1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
 # Run some setup code for this notebook.
importrandom
importnumpy as np
fromcs231n.data_utils import load_CIFAR10
importmatplotlib.pyplot as plt

from__future__ import print_function
 

#This is a bit of magic to make matplotlib figures appear inline in the notebook
#rather than in a new window.
%matplotlibinline
plt.rcParams['figure.figsize']= (10.0, 8.0) # set default size of plots
plt.rcParams['image.interpolation']= 'nearest'
plt.rcParams['image.cmap']= 'gray'

#Some more magic so that the notebook will reload external python modules;
#see http://stackoverflow.com/questions/1907993/autoreload-of-modules-in-ipython
%load_extautoreload
%autoreload2

1
2
3
4
5
6
7
8
9
 # Load the raw CIFAR-10 data.
cifar10_dir= 'cs231n/datasets/cifar-10-batches-py'
X_train,y_train, X_test, y_test = load_CIFAR10(cifar10_dir)

#As a sanity check, we print out the size of the training and test data.
print('Trainingdata shape: ', X_train.shape)
print('Traininglabels shape: ', y_train.shape)
print('Testdata shape: ', X_test.shape)
print('Testlabels shape: ', y_test.shape)

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
 # Visualize some examples fromthe dataset.
#We show a few examples of training images from each class.
classes= ['plane', 'car', 'bird', 'cat', 'deer', 'dog', 'frog', 'horse', 'ship','truck']
num_classes= len(classes)
samples_per_class= 7
fory, cls in enumerate(classes):
    idxs = np.flatnonzero(y_train == y)
    idxs = np.random.choice(idxs,samples_per_class, replace=False)
    for i, idx in enumerate(idxs):
        plt_idx = i * num_classes + y + 1
        plt.subplot(samples_per_class,num_classes, plt_idx)
        plt.imshow(X_train[idx].astype('uint8'))
        plt.axis('off')

        if i == 0:
            plt.title(cls)
plt.show()

1
2
3
4
5
6
7
8
9
10
#Subsample the data for more efficient code execution in this exercise
num_training= 5000
mask= list(range(num_training))
X_train= X_train[mask]
y_train= y_train[mask]
 
num_test= 500
mask= list(range(num_test))
X_test= X_test[mask]
y_test= y_test[mask]

1
2
3
4
5
#Reshape the image data into rows
X_train= np.reshape(X_train, (X_train.shape[0], -1))
X_test= np.reshape(X_test, (X_test.shape[0], -1))

print(X_train.shape,X_test.shape)

1
(5000L,3072L) (500L, 3072L)

1
2
3
4
5
6
fromcs231n.classifiers import KNearestNeighbor
#Create a kNN classifier instance.
#Remember that training a kNN classifier is a noop:
#the Classifier simply remembers the data and does no further processing
classifier= KNearestNeighbor()
classifier.train(X_train,y_train)

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
defcompute_distances_two_loops(self, X):
   """
   Compute the distance between each test point in X and each trainingpoint
   in self.X_train using a nested loop over both the training data and the
   test data.
 

   Inputs:
   - X: A numpy array of shape (num_test, D) containing test data.

   Returns:
   - dists: A numpy array of shape (num_test, num_train) where dists[i, j]
      is the Euclidean distance between the ithtest point and the jth training
      point.
   """

   num_test = X.shape[0]
   num_train = self.X_train.shape[0]
   dists = np.zeros((num_test, num_train)) #500*5000
   for i in xrange(num_test):
      for j in xrange(num_train):
         dists[i,j] = np.sqrt(np.sum(np.square(self.X_train[j,:]- X[i,:])))
       #####################################################################
        # TODO:                                                            #
        # Compute the L2 distance between the ithtest point and the jth    #
        # training point, and store the resultin dists[i, j]. You should   #
        # not use a loop over dimension.                                   #
       #####################################################################
        #pass
       #####################################################################
        #                       END OF YOUR CODE                            #
        #####################################################################
   return dists

1
2
3
4
5
6
#Open cs231n/classifiers/k_nearest_neighbor.py and implement
#compute_distances_two_loops.

