CS231n - CNN for Visual Recognition Assignment1 ---- SVM

CS231n - CNN for Visual Recognition Assignment1 —- SVM

做不出来， 我抄别人的……O(∩_∩)O~

1. linear_svm.py

import numpy as np
from random import shuffle

def svm_loss_naive(W, X, y, reg):
  """
  Structured SVM loss function, naive implementation (with loops).

  Inputs have dimension D, there are C classes, and we operate on minibatches
  of N examples.

  Inputs:
  - W: A numpy array of shape (D, C) containing weights.
  - X: A numpy array of shape (N, D) containing a minibatch of data.
  - y: A numpy array of shape (N,) containing training labels; y[i] = c means
    that X[i] has label c, where 0 <= c < C.
  - reg: (float) regularization strength

  Returns a tuple of:
  - loss as single float
  - gradient with respect to weights W; an array of same shape as W
  """
  dW = np.zeros(W.shape) # initialize the gradient as zero  (3073,10)
  #print(dW.shape)
  #print("..")

  # compute the loss and the gradient
  num_classes = W.shape[1]   #10
  num_train = X.shape[0]     #500
  loss = 0.0
  for i in xrange(num_train):
    scores = X[i].dot(W)
    correct_class_score = scores[y[i]]
    for j in xrange(num_classes):
      if j == y[i]:
        continue
      margin = scores[j] - correct_class_score + 1 # note delta = 1
      if margin > 0:
        loss += margin

        # Compute gradients (one inner and one outer sum)
        # Wonderfully compact and hard to read
        dW[:, y[i]] -= X[i, :].T # this is really a sum over j != y_i
        dW[:, j] += X[i, :].T # sums each contribution of the x_i‘s

  # Right now the loss is a sum over all training examples, but we want it
  # to be an average instead so we divide by num_train.
  loss /= num_train

  # Same with gradient
  dW /= num_train

  # Add regularization to the loss.
  loss += 0.5 * reg * np.sum(W * W)


  # Gradient regularization that carries through per https://piazza.com/class/i37qi08h43qfv?cid=118
  dW += reg*W
  #############################################################################
  # TODO:                                                                     #
  # Compute the gradient of the loss function and store it dW.                #
  # Rather that first computing the loss and then computing the derivative,   #
  # it may be simpler to compute the derivative at the same time that the     #
  # loss is being computed. As a result you may need to modify some of the    #
  # code above to compute the gradient.                                       #
  #############################################################################


  return loss, dW




def svm_loss_vectorized(W, X, y, reg):
  """
  Structured SVM loss function, vectorized implementation.

  Inputs and outputs are the same as svm_loss_naive.
  """
  loss = 0.0
  dW = np.zeros(W.shape) # initialize the gradient as zero

  #print(type(W))
  #print(type(X))

  num_classes = W.shape[1]
  num_train = X.shape[0]


  #print("shape")
  #############################################################################
  # TODO:                                                                     #
  # Implement a vectorized version of the structured SVM loss, storing the    #
  # result in loss.                                                           #
  #############################################################################
  scores = X.dot(W)
  correct_class_score = scores[np.arange(num_train), y]

  #print(scores.shape)
  #print(correct_class_score.shape)
  #print(type(scores))
  #print(type(correct_class_score))

  tmpMat = scores.T - correct_class_score + 1
  tmpMat = tmpMat.T
  tmpMat[np.arange(num_train), y] = 0

  margin = np.maximum(tmpMat, np.zeros((num_train, num_classes)))

  #print(margin.shape)
  loss = np.sum(margin)
  loss /= num_train
  loss += 0.5*reg*np.sum(W*W)
  #############################################################################
  #                             END OF YOUR CODE                              #
  #############################################################################


  #############################################################################
  # TODO:                                                                     #
  # Implement a vectorized version of the gradient for the structured SVM     #
  # loss, storing the result in dW.                                           #
  #                                                                           #
  # Hint: Instead of computing the gradient from scratch, it may be easier    #
  # to reuse some of the intermediate values that you used to compute the     #
  # loss.                                                                     #
  #############################################################################

