2)
displayData(X_rec[:100, :])
plt.title('Recovered faces')
plt.gca().set_aspect('equal', adjustable='box')
def polyFeatures(X, p):
X_poly = X #np.zeros((X.shape[0], p))
for i in range(2, p + 1):
X_at_i = X**i
X_poly = np.hstack((X_poly, X_at_i))
return X_poly
p = 8
# Map X onto Polynomial Features and Normalize
X_poly = polyFeatures(X, p)
# print(X_poly.shape)
# print(X_poly[:,1])
# print(X)
X_poly, mu, sigma = utils.featureNormalize(X_poly)
X_poly = np.concatenate([np.ones((m, 1)), X_poly], axis=1)
# Map X_poly_test and normalize (using mu and sigma)
X_poly_test = polyFeatures(Xtest, p)
# print(X_poly_test.shape)
# print(X_poly_test[:,1])
# print(Xtest)
X_poly_test -= mu
X_poly_test /= sigma
X_poly_test = np.concatenate([np.ones((ytest.size, 1)), X_poly_test], axis=1)
# Map X_poly_val and normalize (using mu and sigma)
X_poly_val = polyFeatures(Xval, p)
X_poly_val -= mu
X_poly_val /= sigma
# Visualize the example dataset
pyplot.plot(X[:, 0], X[:, 1], 'bo', ms=10, mec='k', mew=1)
pyplot.axis([0.5, 6.5, 2, 8])
pyplot.gca().set_aspect('equal')
pyplot.grid(False)
pyplot.show()
## =============== Part 2: Principal Component Analysis ===============
# You should now implement PCA, a dimension reduction technique. You
# should complete the code in pca.m
#
print('\nRunning PCA on example dataset.\n\n')
# Before running PCA, it is important to first normalize X
X_norm, mu, sigma = utils.featureNormalize(X)
# Run PCA
U, S = pca.pca(X_norm)
# Compute mu, the mean of the each feature
# Draw the eigenvectors centered at mean of data. These lines show the
# directions of maximum variations in the dataset.
fig, ax = pyplot.subplots()
ax.plot(X[:, 0], X[:, 1], 'bo', ms=10, mec='k', mew=0.25)
for i in range(2):
ax.arrow(mu[0],
mu[1],
1.5 * S[i] * U[0, i],
print('Загрузка данных...')
X = []
Y = []
with open('ex1data3.csv') as f:
scv_reader = csv.reader(f, delimiter=',')
for row in scv_reader:
X.append([row[0], row[1]])
Y.append([row[2]])
X = np.asarray(X).astype(np.float)
Y = np.asarray(Y).astype(np.float)
m = Y.size
# Задача 1 - Нормализация признаков
print('Нормализация признаков...')
X, mu, sigma = ut.featureNormalize(X)
ones_column = np.ones((m, 1))
X = np.hstack((ones_column, X))
# Задача 2 - Метод градиентного спуска
print('Выполнение градиентного спуска...')
alpha = 0.01
num_iters = 400
theta = np.zeros((3, 1))
theta, J_history = ut.gradient_descent(X, Y, theta, alpha, num_iters)
fig = plt.figure()
ax = plt.axes()
plt.plot(np.arange(J_history.size), J_history)
ax.set_xlabel("Число итераций")