#Test your implementation:
dists= classifier.compute_distances_two_loops(X_test)
print(dists.shape)

1
 (500L, 5000L)

1
2
3
4
#We can visualize the distance matrix: each row is a single test example and
#its distances to training examples
plt.imshow(dists,interpolation='none')
plt.show()

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
def predict_labels(self, dists, k=1):

    """
    Given a matrix of distances between testpoints and training points,
    predict a label for each test point.

    Inputs:
    - dists: A numpy array of shape (num_test,num_train) where dists[i, j]
      gives the distance betwen the ith testpoint and the jth training point.
 
    Returns:
    - y: A numpy array of shape (num_test,)containing predicted labels for the
      test data, where y[i] is the predictedlabel for the test point X[i]. 
    """
    num_test = dists.shape[0]
    y_pred = np.zeros(num_test) #500*1
    for i in xrange(num_test):
      # A list of length k storing the labelsof the k nearest neighbors to
      # the ith test point.
      closest_y = []
     #########################################################################
      # TODO:                                                                #
      # Use the distance matrix to find the knearest neighbors of the ith    #
      # testing point, and use self.y_train tofind the labels of these       #
      # neighbors. Store these labels inclosest_y.                           #
      # Hint: Look up the functionnumpy.argsort.                             #
     #########################################################################

      closest_y = np.argsort(dists[i,:]) # i'm socool
      #pass
     #########################################################################
      # TODO:                                                                #
      # Now that you have found the labels ofthe k nearest neighbors, you    #
      # need to find the most common label inthe list closest_y of labels.   #
      # Store this label in y_pred[i]. Breakties by choosing the smaller     #
      # label.                                                               #
     #########################################################################

      y_pred[i] =np.argmax(np.bincount(self.y_train[closest_y[:k]]))

      #pass
      #########################################################################
      #                           END OF YOURCODE                             #
     #########################################################################
    return y_pred

1
2
3
4
5
6
7
# Now implement the function predict_labels and run the code below:
# We use k = 1 (which is Nearest Neighbor).
y_test_pred = classifier.predict_labels(dists, k=1)
# Compute and print the fraction of correctly predicted examples
num_correct = np.sum(y_test_pred == y_test)
accuracy = float(num_correct) / num_test
print('Got %d / %d correct => accuracy: %f' % (num_correct, num_test, accuracy))

1
Got 137/500 correct => accuracy: 0.274000

1
2
3
4
5
y_test_pred = classifier.predict_labels(dists, k=5)
num_correct = np.sum(y_test_pred == y_test)
accuracy = float(num_correct) / num_test
print('Got %d / %d correct => accuracy: %f' % (num_correct, num_test, accuracy)) 

1
Got 139/500 correct => accuracy: 0.278000

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
def compute_distances_one_loop(self, X):

    """
    Compute the distance between each test point in X and each training point
    in self.X_train using a single loop over the test data.

    Input / Output: Same as compute_distances_two_loops
    """
    num_test = X.shape[0]
    num_train = self.X_train.shape[0]
    dists = np.zeros((num_test, num_train))
    for i in xrange(num_test):
      #######################################################################
      # TODO:                                                               #
      # Compute the L2 distance between the ith test point and all training #
      # points, and store the result in dists[i, :].                        #
      #######################################################################
      dists[i,:] = np.sqrt(np.sum(np.square(self.X_train - X[i,:]),axis = 1))
      #pass
      #######################################################################
      #                         END OF YOUR CODE                            #
      #######################################################################
    return dist

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
 # Now lets speed up distance matrix computation by using partial vectorization
# with one loop. Implement the function compute_distances_one_loop and run the
# code below:
dists_one = classifier.compute_distances_one_loop(X_test)
print(dists_one.shape)
# To ensure that our vectorized implementation is correct, we make sure that it
# agrees with the naive implementation. There are many ways to decide whether
# two matrices are similar; one of the simplest is the Frobenius norm. In case
# you haven't seen it before, the Frobenius norm of two matrices is the square
# root of the squared sum of differences of all elements; in other words, reshape
# the matrices into vectors and compute the Euclidean distance between them.
difference = np.linalg.norm(dists - dists_one, ord='fro')
print('Difference was: %f' % (difference, ))
if difference < 0.001:
    print('Good! The distance matrices are the same')
else:
    print('Uh-oh! The distance matrices are different')

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
def compute_distances_no_loops(self, X):
    """
    Compute the distance between each test point in X and each training point
    in self.X_train using no explicit loops.