  # Binarize into integers
  binary = margin
  binary[margin > 0] = 1

  # Perform the two operations simultaneously
  # (1) for all j: dW[j,:] = sum_{i, j produces positive margin with i} X[:,i].T
  # (2) for all i: dW[y[i],:] = sum_{j != y_i, j produces positive margin with i} -X[:,i].T
  col_sum = np.sum(binary, axis=1)
  binary[np.arange(num_train), y] = -col_sum[range(num_train)]
  dW = np.dot(X.T, binary)

  # Divide
  dW /= num_train

  # Regularize
  dW += reg*W



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

  return loss, dW

1. SVM.ipynb

# -*- coding: utf-8 -*-

__author__ = ‘ZengDong‘
#日期 =  21:03

# Run some setup code for this notebook.

import random
import numpy as np
import matplotlib.pyplot as plt

import sys;
sys.path.append("D:/Python_machinelearning/assignment1/cs231n/");

from data_utils import load_CIFAR10

"""
import imp;
data_utils = imp.load_source(‘data_utils‘, ‘D:/Python_machinelearning/assignment1/cs231n/data_utils.py‘);
load_CIFAR10 = data_utils.load_CIFAR10;
"""

# This is a bit of magic to make matplotlib figures appear inline in the notebook
# rather than in a new window.

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 the raw CIFAR-10 data.
cifar10_dir = ‘D:/Python_machinelearning/DataSet_CNN/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 ‘Training data shape: ‘, X_train.shape
print ‘Training labels shape: ‘, y_train.shape
print ‘Test data shape: ‘, X_test.shape
print ‘Test labels shape: ‘, y_test.shape

"""
Training data shape:  (50000L, 32L, 32L, 3L)
Training labels shape:  (50000L,)
Test data shape:  (10000L, 32L, 32L, 3L)
Test labels shape:  (10000L,)
"""


# Split the data into train, val, and test sets. In addition we will
# create a small development set as a subset of the training data;
# we can use this for development so our code runs faster.
num_training = 49000
num_validation = 1000
num_test = 1000
num_dev = 500

# Our validation set will be num_validation points from the original
# training set.
mask = range(num_training, num_training + num_validation)
X_val = X_train[mask]
y_val = y_train[mask]

# Our training set will be the first num_train points from the original
# training set.
mask = range(num_training)
X_train = X_train[mask]
y_train = y_train[mask]

# We will also make a development set, which is a small subset of
# the training set.
mask = np.random.choice(num_training, num_dev, replace=False)
X_dev = X_train[mask]
y_dev = y_train[mask]

# We use the first num_test points of the original test set as our
# test set.
mask = range(num_test)
X_test = X_test[mask]
y_test = y_test[mask]

print("@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@")
print ‘Train data shape: ‘, X_train.shape
print ‘Train labels shape: ‘, y_train.shape
print ‘Validation data shape: ‘, X_val.shape
print ‘Validation labels shape: ‘, y_val.shape
print ‘Test data shape: ‘, X_test.shape
print ‘Test labels shape: ‘, y_test.shape

"""
Train data shape:  (49000L, 32L, 32L, 3L)
Train labels shape:  (49000L,)
Validation data shape:  (1000L, 32L, 32L, 3L)
Validation labels shape:  (1000L,)
Test data shape:  (1000L, 32L, 32L, 3L)
Test labels shape:  (1000L,)
"""

print("##################################################")
# Preprocessing: reshape the image data into rows
X_train = np.reshape(X_train, (X_train.shape[0], -1))
X_val = np.reshape(X_val, (X_val.shape[0], -1))
X_test = np.reshape(X_test, (X_test.shape[0], -1))
X_dev = np.reshape(X_dev, (X_dev.shape[0], -1))

# As a sanity check, print out the shapes of the data
print ‘Training data shape: ‘, X_train.shape
print ‘Validation data shape: ‘, X_val.shape
print ‘Test data shape: ‘, X_test.shape
print ‘dev data shape: ‘, X_dev.shape

"""
Training data shape:  (49000L, 3072L)
Validation data shape:  (1000L, 3072L)
Test data shape:  (1000L, 3072L)
dev data shape:  (500L, 3072L)
"""

