def output(partId):
# Random Test Cases
X = np.sin(np.arange(1, 166)).reshape(15, 11, order='F')
Z = np.cos(np.arange(1, 122)).reshape(11, 11, order='F')
C = Z[:5, :]
idx = np.arange(1, 16) % 3
if partId == '1':
idx = findClosestCentroids(X, C) + 1
out = formatter('%0.5f ', idx.ravel('F'))
elif partId == '2':
centroids = computeCentroids(X, idx, 3)
out = formatter('%0.5f ', centroids.ravel('F'))
elif partId == '3':
U, S = pca(X)
out = formatter(
'%0.5f ', np.abs(np.hstack([U.ravel('F'),
np.diag(S).ravel('F')])))
elif partId == '4':
X_proj = projectData(X, Z, 5)
out = formatter('%0.5f ', X_proj.ravel('F'))
elif partId == '5':
X_rec = recoverData(X[:, :5], Z, 5)
out = formatter('%0.5f ', X_rec.ravel('F'))
return out
# first k eigenvectors. The code will then plot the data in this reduced
# dimensional space. This will show you what the data looks like when
# using only the corresponding eigenvectors to reconstruct it.
#
# You should complete the code in projectData.py and recoverData.py
#
print '\nDimension reduction on example dataset.\n'
# Plot the normalized dataset (returned from pca)
plot(X_norm[:, 0], X_norm[:, 1], 'bo')
axis([-4, 3, -4, 3])
axis('equal')
# Project the data onto K = 1 dimension
K = 1
Z = projectData(X_norm, U, K)
print 'Projection of the first example: %f' % Z[0]
print '\n(this value should be about 1.481274)\n'
X_rec = recoverData(Z, U, K)
print 'Approximation of the first example: %f %f' % (X_rec[0, 0], X_rec[0, 1])
print '\n(this value should be about -1.047419 -1.047419)\n'
# Draw lines connecting the projected points to the original points
hold(True)
plot(X_rec[:, 0], X_rec[:, 1], 'ro')
for i in range(size(X_norm, 0)):
drawLine(X_norm[i, :], X_rec[i, :], '--k', linewidth=1)
hold(False)
fig.show()
# first k eigenvectors. The code will then plot the data in this reduced
# dimensional space. This will show you what the data looks like when
# using only the corresponding eigenvectors to reconstruct it.
#
# You should complete the code in projectData.py and recoverData.py
#
print '\nDimension reduction on example dataset.\n'
# Plot the normalized dataset (returned from pca)
plot(X_norm[:, 0], X_norm[:, 1], 'bo')
axis([-4, 3, -4, 3])
axis('equal')
# Project the data onto K = 1 dimension
K = 1
Z = projectData(X_norm, U, K)
print 'Projection of the first example: %f' % Z[0]
print '\n(this value should be about 1.481274)\n'
X_rec = recoverData(Z, U, K)
print 'Approximation of the first example: %f %f' % (X_rec[0,0], X_rec[0,1])
print '\n(this value should be about -1.047419 -1.047419)\n'
# Draw lines connecting the projected points to the original points
hold(True)
plot(X_rec[:, 0], X_rec[:, 1], 'ro')
for i in range(size(X_norm, 0)):
drawLine(X_norm[i,:], X_rec[i,:], '--k', linewidth=1)
hold(False)
fig.show()
def ex7_pca():
## Machine Learning Online Class
# Exercise 7 | Principle Component Analysis and K-Means Clustering
#
# Instructions
# ------------
#
# This file contains code that helps you get started on the
# exercise. You will need to complete the following functions:
#
# pca.m
# projectData.m
# recoverData.m
# computeCentroids.m
# findClosestCentroids.m
# kMeansInitCentroids.m
#
# For this exercise, you will not need to change any code in this file,
# or any other files other than those mentioned above.
#
## Initialization
#clear ; close all; clc
## ================== Part 1: Load Example Dataset ===================
# We start this exercise by using a small dataset that is easily to
# visualize
#
print('Visualizing example dataset for PCA.\n')
# The following command loads the dataset. You should now have the
# variable X in your environment
mat = scipy.io.loadmat('ex7data1.mat')
X = mat['X']
# Visualize the example dataset
plt.plot(X[:, 0], X[:, 1], 'wo', ms=10, mec='b', mew=1)
plt.axis([0.5, 6.5, 2, 8])
plt.savefig('figure1.png')
print('Program paused. Press enter to continue.')
#pause
## =============== 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')
# Before running PCA, it is important to first normalize X
X_norm, mu, sigma = featureNormalize(X)
# Run PCA
U, S = 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.
#hold on
print(S)
print(U)
drawLine(mu, mu + 1.5 * np.dot(S[0], U[:,0].T))
drawLine(mu, mu + 1.5 * np.dot(S[1], U[:,1].T))
#hold off
plt.savefig('figure2.png')
print('Top eigenvector: ')
print(' U(:,1) = %f %f ' % (U[0,0], U[1,0]))
print('\n(you should expect to see -0.707107 -0.707107)')
print('Program paused. Press enter to continue.')
