features


Image features exercise

Complete and hand in this completed worksheet (including its outputs and any supporting code outside of the worksheet) with your assignment submission. For more details see the assignments page on the course website.

We have seen that we can achieve reasonable performance on an image classification task by training a linear classifier on the pixels of the input image. In this exercise we will show that we can improve our classification performance by training linear classifiers not on raw pixels but on features that are computed from the raw pixels.

All of your work for this exercise will be done in this notebook.


In [2]:
import random
import numpy as np
from cs231n.data_utils import load_CIFAR10
import matplotlib.pyplot as plt
%matplotlib inline
plt.rcParams['figure.figsize'] = (10.0, 8.0) # set default size of plots
plt.rcParams['image.interpolation'] = 'nearest'
plt.rcParams['image.cmap'] = 'gray'

# for auto-reloading extenrnal modules
# see http://stackoverflow.com/questions/1907993/autoreload-of-modules-in-ipython
%load_ext autoreload
%autoreload 2

Load data

Similar to previous exercises, we will load CIFAR-10 data from disk.


In [3]:
from cs231n.features import color_histogram_hsv, hog_feature

def get_CIFAR10_data(num_training=49000, num_validation=1000, num_test=1000):
  # 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)
  
  # Subsample the data
  mask = range(num_training, num_training + num_validation)
  X_val = X_train[mask]
  y_val = y_train[mask]
  mask = range(num_training)
  X_train = X_train[mask]
  y_train = y_train[mask]
  mask = range(num_test)
  X_test = X_test[mask]
  y_test = y_test[mask]

  return X_train, y_train, X_val, y_val, X_test, y_test

X_train, y_train, X_val, y_val, X_test, y_test = get_CIFAR10_data()

Extract Features

For each image we will compute a Histogram of Oriented Gradients (HOG) as well as a color histogram using the hue channel in HSV color space. We form our final feature vector for each image by concatenating the HOG and color histogram feature vectors.

Roughly speaking, HOG should capture the texture of the image while ignoring color information, and the color histogram represents the color of the input image while ignoring texture. As a result, we expect that using both together ought to work better than using either alone. Verifying this assumption would be a good thing to try for the bonus section.

The hog_feature and color_histogram_hsv functions both operate on a single image and return a feature vector for that image. The extract_features function takes a set of images and a list of feature functions and evaluates each feature function on each image, storing the results in a matrix where each column is the concatenation of all feature vectors for a single image.


In [4]:
from cs231n.features import *

num_color_bins = 10 # Number of bins in the color histogram
feature_fns = [hog_feature, lambda img: color_histogram_hsv(img, nbin=num_color_bins)]
X_train_feats = extract_features(X_train, feature_fns, verbose=True)
X_val_feats = extract_features(X_val, feature_fns)
X_test_feats = extract_features(X_test, feature_fns)

# Preprocessing: Subtract the mean feature
mean_feat = np.mean(X_train_feats, axis=0, keepdims=True)
X_train_feats -= mean_feat
X_val_feats -= mean_feat
X_test_feats -= mean_feat

# Preprocessing: Divide by standard deviation. This ensures that each feature
# has roughly the same scale.
std_feat = np.std(X_train_feats, axis=0, keepdims=True)
X_train_feats /= std_feat
X_val_feats /= std_feat
X_test_feats /= std_feat

# Preprocessing: Add a bias dimension
X_train_feats = np.hstack([X_train_feats, np.ones((X_train_feats.shape[0], 1))])
X_val_feats = np.hstack([X_val_feats, np.ones((X_val_feats.shape[0], 1))])
X_test_feats = np.hstack([X_test_feats, np.ones((X_test_feats.shape[0], 1))])


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Train SVM on features

Using the multiclass SVM code developed earlier in the assignment, train SVMs on top of the features extracted above; this should achieve better results than training SVMs directly on top of raw pixels.


In [6]:
# Use the validation set to tune the learning rate and regularization strength

from cs231n.classifiers.linear_classifier import LinearSVM

learning_rates = [-9, -7]
regularization_strengths = [5, 7]

results = {}
best_val = -1
best_svm = None

for _ in np.arange(50):
    i = 10 ** np.random.uniform(low=learning_rates[0], high=learning_rates[1])
    j = 10 ** np.random.uniform(low=regularization_strengths[0], high=regularization_strengths[1])
    
    svm = LinearSVM()
    svm.train(X_train_feats, y_train, learning_rate=i, reg=j, 
              num_iters=500, verbose=False)
    y_train_pred = svm.predict(X_train_feats)
    y_val_pred = svm.predict(X_val_feats)
    accuracy = (np.mean(y_train == y_train_pred), np.mean(y_val == y_val_pred))
    
    results[(i, j)] = accuracy
    
    if accuracy[1] > best_val:
        best_val = accuracy[1]

