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
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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()
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.
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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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# 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
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# 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, )
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()
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# 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
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()
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.
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print X_train_feats.shape
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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)])
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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)
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# 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
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.