[CS231n@Stanford] Assignment1-Q2 (python) SVM实现

linear_svm.py

<span style="font-size:18px;">import numpy as npfrom random import shuffledef 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  # compute the loss and the gradient  num_classes = W.shape[1]  num_train = X.shape[0]  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        dW[:, j] += X[i].T        dW[:, y[i]] -= X[i].T          # 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  # Add regularization to the loss.  loss += 0.5 * reg * np.sum(W * 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.                                       #  #############################################################################  dW  = dW/num_train + reg * W  return loss, dWdef 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  #############################################################################  # TODO:                                                                     #  # Implement a vectorized version of the structured SVM loss, storing the    #  # result in loss.                                                           #  #############################################################################  num_train = X.shape[0]  num_classes = W.shape[1]  scores = X.dot(W)    scores_correct = scores[np.arange(num_train), y]     scores_correct = np.reshape(scores_correct, (num_train, 1))    margins = scores - scores_correct + 1.0   margins[np.arange(num_train), y] = 0.0  margins[margins <= 0] = 0.0  loss = np.sum(margins)  loss /= num_train  loss += 0.5 * reg * np.sum(W * W)  pass  #############################################################################  #                             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.                                                                     #  #############################################################################    margins[margins > 0] = 1.0  margins[np.arange(num_train), y] = -np.sum(margins, axis=1)   dW += np.dot(X.T, margins)/num_train + reg * W     # D by C    pass  #############################################################################  #                             END OF YOUR CODE                              #  #############################################################################  return loss, dW</span>

linear_classifier.py

<span style="font-size:18px;">import numpy as npfrom linear_svm import *from softmax import *class LinearClassifier(object):  def __init__(self):    self.W = None  def train(self, X, y, learning_rate=1e-3, reg=1e-5, num_iters=100,            batch_size=200, verbose=False):    """    Train this linear classifiers using stochastic gradient descent.    Inputs:    - X: A numpy array of shape (N, D) containing training data; there are N      training samples each of dimension D.    - y: A numpy array of shape (N,) containing training labels; y[i] = c      means that X[i] has label 0 <= c < C for C classes.    - learning_rate: (float) learning rate for optimization.    - reg: (float) regularization strength.    - num_iters: (integer) number of steps to take when optimizing    - batch_size: (integer) number of training examples to use at each step.    - verbose: (boolean) If true, print progress during optimization.    Outputs:    A list containing the value of the loss function at each training iteration.    """    num_train, dim = X.shape    num_classes = np.max(y) + 1 # assume y takes values 0...K-1 where K is number of classes    if self.W is None:      # lazily initialize W      self.W = 0.001 * np.random.randn(dim, num_classes)    # Run stochastic gradient descent to optimize W    loss_history = []    for it in xrange(num_iters):      X_batch = None      y_batch = None      #########################################################################      # TODO:                                                                 #      # Sample batch_size elements from the training data and their           #      # corresponding labels to use in this round of gradient descent.        #      # Store the data in X_batch and their corresponding labels in           #      # y_batch; after sampling X_batch should have shape (dim, batch_size)   #      # and y_batch should have shape (batch_size,)                           #      #                                                                       #      # Hint: Use np.random.choice to generate indices. Sampling with         #      # replacement is faster than sampling without replacement.              #      #########################################################################           sample_index = np.random.choice(num_train, batch_size ,replace = False)      X_batch = X[sample_index,:]      y_batch = y[sample_index]                  pass      #########################################################################      #                       END OF YOUR CODE                                #      #########################################################################      # evaluate loss and gradient      loss, grad = self.loss(X_batch, y_batch, reg)      loss_history.append(loss)      # perform parameter update      #########################################################################      # TODO:                                                                 #      # Update the weights using the gradient and the learning rate.          #      #########################################################################      self.W -= learning_rate * grad            pass      #########################################################################      #                       END OF YOUR CODE                                #      #########################################################################      if verbose and it % 100 == 0:        print 'iteration %d / %d: loss %f' % (it, num_iters, loss)    return loss_history  def predict(self, X):    """    Use the trained weights of this linear classifiers to predict labels for    data points.    Inputs:    - X: D x N array of training data. Each column is a D-dimensional point.    Returns:    - y_pred: Predicted labels for the data in X. y_pred is a 1-dimensional      array of length N, and each element is an integer giving the predicted      class.    """    y_pred = np.zeros(X.shape[1])    ###########################################################################    # TODO:                                                                   #    # Implement this method. Store the predicted labels in y_pred.            #    ###########################################################################    pass       scores = X.dot(self.W)    y_pred = np.argmax(scores, axis = 1)        ###########################################################################    #                           END OF YOUR CODE                              #    ###########################################################################    return y_pred    def loss(self, X_batch, y_batch, reg):    """    Compute the loss function and its derivative.     Subclasses will override this.    Inputs:    - X_batch: A numpy array of shape (N, D) containing a minibatch of N      data points; each point has dimension D.    - y_batch: A numpy array of shape (N,) containing labels for the minibatch.    - reg: (float) regularization strength.    Returns: A tuple containing:    - loss as a single float    - gradient with respect to self.W; an array of the same shape as W    """    passclass LinearSVM(LinearClassifier):  """ A subclass that uses the Multiclass SVM loss function """  def loss(self, X_batch, y_batch, reg):    return svm_loss_vectorized(self.W, X_batch, y_batch, reg)class Softmax(LinearClassifier):  """ A subclass that uses the Softmax + Cross-entropy loss function """  def loss(self, X_batch, y_batch, reg):    return softmax_loss_vectorized(self.W, X_batch, y_batch, reg)</span><span style="font-size:14px;"></span>

svm.ipynb的需完成代码

<span style="font-size:18px;"># In the file linear_classifier.py, implement SGD in the function# LinearClassifier.train() and then run it with the code below.from linear_classifier import LinearSVM# 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.                                      #################################################################################passiters = 2000for lr in learning_rates:    for reg in regularization_strengths:        svm = LinearSVM()        svm.train(X_train, y_train, learning_rate=lr, reg=reg, 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, reg)] = (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</span>

lr 1.000000e-07 reg 5.000000e+04 train accuracy: 0.370367 val accuracy: 0.375000
lr 1.000000e-07 reg 1.000000e+05 train accuracy: 0.354571 val accuracy: 0.364000
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: 0.375000
linear SVM on raw pixels final test set accuracy: 0.369000