# Preprocessing: subtract the mean image
# first: compute the image mean based on the training data
mean_image = np.mean(X_train, axis=0)
print ‘mean_image shape: ‘, mean_image.shape   #mean_image shape:  (3072L,)
print mean_image[:10] # print a few of the elements
plt.figure(figsize=(4,4))
plt.imshow(mean_image.reshape((32,32,3)).astype(‘uint8‘)) # visualize the mean image
plt.show()

# second: subtract the mean image from train and test data
X_train -= mean_image
X_val -= mean_image
X_test -= mean_image
X_dev -= mean_image

# third: append the bias dimension of ones (i.e. bias trick) so that our SVM
# only has to worry about optimizing a single weight matrix W.
X_train = np.hstack([X_train, np.ones((X_train.shape[0], 1))])
X_val = np.hstack([X_val, np.ones((X_val.shape[0], 1))])
X_test = np.hstack([X_test, np.ones((X_test.shape[0], 1))])
X_dev = np.hstack([X_dev, np.ones((X_dev.shape[0], 1))])

print X_train.shape, X_val.shape, X_test.shape, X_dev.shape
#  (49000L, 3073L) (1000L, 3073L) (1000L, 3073L) (500L, 3073L)


print("$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$")
sys.path.append("D:/Python_machinelearning/assignment1/cs231n/classifiers/");
from linear_svm import svm_loss_naive
import time
# generate a random SVM weight matrix of small numbers
W = np.random.randn(3073, 10) * 0.0001
loss, grad = svm_loss_naive(W, X_dev, y_dev, 0.00001)
print ‘loss: %f‘ % (loss, )      #输出： loss: 9.043362



print("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~")
# Once you‘ve implemented the gradient, recompute it with the code below
# and gradient check it with the function we provided for you
# Compute the loss and its gradient at W.
loss, grad = svm_loss_naive(W, X_dev, y_dev, 0.0)
# Numerically compute the gradient along several randomly chosen dimensions, and
# compare them with your analytically computed gradient. The numbers should match
# almost exactly along all dimensions.
from gradient_check import grad_check_sparse
f = lambda w: svm_loss_naive(w, X_dev, y_dev, 0.0)[0]
grad_numerical = grad_check_sparse(f, W, grad)

# do the gradient check once again with regularization turned on
# you didn‘t forget the regularization gradient did you?
loss, grad = svm_loss_naive(W, X_dev, y_dev, 1e2)
f = lambda w: svm_loss_naive(w, X_dev, y_dev, 1e2)[0]
grad_numerical = grad_check_sparse(f, W, grad)

"""
numerical: 16.827422 analytic: 16.843246, relative error: 4.699724e-04
numerical: -13.503242 analytic: -13.503242, relative error: 4.030047e-12
numerical: 0.617906 analytic: 0.617906, relative error: 1.962232e-11
numerical: -27.367214 analytic: -27.367214, relative error: 5.552248e-12
numerical: 18.299706 analytic: 18.299706, relative error: 9.867578e-12
numerical: -5.215817 analytic: -5.258408, relative error: 4.066302e-03
numerical: 2.364188 analytic: 2.364188, relative error: 6.733005e-11
numerical: 19.125714 analytic: 19.125714, relative error: 1.356761e-11
numerical: 0.374473 analytic: 0.374473, relative error: 1.631035e-10
numerical: -2.294251 analytic: -2.294251, relative error: 3.794873e-11
numerical: 7.735265 analytic: 7.735265, relative error: 2.444749e-11
numerical: 2.500460 analytic: 2.500460, relative error: 1.385820e-10
numerical: 6.770408 analytic: 6.770408, relative error: 1.792641e-11
numerical: -5.573265 analytic: -5.573265, relative error: 2.852371e-11
numerical: 29.499605 analytic: 29.499605, relative error: 1.710384e-12
numerical: 32.738558 analytic: 32.738558, relative error: 1.267704e-12
numerical: 7.342918 analytic: 7.342918, relative error: 2.764887e-11
numerical: 14.070289 analytic: 14.070289, relative error: 1.837961e-11
numerical: -11.101269 analytic: -11.101269, relative error: 6.572489e-12
numerical: 12.151276 analytic: 12.151276, relative error: 2.921727e-11
"""