# Print out results.
for lr, reg in sorted(results):
    train_accuracy, val_accuracy = results[(lr, reg)]
    print 'lr %e reg %e train accuracy: %f val accuracy: %f' % (
                lr, reg, train_accuracy, val_accuracy)
    
print 'best validation accuracy achieved during cross-validation: %f' % best_val


lr 1.351903e-09 reg 3.640846e+05 train accuracy: 0.090898 val accuracy: 0.097000
lr 1.377683e-09 reg 1.311876e+06 train accuracy: 0.093347 val accuracy: 0.106000
lr 1.578317e-09 reg 7.898379e+05 train accuracy: 0.096571 val accuracy: 0.105000
lr 1.681934e-09 reg 3.898770e+05 train accuracy: 0.111020 val accuracy: 0.115000
lr 1.817105e-09 reg 1.839318e+05 train accuracy: 0.098755 val accuracy: 0.099000
lr 1.853345e-09 reg 4.239745e+05 train accuracy: 0.098918 val accuracy: 0.091000
lr 2.020276e-09 reg 5.165705e+06 train accuracy: 0.085816 val accuracy: 0.088000
lr 2.057186e-09 reg 2.613527e+06 train accuracy: 0.096694 val accuracy: 0.108000
lr 2.131929e-09 reg 3.449305e+06 train accuracy: 0.116959 val accuracy: 0.107000
lr 2.159976e-09 reg 2.189374e+06 train accuracy: 0.107837 val accuracy: 0.092000
lr 2.928315e-09 reg 1.429740e+06 train accuracy: 0.100327 val accuracy: 0.100000
lr 2.931493e-09 reg 2.505679e+06 train accuracy: 0.095082 val accuracy: 0.106000
lr 3.114981e-09 reg 2.710443e+06 train accuracy: 0.078265 val accuracy: 0.096000
lr 3.827814e-09 reg 1.115571e+05 train accuracy: 0.114857 val accuracy: 0.104000
lr 3.879153e-09 reg 9.557604e+06 train accuracy: 0.412837 val accuracy: 0.413000
lr 3.914654e-09 reg 4.175428e+05 train accuracy: 0.103082 val accuracy: 0.095000
lr 3.919152e-09 reg 1.309679e+06 train accuracy: 0.116143 val accuracy: 0.133000
lr 3.994593e-09 reg 5.542440e+05 train accuracy: 0.104980 val accuracy: 0.097000
lr 4.096986e-09 reg 7.157264e+05 train accuracy: 0.100857 val accuracy: 0.102000
lr 4.485718e-09 reg 1.019602e+06 train accuracy: 0.117857 val accuracy: 0.114000
lr 4.947825e-09 reg 1.456330e+05 train accuracy: 0.093980 val accuracy: 0.085000
lr 4.984726e-09 reg 1.025782e+06 train accuracy: 0.083429 val accuracy: 0.071000
lr 5.052492e-09 reg 1.010971e+06 train accuracy: 0.107837 val accuracy: 0.100000
lr 5.532731e-09 reg 4.253397e+06 train accuracy: 0.415510 val accuracy: 0.429000
lr 6.780723e-09 reg 2.649520e+06 train accuracy: 0.344224 val accuracy: 0.352000
lr 7.097746e-09 reg 2.959628e+05 train accuracy: 0.112388 val accuracy: 0.103000
lr 7.929478e-09 reg 1.111766e+05 train accuracy: 0.090408 val accuracy: 0.083000
lr 8.202979e-09 reg 6.013330e+06 train accuracy: 0.408755 val accuracy: 0.407000
lr 9.463424e-09 reg 1.686360e+05 train accuracy: 0.083122 val accuracy: 0.092000
lr 1.050412e-08 reg 2.428202e+06 train accuracy: 0.419673 val accuracy: 0.428000
lr 1.097201e-08 reg 8.777657e+06 train accuracy: 0.401857 val accuracy: 0.417000
lr 1.190135e-08 reg 3.513147e+05 train accuracy: 0.095959 val accuracy: 0.094000
lr 1.277806e-08 reg 1.222194e+05 train accuracy: 0.103000 val accuracy: 0.112000
lr 1.495717e-08 reg 1.967125e+05 train accuracy: 0.096571 val accuracy: 0.106000
lr 1.520432e-08 reg 8.715570e+05 train accuracy: 0.202755 val accuracy: 0.198000
lr 2.162436e-08 reg 1.055675e+06 train accuracy: 0.418469 val accuracy: 0.432000
lr 2.385691e-08 reg 1.769879e+06 train accuracy: 0.418735 val accuracy: 0.412000
lr 2.423605e-08 reg 1.791804e+06 train accuracy: 0.408939 val accuracy: 0.411000
lr 3.310291e-08 reg 1.068150e+05 train accuracy: 0.079245 val accuracy: 0.072000
lr 3.968540e-08 reg 1.270340e+05 train accuracy: 0.094918 val accuracy: 0.069000
lr 4.112457e-08 reg 7.947090e+05 train accuracy: 0.415531 val accuracy: 0.422000
lr 4.295785e-08 reg 1.018801e+06 train accuracy: 0.410939 val accuracy: 0.418000
lr 4.432005e-08 reg 8.940344e+05 train accuracy: 0.410306 val accuracy: 0.420000
lr 4.618851e-08 reg 1.972912e+06 train accuracy: 0.402714 val accuracy: 0.396000
lr 4.778397e-08 reg 7.733215e+06 train accuracy: 0.383980 val accuracy: 0.367000
lr 5.246924e-08 reg 2.861729e+06 train accuracy: 0.394143 val accuracy: 0.374000
lr 6.092357e-08 reg 2.168515e+06 train accuracy: 0.400224 val accuracy: 0.406000
lr 6.208234e-08 reg 1.182245e+05 train accuracy: 0.134959 val accuracy: 0.132000
lr 7.828385e-08 reg 1.786401e+06 train accuracy: 0.398755 val accuracy: 0.409000
lr 8.039514e-08 reg 2.592170e+06 train accuracy: 0.412571 val accuracy: 0.403000
best validation accuracy achieved during cross-validation: 0.432000