    Input / Output: Same as compute_distances_two_loops
    """
    num_test = X.shape[0]
    num_train = self.X_train.shape[0]
    dists = np.zeros((num_test, num_train)) 
    #########################################################################
    # TODO:                                                                 #
    # Compute the L2 distance between all test points and all training      #
    # points without using any explicit loops, and store the result in      #
    # dists.                                                                #
    #                                                                       #
    # You should implement this function using only basic array operations; #
    # in particular you should not use functions from scipy.                #
    #                                                                       #
    # HINT: Try to formulate the l2 distance using matrix multiplication    #
    #       and two broadcast sums.                                         #
    #########################################################################
    dists += np.sum(self.X_train ** 2, axis=1).reshape(1, num_train) #1*5000，第一次广播
    dists += np.sum(X ** 2, axis=1).reshape(num_test,1) #500*1，第二次广播
    dists -= 2 * np.dot(X, self.X_train.T) #500*5000
    dists = np.sqrt(dists)
    #pass
    #########################################################################
    #                         END OF YOUR CODE                              #
    #########################################################################
    return dists

1
2
3
4
5
6
7
8
9
10
11
12
# Now implement the fully vectorized version inside compute_distances_no_loops
# and run the code
dists_two = classifier.compute_distances_no_loops(X_test)

# check that the distance matrix agrees with the one we computed before:
difference = np.linalg.norm(dists - dists_two, ord='fro')
print('Difference was: %f' % (difference, ))
if difference < 0.001:
    print('Good! The distance matrices are the same')
else:
    print('Uh-oh! The distance matrices are different')

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
# Let's compare how fast the implementations are
def time_function(f, *args):
    """
    Call a function f with args and return the time (in seconds) that it took to execute.
    """
    import time
    tic = time.time()
    f(*args)
    toc = time.time()
    return toc - tic

two_loop_time = time_function(classifier.compute_distances_two_loops, X_test)
print('Two loop version took %f seconds' % two_loop_time)

one_loop_time = time_function(classifier.compute_distances_one_loop, X_test)
print('One loop version took %f seconds' % one_loop_time)

no_loop_time = time_function(classifier.compute_distances_no_loops, X_test)
print('No loop version took %f seconds' % no_loop_time)

# you should see significantly faster performance with the fully vectorized implementation

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
num_folds = 5
k_choices = [1, 3, 5, 8, 10, 12, 15, 20, 50, 100]

X_train_folds = []
y_train_folds = []
################################################################################
# TODO:                                                                        #
# Split up the training data into folds. After splitting, X_train_folds and    #
# y_train_folds should each be lists of length num_folds, where                #
# y_train_folds[i] is the label vector for the points in X_train_folds[i].     #
# Hint: Look up the numpy array_split function.                                #
################################################################################
# split self.X_train to 5 folds
avg_size = int(X_train.shape[0] / num_folds) # will abandon the rest if not divided evenly.
for i in range(num_folds):
    X_train_folds.append(X_train[i * avg_size : (i+1) * avg_size])
    y_train_folds.append(y_train[i * avg_size : (i+1) * avg_size])

pass
################################################################################
#                                 END OF YOUR CODE                             #
################################################################################

# A dictionary holding the accuracies for different values of k that we find
# when running cross-validation. After running cross-validation,
# k_to_accuracies[k] should be a list of length num_folds giving the different
# accuracy values that we found when using that value of k.
k_to_accuracies = {}


################################################################################
# TODO:                                                                        #
# Perform k-fold cross validation to find the best value of k. For each        #
# possible value of k, run the k-nearest-neighbor algorithm num_folds times,   #
# where in each case you use all but one of the folds as training data and the #
# last fold as a validation set. Store the accuracies for all fold and all     #
# values of k in the k_to_accuracies dictionary.                               #
################################################################################
for k in k_choices:
    accuracies = []
    print(k)
    for i in range(num_folds):
        X_train_cv = np.vstack(X_train_folds[0:i] + X_train_folds[i+1:])
        y_train_cv = np.hstack(y_train_folds[0:i] + y_train_folds[i+1:])
        X_valid_cv = X_train_folds[i]
        y_valid_cv = y_train_folds[i]
        
        classifier.train(X_train_cv, y_train_cv)
        dists = classifier.compute_distances_no_loops(X_valid_cv)
        accuracy = float(np.sum(classifier.predict_labels(dists, k) == y_valid_cv)) / y_valid_cv.shape[0]
        accuracies.append(accuracy)
    k_to_accuracies[k] = accuracies
pass
################################################################################
#                                 END OF YOUR CODE                             #
################################################################################