# Next implement the function svm_loss_vectorized; for now only compute the loss;
# we will implement the gradient in a moment.
tic = time.time()
loss_naive, grad_naive = svm_loss_naive(W, X_dev, y_dev, 0.00001)
toc = time.time()
print ‘Naive loss: %e computed in %fs‘ % (loss_naive, toc - tic)

from linear_svm import svm_loss_vectorized
tic = time.time()
loss_vectorized, _ = svm_loss_vectorized(W, X_dev, y_dev, 0.00001)
toc = time.time()
print ‘Vectorized loss: %e computed in %fs‘ % (loss_vectorized, toc - tic)

# The losses should match but your vectorized implementation should be much faster.
print ‘difference: %f‘ % (loss_naive - loss_vectorized)

"""
Naive loss: 8.352418e+00 computed in 0.186000s
Vectorized loss: 8.352418e+00 computed in 0.013000s
difference: -0.000000
"""



# Complete the implementation of svm_loss_vectorized, and compute the gradient
# of the loss function in a vectorized way.

# The naive implementation and the vectorized implementation should match, but
# the vectorized version should still be much faster.
tic = time.time()
_, grad_naive = svm_loss_naive(W, X_dev, y_dev, 0.00001)
toc = time.time()
print ‘Naive loss and gradient: computed in %fs‘ % (toc - tic)

tic = time.time()
_, grad_vectorized = svm_loss_vectorized(W, X_dev, y_dev, 0.00001)
toc = time.time()
print ‘Vectorized loss and gradient: computed in %fs‘ % (toc - tic)

# The loss is a single number, so it is easy to compare the values computed
# by the two implementations. The gradient on the other hand is a matrix, so
# we use the Frobenius norm to compare them.
difference = np.linalg.norm(grad_naive - grad_vectorized, ord=‘fro‘)
print ‘difference: %f‘ % difference

"""
Naive loss and gradient: computed in 0.206000s
Vectorized loss and gradient: computed in 0.011000s
difference: 0.000000
"""


# In the file linear_classifier.py, implement SGD in the function
# LinearClassifier.train() and then run it with the code below.
sys.path.append("D:/Python_machinelearning/assignment1/cs231n/classifiers/");
from linear_classifier import LinearSVM
svm = LinearSVM()
tic = time.time()
loss_hist = svm.train(X_train, y_train, learning_rate=1e-7, reg=5e4,
                      num_iters=1500, verbose=True)
toc = time.time()
print ‘That took %fs‘ % (toc - tic)

"""
iteration 0 / 1500: loss 779.051222
iteration 100 / 1500: loss 284.127354
iteration 200 / 1500: loss 106.113881
iteration 300 / 1500: loss 42.507745
iteration 400 / 1500: loss 19.020714
iteration 500 / 1500: loss 9.490041
iteration 600 / 1500: loss 7.215475
iteration 700 / 1500: loss 5.842398
iteration 800 / 1500: loss 5.920409
iteration 900 / 1500: loss 5.481854
iteration 1000 / 1500: loss 5.386083
iteration 1100 / 1500: loss 5.165029
iteration 1200 / 1500: loss 5.188355
iteration 1300 / 1500: loss 5.219570
iteration 1400 / 1500: loss 5.166124
That took 11.233000s
"""

# A useful debugging strategy is to plot the loss as a function of
# iteration number:
plt.plot(loss_hist)
plt.xlabel(‘Iteration number‘)
plt.ylabel(‘Loss value‘)
plt.show()



# Write the LinearSVM.predict function and evaluate the performance on both the
# training and validation set
print(X_train.shape)   #(49000L, 3073L)
print(y_train.shape)   #(49000L,)
y_train_pred = svm.predict(X_train)
print ‘training accuracy: %f‘ % (np.mean(y_train == y_train_pred), )    #training accuracy: 0.365224
y_val_pred = svm.predict(X_val)
print ‘validation accuracy: %f‘ % (np.mean(y_val == y_val_pred), )      #validation accuracy: 0.385000


# Use the validation set to tune hyperparameters (regularization strength and
# learning rate). You should experiment with different ranges for the learning
# rates and regularization strengths; if you are careful you should be able to
# get a classification accuracy of about 0.4 on the validation set.
learning_rates = [1e-7, 5e-5]
regularization_strengths = [5e4, 1e5]

# results is dictionary mapping tuples of the form
# (learning_rate, regularization_strength) to tuples of the form
# (training_accuracy, validation_accuracy). The accuracy is simply the fraction
# of data points that are correctly classified.
results = {}
best_val = -1   # The highest validation accuracy that we have seen so far.
best_svm = None # The LinearSVM object that achieved the highest validation rate.