In [7]:
# Get the best hyperparameter from result
best_lr = 0.0
best_reg = 0.0

for lr, reg in results:
    if results[(lr, reg)][1] == best_val:
        best_lr = lr
        best_reg = reg
        break
        
print 'Best learning rate: %f, best regularisation strength: %f' % (best_lr, best_reg, )


Best learning rate: 0.000000, best regularisation strength: 1055675.439204

In [8]:
# Train the classifier with the best hyperparameters
best_svm = LinearSVM()
loss_hist = best_svm.train(X_train_feats, y_train, learning_rate=best_lr, reg=best_reg, 
                           num_iters=2000, verbose=True)

# plot the loss as a function of iteration number:
plt.plot(loss_hist)
plt.xlabel('Iteration number')
plt.ylabel('Loss value')
plt.show()


iteration 0 / 2000: loss 820.123936
iteration 100 / 2000: loss 17.002393
iteration 200 / 2000: loss 9.078919
iteration 300 / 2000: loss 9.000740
iteration 400 / 2000: loss 8.999976
iteration 500 / 2000: loss 8.999967
iteration 600 / 2000: loss 8.999970
iteration 700 / 2000: loss 8.999967
iteration 800 / 2000: loss 8.999965
iteration 900 / 2000: loss 8.999970
iteration 1000 / 2000: loss 8.999972
iteration 1100 / 2000: loss 8.999964
iteration 1200 / 2000: loss 8.999968
iteration 1300 / 2000: loss 8.999971
iteration 1400 / 2000: loss 8.999969
iteration 1500 / 2000: loss 8.999967
iteration 1600 / 2000: loss 8.999971
iteration 1700 / 2000: loss 8.999968
iteration 1800 / 2000: loss 8.999970
iteration 1900 / 2000: loss 8.999964

In [9]:
# Evaluate your trained SVM on the test set
y_test_pred = best_svm.predict(X_test_feats)
test_accuracy = np.mean(y_test == y_test_pred)
print test_accuracy


0.415

In [10]:
# An important way to gain intuition about how an algorithm works is to
# visualize the mistakes that it makes. In this visualization, we show examples
# of images that are misclassified by our current system. The first column
# shows images that our system labeled as "plane" but whose true label is
# something other than "plane".

examples_per_class = 8
classes = ['plane', 'car', 'bird', 'cat', 'deer', 'dog', 'frog', 'horse', 'ship', 'truck']
for cls, cls_name in enumerate(classes):
    idxs = np.where((y_test != cls) & (y_test_pred == cls))[0]
    idxs = np.random.choice(idxs, examples_per_class, replace=False)
    for i, idx in enumerate(idxs):
        plt.subplot(examples_per_class, len(classes), i * len(classes) + cls + 1)
        plt.imshow(X_test[idx].astype('uint8'))
        plt.axis('off')
        if i == 0:
            plt.title(cls_name)
plt.show()


Inline question 1:

Describe the misclassification results that you see. Do they make sense?