# Print out the computed accuracies
for k in sorted(k_to_accuracies):
    for accuracy in k_to_accuracies[k]:
        print('k = %d, accuracy = %f' % (k, accuracy))

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
1
3
5
8
10
12
15
20
50
100
k = 1, accuracy = 0.263000
k = 1, accuracy = 0.257000
k = 1, accuracy = 0.264000
k = 1, accuracy = 0.278000
k = 1, accuracy = 0.266000
k = 3, accuracy = 0.239000
k = 3, accuracy = 0.249000
k = 3, accuracy = 0.240000
k = 3, accuracy = 0.266000
k = 3, accuracy = 0.254000
k = 5, accuracy = 0.248000
k = 5, accuracy = 0.266000
k = 5, accuracy = 0.280000
k = 5, accuracy = 0.292000
k = 5, accuracy = 0.280000
k = 8, accuracy = 0.262000
k = 8, accuracy = 0.282000
k = 8, accuracy = 0.273000
k = 8, accuracy = 0.290000
k = 8, accuracy = 0.273000
k = 10, accuracy = 0.265000
k = 10, accuracy = 0.296000
k = 10, accuracy = 0.276000
k = 10, accuracy = 0.284000
k = 10, accuracy = 0.280000
k = 12, accuracy = 0.260000
k = 12, accuracy = 0.295000
k = 12, accuracy = 0.279000
k = 12, accuracy = 0.283000
k = 12, accuracy = 0.280000
k = 15, accuracy = 0.252000
k = 15, accuracy = 0.289000
k = 15, accuracy = 0.278000
k = 15, accuracy = 0.282000
k = 15, accuracy = 0.274000
k = 20, accuracy = 0.270000
k = 20, accuracy = 0.279000
k = 20, accuracy = 0.279000
k = 20, accuracy = 0.282000
k = 20, accuracy = 0.285000
k = 50, accuracy = 0.271000
k = 50, accuracy = 0.288000
k = 50, accuracy = 0.278000
k = 50, accuracy = 0.269000
k = 50, accuracy = 0.266000
k = 100, accuracy = 0.256000
k = 100, accuracy = 0.270000
k = 100, accuracy = 0.263000
k = 100, accuracy = 0.256000
k = 100, accuracy = 0.263000

1
2
3
4
5
6
7
8
9
10
11
12
13
14
# plot the raw observations
for k in k_choices:
    accuracies = k_to_accuracies[k]
    plt.scatter([k] * len(accuracies), accuracies)

# plot the trend line with error bars that correspond to standard deviation
accuracies_mean = np.array([np.mean(v) for k,v in sorted(k_to_accuracies.items())])
accuracies_std = np.array([np.std(v) for k,v in sorted(k_to_accuracies.items())])
plt.errorbar(k_choices, accuracies_mean, yerr=accuracies_std)
plt.title('Cross-validation on k')
plt.xlabel('k')
plt.ylabel('Cross-validation accuracy')
plt.show()

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
# Based on the cross-validation results above, choose the best value for k,   
# retrain the classifier using all the training data, and test it on the test
# data. You should be able to get above 28% accuracy on the test data.
temp = 0
for k in k_choices:
    accuracies = k_to_accuracies[k]    
    if temp < accuracies[np.argmax(accuracies)]:
        temp = accuracies[np.argmax(accuracies)]
        best_k = k
print(best_k)


classifier = KNearestNeighbor()
classifier.train(X_train, y_train)
y_test_pred = classifier.predict(X_test, k=best_k)

# Compute and display the accuracy
num_correct = np.sum(y_test_pred == y_test)
accuracy = float(num_correct) / num_test
print('Got %d / %d correct => accuracy: %f' % (num_correct, num_test, accuracy))

1
2
3
10
Got 141 / 500 correct => accuracy: 0.282000