Numerous ex7 fixes

- More consistent display of plots
- Improved coloring of clusters in ex7_pca
- Dropping unused return 'val' from findClosestCentroids
- Specifying S must be a diagonal matrix

ex7/ex7.py

@@ -48,7 +48,7 @@
 
 # Find the closest centroids for the examples using the
 # initial_centroids
-val, idx = findClosestCentroids(X, initial_centroids)
+idx = findClosestCentroids(X, initial_centroids)
 
 print('Closest centroids for the first 3 examples:')
 print(idx[0:3].tolist())
@@ -155,7 +155,7 @@
 print('Applying K-Means to compress an image.')
 
 # Find closest cluster members
-_, idx = findClosestCentroids(X, centroids)
+idx = findClosestCentroids(X, centroids)
 
 # Essentially, now we have represented the image X as in terms of the
 # indices in idx. 
@@ -168,15 +168,15 @@
 X_recovered = X_recovered.reshape(img_size[0], img_size[1], 3)
 
 # Display the original image 
+plt.figure()
 plt.subplot(1, 2, 1)
 plt.imshow(A)
 plt.title('Original')
-show()
 
 # Display compressed image side by side
 plt.subplot(1, 2, 2)
 plt.imshow(X_recovered)
 plt.title('Compressed, with %d colors.' % K)
 show()
 
-input('Program paused. Press Enter to continue...')
+input('Program paused. Press Enter to continue...')

ex7/ex7_pca.py

@@ -46,6 +46,7 @@
 X = data['X']
 
 # Visualize the example dataset
+plt.figure()
 plt.scatter(X[:, 0], X[:, 1], marker='o', color='b', facecolors='none', lw=1.0)
 plt.axis([0.5, 6.5, 2, 8])
 plt.axis('equal')
@@ -70,12 +71,16 @@
 # Draw the eigenvectors centered at mean of data. These lines show the
 # directions of maximum variations in the dataset.
 mu2 = mu + 1.5 * S.dot(U.T)
+plt.figure()
+plt.scatter(X[:, 0], X[:, 1], marker='o', color='b', facecolors='none', lw=1.0)
+plt.axis([0.5, 6.5, 2, 8])
+plt.axis('equal')
 plt.plot([mu[0], mu2[0, 0]], [mu[1], mu2[0, 1]], '-k', lw=2)
 plt.plot([mu[0], mu2[1, 0]], [mu[1], mu2[1, 1]], '-k', lw=2)
 show()
 
 print('Top eigenvector: ')
-print(' U(:,1) = %f %f ', U[0,0], U[1,0])
+print(' U(:,1) = %f %f ' % (U[0, 0], U[1, 0]))
 print('(you should expect to see -0.707107 -0.707107)')
 
 input('Program paused. Press Enter to continue...')
@@ -96,25 +101,24 @@
             color='b', facecolors='none', lw=1.0)
 plt.axis([-4, 3, -4, 3])  # axis square
 plt.axis('equal')
-show()
 
 # 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('Projection of the first example: %f' % Z[0])
 print('(this value should be about 1.481274)')
 
 X_rec = recoverData(Z, U, K)
-print('Approximation of the first example: %f %f'% (X_rec[0, 0], X_rec[0, 1]))
+print('Approximation of the first example: %f %f' % (X_rec[0, 0], X_rec[0, 1]))
 print('(this value should be about  -1.047419 -1.047419)')
 
 #  Draw lines connecting the projected points to the original points
 plt.scatter(X_rec[:, 0], X_rec[:, 1], marker='o',
             color='r', facecolor='none', lw=1.0)
 for i in range(len(X_norm)):
     plt.plot([X_norm[i, 0], X_rec[i, 0]], [X_norm[i, 1], X_rec[i, 1]], '--k')
-
 show()
+
 input('Program paused. Press Enter to continue...')
 
 #  =============== Part 4: Loading and Visualizing Face Data =============
@@ -128,6 +132,7 @@
 X = data['X']
 
 # Display the first 100 faces in the dataset
+plt.figure()
 displayData(X[0:100, :])
 
 input('Program paused. Press Enter to continue...')
@@ -146,6 +151,7 @@
 U, S, V = pca(X_norm)
 
 #  Visualize the top 36 eigenvectors found
+plt.figure()
 displayData(U[:, 1:36].T)
 
 input('Program paused. Press Enter to continue...')
@@ -174,6 +180,7 @@
 X_rec = recoverData(Z, U, K)
 
 # Display normalized data
+plt.figure()
 plt.subplot(1, 2, 1)
 displayData(X_norm[:100,:])
 plt.title('Original faces')
@@ -211,7 +218,8 @@
 
 # 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.random(1000) * len(X)) + 1
+sel = np.floor(np.random.random(1000) * len(X))
+sel = sel.astype(int)
 
 # Setup Color Palette
 
@@ -223,9 +231,11 @@
 ys = Xs[:, 1]
 zs = Xs[:, 2]
 cmap = plt.get_cmap("jet")
-idxn = sel.astype('float') / max(sel.astype('float'))
+idxn = idx[sel]
+idxn = idxn.astype('float') / max(idxn.astype('float'))
 colors = cmap(idxn)
-# ax = Axes3D(fig)
+
+ax = Axes3D(fig)
 ax.scatter3D(xs, ys, zs=zs, edgecolors=colors,
              marker='o', facecolors='none', lw=0.4, s=10)
 