################################################################################
# TODO:                                                                        #
# Write code that chooses the best hyperparameters by tuning on the validation #
# set. For each combination of hyperparameters, train a linear SVM on the      #
# training set, compute its accuracy on the training and validation sets, and  #
# store these numbers in the results dictionary. In addition, store the best   #
# validation accuracy in best_val and the LinearSVM object that achieves this  #
# accuracy in best_svm.                                                        #
#                                                                              #
# Hint: You should use a small value for num_iters as you develop your         #
# validation code so that the SVMs don‘t take much time to train; once you are #
# confident that your validation code works, you should rerun the validation   #
# code with a larger value for num_iters.                                      #
################################################################################
iters = 2000 #100
for lr in learning_rates:
    for rs in regularization_strengths:
        svm = LinearSVM()
        svm.train(X_train, y_train, learning_rate=lr, reg=rs, num_iters=iters)

        y_train_pred = svm.predict(X_train)
        acc_train = np.mean(y_train == y_train_pred)
        y_val_pred = svm.predict(X_val)
        acc_val = np.mean(y_val == y_val_pred)

        results[(lr, rs)] = (acc_train, acc_val)

        if best_val < acc_val:
            best_val = acc_val
            best_svm = svm
################################################################################
#                              END OF YOUR CODE                                #
################################################################################

# 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 1.000000e-07 reg 5.000000e+04 train accuracy: 0.365918 val accuracy: 0.382000
lr 1.000000e-07 reg 1.000000e+05 train accuracy: 0.356306 val accuracy: 0.359000
lr 5.000000e-05 reg 5.000000e+04 train accuracy: 0.100265 val accuracy: 0.087000
lr 5.000000e-05 reg 1.000000e+05 train accuracy: 0.100265 val accuracy: 0.087000
best validation accuracy achieved during cross-validation: 0.382000
"""


# Visualize the cross-validation results
import math
x_scatter = [math.log10(x[0]) for x in results]
y_scatter = [math.log10(x[1]) for x in results]

# plot training accuracy
marker_size = 100
colors = [results[x][0] for x in results]
plt.subplot(2, 1, 1)
plt.scatter(x_scatter, y_scatter, marker_size, c=colors)
plt.colorbar()
plt.xlabel(‘log learning rate‘)
plt.ylabel(‘log regularization strength‘)
plt.title(‘CIFAR-10 training accuracy‘)

# plot validation accuracy
colors = [results[x][1] for x in results] # default size of markers is 20
plt.subplot(2, 1, 2)
plt.scatter(x_scatter, y_scatter, marker_size, c=colors)
plt.colorbar()
plt.xlabel(‘log learning rate‘)
plt.ylabel(‘log regularization strength‘)
plt.title(‘CIFAR-10 validation accuracy‘)
plt.show()


# Evaluate the best svm on test set
y_test_pred = best_svm.predict(X_test)
test_accuracy = np.mean(y_test == y_test_pred)
print ‘linear SVM on raw pixels final test set accuracy: %f‘ % test_accuracy

"""
linear SVM on raw pixels final test set accuracy: 0.357000
"""



# Visualize the learned weights for each class.
# Depending on your choice of learning rate and regularization strength, these may
# or may not be nice to look at.
w = best_svm.W[:-1,:] # strip out the bias
w = w.reshape(32, 32, 3, 10)
w_min, w_max = np.min(w), np.max(w)
classes = [‘plane‘, ‘car‘, ‘bird‘, ‘cat‘, ‘deer‘, ‘dog‘, ‘frog‘, ‘horse‘, ‘ship‘, ‘truck‘]
for i in xrange(10):
  plt.subplot(2, 5, i + 1)
  # Rescale the weights to be between 0 and 255
  wimg = 255.0 * (w[:, :, :, i].squeeze() - w_min) / (w_max - w_min)
  plt.imshow(wimg.astype(‘uint8‘))
  plt.axis(‘off‘)
  plt.title(classes[i])

plt.show()

部分截图：