Neural Network on image features

Earlier in this assigment we saw that training a two-layer neural network on raw pixels achieved better classification performance than linear classifiers on raw pixels. In this notebook we have seen that linear classifiers on image features outperform linear classifiers on raw pixels.

For completeness, we should also try training a neural network on image features. This approach should outperform all previous approaches: you should easily be able to achieve over 55% classification accuracy on the test set; our best model achieves about 60% classification accuracy.


In [11]:
print X_train_feats.shape


(49000, 155)

In [ ]:
from cs231n.classifiers.neural_net import TwoLayerNet

input_dim = X_train_feats.shape[1]
hidden_dim = 200
num_classes = 10

net = TwoLayerNet(input_dim, hidden_dim, num_classes)
best_net = None

learning = [1e-5, 1]
regularization = [1e0, 1e4]
decay = [0.9, 1]

results = {}
best_val = -1

for _ in np.arange(0, 50):
    i = np.random.uniform(low=learning[0], high=learning[1])
    j = np.random.uniform(low=regularization[0], high=regularization[1])
    k = np.random.uniform(low=decay[0], high=decay[1])

    # Train the network
    net = TwoLayerNet(input_dim, hidden_dim, num_classes)
    stats = net.train(X_train_feats, y_train, X_val_feats, y_val,
                      num_iters=500, batch_size=200,
                      learning_rate=i, learning_rate_decay=k,
                      reg=j, verbose=False)

    # Predict on the validation set
    val_acc = (net.predict(X_val_feats) == y_val).mean()
    
    results[(i, j, k)] = val_acc
    if val_acc > best_val:
        best_val = val_acc
        best_net = net
        
for i, j, k in results:
    print 'lr: %f, reg: %f, dec: %f -> %f' % (i, j, k, results[(i, j, k)])

In [23]:
print best_val

# Find the best learning rate and regularization strength
best_lr = 0.
best_reg = 0.
best_decay = 0.

for lr, reg, dec in sorted(results):
    if results[(lr, reg, dec)] == best_val:
        best_lr = lr
        best_reg = reg
        best_decay = dec
        break
        
print best_lr, best_decay, best_reg

stats = best_net.train(X_train_feats, y_train, X_val_feats, y_val,
                       num_iters=2000, batch_size=400,
                       learning_rate=best_lr, learning_rate_decay=best_decay,
                       reg=best_reg, verbose=True)


0.107
0.000871479072444 0.930937309316 0.0910125679303
iteration 0 / 2000: loss 2.302702
iteration 100 / 2000: loss 2.302475
iteration 200 / 2000: loss 2.302590
iteration 300 / 2000: loss 2.302459
iteration 400 / 2000: loss 2.302579
iteration 500 / 2000: loss 2.302654
iteration 600 / 2000: loss 2.302253
iteration 700 / 2000: loss 2.302533
iteration 800 / 2000: loss 2.302543
iteration 900 / 2000: loss 2.302380
iteration 1000 / 2000: loss 2.302541
iteration 1100 / 2000: loss 2.302705
iteration 1200 / 2000: loss 2.302548
iteration 1300 / 2000: loss 2.302359
iteration 1400 / 2000: loss 2.302471
iteration 1500 / 2000: loss 2.302709
iteration 1600 / 2000: loss 2.302449
iteration 1700 / 2000: loss 2.302500
iteration 1800 / 2000: loss 2.302909
iteration 1900 / 2000: loss 2.302310

In [22]:
# Run your neural net classifier on the test set. You should be able to
# get more than 55% accuracy.

test_acc = (best_net.predict(X_test_feats) == y_test).mean()
print test_acc


0.1

Bonus: Design your own features!

You have seen that simple image features can improve classification performance. So far we have tried HOG and color histograms, but other types of features may be able to achieve even better classification performance.

For bonus points, design and implement a new type of feature and use it for image classification on CIFAR-10. Explain how your feature works and why you expect it to be useful for image classification. Implement it in this notebook, cross-validate any hyperparameters, and compare its performance to the HOG + Color histogram baseline.

Bonus: Do something extra!

Use the material and code we have presented in this assignment to do something interesting. Was there another question we should have asked? Did any cool ideas pop into your head as you were working on the assignment? This is your chance to show off!