#pause
## =================== Part 3: Dimension Reduction ===================
# You should now implement the projection step to map the data onto the
# first k eigenvectors. The code will then plot the data in this reduced
# dimensional space. This will show you what the data looks like when
# using only the corresponding eigenvectors to reconstruct it.
#
# You should complete the code in projectData.m
#
print('\nDimension reduction on example dataset.\n\n')
# Plot the normalized dataset (returned from pca)
fig = plt.figure()
plt.plot(X_norm[:, 0], X_norm[:, 1], 'bo')
# Project the data onto K = 1 dimension
K = 1
Z = projectData(X_norm, U, K)
print('Projection of the first example: %f' % Z[0])
print('\n(this value should be about 1.481274)\n')
X_rec = recoverData(Z, U, K)
print('Approximation of the first example: %f %f' % (X_rec[0, 0], X_rec[0, 1]))
print('\n(this value should be about -1.047419 -1.047419)\n')
# Draw lines connecting the projected points to the original points
plt.plot(X_rec[:, 0], X_rec[:, 1], 'ro')
for i in range(X_norm.shape[0]):
drawLine(X_norm[i,:], X_rec[i,:])
#end
plt.savefig('figure3.png')
print('Program paused. Press enter to continue.\n')
#pause
## =============== Part 4: Loading and Visualizing Face Data =============
# We start the exercise by first loading and visualizing the dataset.
# The following code will load the dataset into your environment
#
print('\nLoading face dataset.\n\n')
# Load Face dataset
mat = scipy.io.loadmat('ex7faces.mat')
X = mat['X']
# Display the first 100 faces in the dataset
displayData(X[:100, :])
plt.savefig('figure4.png')
print('Program paused. Press enter to continue.\n')
#pause
## =========== Part 5: PCA on Face Data: Eigenfaces ===================
# Run PCA and visualize the eigenvectors which are in this case eigenfaces
# We display the first 36 eigenfaces.
#
print('\nRunning PCA on face dataset.\n(this mght take a minute or two ...)\n')
# Before running PCA, it is important to first normalize X by subtracting
# the mean value from each feature
X_norm, mu, sigma = featureNormalize(X)
# Run PCA
U, S = pca(X_norm)
# Visualize the top 36 eigenvectors found
displayData(U[:, :36].T)
plt.savefig('figure5.png')
print('Program paused. Press enter to continue.')
#pause
## ============= 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('\nDimension reduction for face dataset.\n')
K = 100
Z = projectData(X_norm, U, K)
print('The projected data Z has a size of: ')
print(formatter('%d ', Z.shape))
print('\n\nProgram paused. Press enter to continue.')
#pause
## ==== 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('\nVisualizing the projected (reduced dimension) faces.\n')
K = 100
X_rec = recoverData(Z, U, K)
# Display normalized data
#subplot(1, 2, 1)
displayData(X_norm[:100,:])
plt.gcf().suptitle('Original faces')
#axis square
plt.savefig('figure6.a.png')
# Display reconstructed data from only k eigenfaces
#subplot(1, 2, 2)
displayData(X_rec[:100,:])
plt.gcf().suptitle('Recovered faces')
#axis square
plt.savefig('figure6.b.png')
print('Program paused. Press enter to continue.')
#pause
## === Part 8(a): Optional (ungraded) Exercise: PCA for Visualization ===
# One useful application of PCA is to use it to visualize high-dimensional
# data. In the last K-Means exercise you ran K-Means on 3-dimensional
# pixel colors of an image. We first visualize this output in 3D, and then
# apply PCA to obtain a visualization in 2D.
#close all; close all; clc
# 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 = matplotlib.image.imread('bird_small.png')
# If imread does not work for you, you can try instead
# load ('bird_small.mat')
A = A / 255
X = A.reshape(-1, 3)
K = 16
max_iters = 10
initial_centroids = kMeansInitCentroids(X, K)
centroids, idx = runkMeans('7', X, initial_centroids, max_iters)
# 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.random.choice(X.shape[0], size=1000)
# Setup Color Palette
#palette = hsv(K)
#colors = palette(idx(sel), :)
# Visualize the data and centroid memberships in 3D
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.scatter(X[sel, 0], X[sel, 1], X[sel, 2], cmap='rainbow', c=idx[sel], s=8**2)
ax.set_title('Pixel dataset plotted in 3D. Color shows centroid memberships')
plt.savefig('figure8.png')
print('Program paused. Press enter to continue.')
#pause
## === Part 8(b): Optional (ungraded) Exercise: PCA for Visualization ===
# Use PCA to project this cloud to 2D for visualization
# Subtract the mean to use PCA
X_norm, mu, sigma = featureNormalize(X)
# PCA and project the data to 2D
U, S = pca(X_norm)
Z = projectData(X_norm, U, 2)
# Plot in 2D
fig = plt.figure()
plotDataPoints(Z[sel, :], [idx[sel]], K, 0)
plt.title('Pixel dataset plotted in 2D, using PCA for dimensionality reduction')
plt.savefig('figure9.png')
print('Program paused. Press enter to continue.\n')
# print(np.shape(data))
# print(np.shape(data_modified))
displayData(data_modified[0:100], None)
[X_norm, mu, sigma] = featureNormalize(data_modified)
[u, s] = pca(X_norm)
u = np.transpose(u)
displayData(u[:36], None)
k = 100
# print('----------------------')
# print(m)
# print(n)
# print(np.shape(u))
# print(np.shape(u[:36]))
z = projectData(X_norm, u, k)
X_rec = recoverData(z, u, k)
print(np.shape(data))
print(np.shape(X_rec))
displayData(X_rec[:100], None)
# =============== Optional (ungraded) Exercise: PCA for Visualization =============
# print('Applying K-Means to compress an image.')
# fname = "bird_small.png"
# image1 = np.array(plt.imread(fname))
# image = image1/255
# image_size = image.size
# # print(image)
# # print(image_size)
# # print(image.shape)
# x = image.shape[0]