@@ -246,10 +256,9 @@
 # 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)
+plotDataPoints(zs, idxn)
 plt.title('Pixel dataset plotted in 2D, using PCA for dimensionality reduction')
 show()
+
 input('Program paused. Press Enter to continue...')

ex7/findClosestCentroids.py

@@ -11,7 +11,7 @@ def findClosestCentroids(X, centroids):
     K = len(centroids)
 
     # You need to return the following variables correctly.
-    idx = np.zeros(X.shape[0])
+    idx = np.zeros(X.shape[0], dtype=int)
 
     # ====================== YOUR CODE HERE ======================
     # Instructions: Go over every example, find its closest centroid, and store
@@ -21,7 +21,8 @@ def findClosestCentroids(X, centroids):
     #               range 1..K
     #
     # Note: You can use a for-loop over the examples to compute this.
+    #
     # =============================================================
 
-    return val, idx
+    return idx
 

ex7/pca.py

@@ -10,6 +10,7 @@ def pca(X):
     m, n = X.shape
 
     # You need to return the following variables correctly.
+    # S must be a diagonal matrix.
 
     # ====================== YOUR CODE HERE ======================
     # Instructions: You should first compute the covariance matrix. Then, you

ex7/plotDataPoints.py

@@ -12,10 +12,8 @@ def plotDataPoints(X, idx):
     #
     # # Plot the data
 
-    # c = dict(enumerate(np.eye(3)))
-    # colors=idx
-    map = plt.get_cmap("jet")
+    cmap = plt.get_cmap("jet")
     idxn = idx.astype('float') / max(idx.astype('float'))
-    colors = map(idxn)
-    plt.scatter(X[:, 0], X[:, 1], 15, edgecolors=colors, marker='o', facecolors='none', lw=0.5)
-    show()
+    colors = cmap(idxn)
+    plt.scatter(X[:, 0], X[:, 1], 15, edgecolors=colors,
+                marker='o', facecolors='none', lw=0.5)

ex7/plotProgresskMeans.py

@@ -4,7 +4,7 @@
 from show import show
 
 
-def plotProgresskMeans(X, centroids, previous, idx, K, i, color):
+def plotProgresskMeans(X, centroids, previous, idx, K, i, color, ax):
     """plots the data
     points with colors assigned to each centroid. With the previous
     centroids, it also plots a line between the previous locations and
@@ -15,16 +15,15 @@ def plotProgresskMeans(X, centroids, previous, idx, K, i, color):
     plotDataPoints(X, idx)
 
     # Plot the centroids as black x's
-    plt.scatter(centroids[:, 0], centroids[:, 1],
-                marker='x', s=60, lw=3, edgecolor='k')
+    ax.scatter(centroids[:, 0], centroids[:, 1],
+                marker='x', s=60, lw=3, color='black')
 
     # 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)
+        ax.plot([centroids[j, 0], previous[j, 0]],
+                [centroids[j, 1], previous[j, 1]], color='black')
 
     # Title
     plt.title('Iteration number %d' % i)
-    show()
     input('Program paused. Press Enter to continue...')
 

ex7/runkMeans.py

@@ -1,10 +1,12 @@
-from computeCentroids import computeCentroids
-from plotProgresskMeans import plotProgresskMeans
-from findClosestCentroids import findClosestCentroids
 import matplotlib.pyplot as plt
 import numpy as np
 import itertools
 
+from computeCentroids import computeCentroids
+from plotProgresskMeans import plotProgresskMeans
+from findClosestCentroids import findClosestCentroids
+from show import show
+
 
 def runkMeans(X, initial_centroids, max_iters, plot_progress=False):
     """runs the K-Means algorithm on data matrix X, where each
@@ -19,7 +21,8 @@ def runkMeans(X, initial_centroids, max_iters, plot_progress=False):
 
     # Plot the data if we are plotting progress
     if plot_progress:
-        plt.figure()
+        fig = plt.figure()
+        ax = plt.gca()
 
     # Initialize values
     m, n = X.shape
@@ -37,15 +40,17 @@ def runkMeans(X, initial_centroids, max_iters, plot_progress=False):
         print('K-Means iteration %d/%d...' % (i, max_iters))
 
         # For each example in X, assign it to the closest centroid
-        _, idx = findClosestCentroids(X, centroids)
+        idx = findClosestCentroids(X, centroids)
 
         # Optionally, plot progress here
         if plot_progress:
             color = rgb[int(next(c))]
             plotProgresskMeans(X, np.array(centroids),
-                               np.array(previous_centroids), idx, K, i, color)
+                               np.array(previous_centroids),
+                               idx, K, i, color, ax)
             previous_centroids = centroids
-            # raw_input("Press Enter to continue...")
+            show()
+            fig.canvas.draw()
 
         # Given the memberships, compute new centroids
         centroids = computeCentroids(X, idx, K)