def plotProgresskMeans(X, centroids, previous, idx, K, i, color):
"""plots the data
points with colors assigned to each centroid. With the previous
centroids, it also plots a line between the previous locations and
current locations of the centroids.
"""
# Plot the examples
plotDataPoints(X, idx)
# Plot the centroids as black x's
plt.scatter(centroids[:, 0],
centroids[:, 1],
marker='x',
s=60,
lw=3,
edgecolor='k')
# Plot the history of the centroids with lines
for j in range(len(centroids)):
plt.plot([centroids[j, 0], previous[j, 0]],
[centroids[j, 1], previous[j, 1]],
c=color)
# Title
plt.title('Iteration number %d' % i)
plt.show()
input("Program paused. Press Enter to continue...")
def plotProgresskMeans(X, centroids, previous, idx, K, i):
#PLOTPROGRESSKMEANS is a helper function that displays the progress of
#k-Means as it is running. It is intended for use only with 2D data.
# PLOTPROGRESSKMEANS(X, centroids, previous, idx, K, i) plots the data
# points with colors assigned to each centroid. With the previous
# centroids, it also plots a line between the previous locations and
# current locations of the centroids.
#
# Plot the examples
plotDataPoints(X, idx, K, i)
current = centroids
for last in previous[::-1]:
# Plot the centroids as black x's
plt.plot(current[:, 0],
current[:, 1],
linestyle='None',
marker='x',
markeredgecolor='k',
ms=10,
lw=3)
# Plot the history of the centroids with lines
for j in range(current.shape[0]):
drawLine(current[j, :], last[j, :])
current = last
#end
# Title
plt.title('Iteration number %d' % i)
def plotProgresskMeans(X, centroids, idx, K, i=0):
'''
PLOTPROGRESSKMEANS(X, centroids, previous, idx, K, i) plots the data
points with colors assigned to each centroid. With the previous
centroids, it also plots a line between the previous locations and
current locations of the centroids.
'''
from plotDataPoints import plotDataPoints
import matplotlib.pyplot as plt
import numpy as np
# Plot the examples
plotDataPoints(X, idx, K)
# Plot the centroids as black x's
plt.plot(centroids[:,0], centroids[:, 1], 'x', \
markeredgecolor = '#414042', markersize = 7, markeredgewidth = 2)
# Plot the history of the centroids with lines
for j in range(K):
# Group for centroids
k = centroids[range(j, centroids.shape[0], K), :]
plt.plot(k[:, 0], k[:, 1], color='k', linewidth=0.5)
# Title
plt.title('Iteration number %d' % (i))
def plotProgresskMeans(X, centroids, previous, idx, K, i):
#PLOTPROGRESSKMEANS is a helper function that displays the progress of
#k-Means as it is running. It is intended for use only with 2D data.
# PLOTPROGRESSKMEANS(X, centroids, previous, idx, K, i) plots the data
# points with colors assigned to each centroid. With the previous
# centroids, it also plots a line between the previous locations and
# current locations of the centroids.
#
# plt.hold(True)
# Plot the examples
pdp.plotDataPoints(X, idx, K)
# Plot the centroids as black x's
plt.scatter(centroids[:, 0],
centroids[:, 1],
marker='x',
s=400,
c='k',
linewidth=1)
# Plot the history of the centroids with lines
for j in range(centroids.shape[0]):
dl.drawLine(centroids[j, :], previous[j, :], c='b')
# Title
plt.title('Iteration number {:d}'.format(i + 1))
return
def plotProgresskMeans(X, centroids, previous, idx, K, i):
#PLOTPROGRESSKMEANS is a helper function that displays the progress of
#k-Means as it is running. It is intended for use only with 2D data.
# PLOTPROGRESSKMEANS(X, centroids, previous, idx, K, i) plots the data
# points with colors assigned to each centroid. With the previous
# centroids, it also plots a line between the previous locations and
# current locations of the centroids.
#
# plt.hold(True)
# Plot the examples
pdp.plotDataPoints(X, idx, K)
# Plot the centroids as black x's
plt.scatter(centroids[:,0], centroids[:,1], marker='x', s=400, c='k', linewidth=1)
# Plot the history of the centroids with lines
for j in xrange(centroids.shape[0]):
dl.drawLine(centroids[j, :], previous[j, :], c='b')
# Title
plt.title('Iteration number {:d}'.format(i+1))
return
def plotProgresskMeans(X, centroids, previous, idx, K, i):
plotDataPoints(X, idx)
plt.plot(previous[:, 0], previous[:, 1], 'rx', lw=3)
plt.plot(centroids[:, 0], centroids[:, 1], 'kx', lw=3)
for j in range(centroids.shape[0]):
drawLine(centroids[j, :], previous[j, :])
plt.title('Iteration number %d' % i)
plt.show(block=False)
def plotProgressKmeans(X, centroids, previous, idx, K, i):
plotDataPoints(X, idx, K)
plt.scatter(centroids[:, 0], centroids[:, 1], marker='x', edgecolors='b')
for j in range(centroids.shape[0]):
drawLine(centroids[j, :], previous[j, :])
plt.title('Iteration number {}'.format(i))
plt.show()
def plotProgressKMeans(X, history_centroids, idx, K, i):
#PLOTPROGRESSKMEANS is a helper function that displays the progress of
#k-Means as it is running. It is intended for use only with 2D data.
# PLOTPROGRESSKMEANS(X, centroids, previous, idx, K, i) plots the data
# points with colors assigned to each centroid. With the previous
# centroids, it also plots a line between the previous locations and
# current locations of the centroids.
plotDataPoints(X, idx, K)
plt.plot(history_centroids[0:i+1, :, 0], history_centroids[0:i+1, :, 1],
linestyle='', marker='x', markersize=10, linewidth=3, color='k')
plt.title('Iteration number {}'.format(i + 1))
for centroid_idx in range(history_centroids.shape[1]):
for iter_idx in range(i):
drawLine(history_centroids[iter_idx, centroid_idx, :], history_centroids[iter_idx + 1, centroid_idx, :])
def plotProgresskMeans(X, centroids, previous, idx, K, i):
# Plot the examples
plotDataPoints(X, idx, K)
# Plot the centroids as black x's
plt.plot(centroids[:, 0],
centroids[:, 1],
marker='x',
markeredgecolor='k',
markersize=10,
linewidth=3,
linestyle='None')
#plt.scatter(centroids[:,0], centroids[:,1], marker='x', s=400, c='k', linewidth=1)
# Plot the history of the centroids with lines
for j in range(centroids.shape[0]):
drawLine(centroids[j, :], previous[j, :], c='b')
# Title
plt.title('Iteration number ' + str(i))
#return plt
def plotProgresskMeans(X, centroids, previous, idx, K, i):
#PLOTPROGRESSKMEANS is a helper function that displays the progress of
#k-Means as it is running. It is intended for use only with 2D data.
# PLOTPROGRESSKMEANS(X, centroids, previous, idx, K, i) plots the data
# points with colors assigned to each centroid. With the previous
# centroids, it also plots a line between the previous locations and
# current locations of the centroids.
#
# Plot the examples
plotDataPoints(X, idx, K)
# Plot the centroids as black x's
plot(centroids[:,0], centroids[:,1], 'x', mec='k', ms=10, mew=3)
# Plot the history of the centroids with lines
for j in range(size(centroids, 0)):
drawLine(centroids[j, :], previous[j, :], 'b')
# Title
title('Iteration number #%d' % (i+1))
def runkMeans(data, initial_centroids,max_iters, plot_progress):
# Initialize values
(m,n) = np.shape(data);
print(m)
print(n)
k = len(initial_centroids)
centroids = initial_centroids;
previous_centroids = centroids;
idx = [0] * m;
for i in range(max_iters):
print('K-Means iteration #d/#d...\n', i, max_iters);
idx = findClosestCentroids(data, centroids);
if plot_progress:
# plotProgresskMeans(data, centroids, previous_centroids, idx, k, i);
plotDataPoints(data, idx, k)
previous_centroids = centroids;
print('Press enter to continue.\n');
# pause;
# Given the memberships, compute new centroids
centroids = computeCentroids(data, idx, k);
return centroids, idx
def plotProgresskMeans(X, centroids, previous, idx, K, i, color):
"""plots the data
points with colors assigned to each centroid. With the previous
centroids, it also plots a line between the previous locations and
current locations of the centroids.
"""
# Plot the examples
plotDataPoints(X, idx)
# Plot the centroids as black x's
plt.scatter(centroids[:, 0], centroids[:, 1],
marker='x', s=60, lw=3, edgecolor='k')
# Plot the history of the centroids with lines
for j in range(len(centroids)):
plt.plot([centroids[j,0], previous[j,0]],
[centroids[j,1], previous[j,1]], c=color)
# Title
plt.title('Iteration number %d' % i)
show()
raw_input("Program paused. Press Enter to continue...")
X[sel, 1],
X[sel, 2],
s=100,
c=idx[sel],
cmap=cm.hsv,
vmax=K + 1,
facecolors='none')
title('Pixel dataset plotted in 3D. Color shows centroid memberships')
fig.show()
print 'Program paused. Press enter to continue.'
raw_input()
## === 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 = figure()
plotDataPoints(Z[sel, :], idx[sel], K)
title('Pixel dataset plotted in 2D, using PCA for dimensionality reduction')
fig.show()
print 'Program paused. Press enter to continue.'
raw_input()
marker='o',
facecolors='none',
lw=0.4,
s=10)
plt.title('Pixel dataset plotted in 3D. Color shows centroid memberships')
show()
input('Program paused. Press Enter to continue...')
## === 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, V = pca(X_norm)
Z = projectData(X_norm, U, 2)
# Plot in 2D
plt.figure()
zs = np.array([Z[s] for s in sel])
idxs = np.array([idx[s] for s in sel])
# plt.scatter(zs[:,0], zs[:,1])
plotDataPoints(zs, idxs)
plt.title(
'Pixel dataset plotted in 2D, using PCA for dimensionality reduction')
show()
input('Program paused. Press Enter to continue...')
cmap = plt.get_cmap("jet")
idxn = sel.astype('float')/max(sel.astype('float'))
colors = cmap(idxn)
# ax = Axes3D(fig)
ax.scatter3D(xs, ys, zs=zs, edgecolors=colors, marker='o', facecolors='none', lw=0.4, s=10)
plt.title('Pixel dataset plotted in 3D. Color shows centroid memberships')
show()
raw_input('Program paused. Press Enter to continue...')
## === 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, V = pca(X_norm)
Z = projectData(X_norm, U, 2)
# Plot in 2D
plt.figure()
zs = np.array([Z[s] for s in sel])
idxs = np.array([idx[s] for s in sel])
# plt.scatter(zs[:,0], zs[:,1])
plotDataPoints(zs, idxs)
plt.title('Pixel dataset plotted in 2D, using PCA for dimensionality reduction')
show()
raw_input('Program paused. Press Enter to continue...')
# too expensive. If you have a fast computer, you may increase this.
sel = (random.rand(1000) * size(X, 0)).astype(int)
# Visualize the data and centroid memberships in 3D
fig = figure()
ax = Axes3D(fig)
ax.scatter(X[sel, 0], X[sel, 1], X[sel, 2], s=100, c=idx[sel], cmap=cm.hsv, vmax=K+1, facecolors='none')
title('Pixel dataset plotted in 3D. Color shows centroid memberships')
fig.show()
print 'Program paused. Press enter to continue.'
raw_input()
## === 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 = figure()
plotDataPoints(Z[sel, :], idx[sel], K)
title('Pixel dataset plotted in 2D, using PCA for dimensionality reduction')
fig.show()
print 'Program paused. Press enter to continue.'
raw_input()
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')
# function plotProgresskMeans(X, centroids, previous, idx, K, i)
#PLOTPROGRESSKMEANS is a helper function that displays the progress of
#k-Means as it is running. It is intended for use only with 2D data.
# PLOTPROGRESSKMEANS(X, centroids, previous, idx, K, i) plots the data
# points with colors assigned to each centroid. With the previous
# centroids, it also plots a line between the previous locations and
# current locations of the centroids.
#
# Plot the examples
plotDataPoints(X, idx, K);
# Plot the centroids as black x's
plot(centroids(:,1), centroids(:,2), 'x', ...
'MarkerEdgeColor','k', ...
'MarkerSize', 10, 'LineWidth', 3);
# Plot the history of the centroids with lines
for j=1:size(centroids,1)
drawLine(centroids(j, :), previous(j, :));
end
# Title
title(sprintf('Iteration number #d', i))
end
from plotDataPoints import plotDataPoints
def plotProgresskMeans(data, centroids, previous, idx, k ,i):
plotDataPoints(data, idx, k)
def plotProgresskMeans(data, centroids, previous, idx, k ,i):
plotDataPoints(data, idx, k)