CNN for Visual Recognition (assignment1_Q1)

参考：http://cs231n.github.io/assignment1/

Q1: k-Nearest Neighbor classifier (30 points)

import numpy as np
from matplotlib.cbook import todate

class KNearestNeighbor:
  """ a kNN classifier with L2 distance """

  def __init__(self):
    pass

  def train(self, X, y):
    """
    Train the classifier. For k-nearest neighbors this is just 
    memorizing the training data.

    Input:
    X - A num_train x dimension array where each row is a training point.
    y - A vector of length num_train, where y[i] is the label for X[i, :]
    """
    self.X_train = X
    self.y_train = y
    
  def predict(self, X, k=1, num_loops=0):
    """
    Predict labels for test data using this classifier.

    Input:
    X - A num_test x dimension array where each row is a test point.
    k - The number of nearest neighbors that vote for predicted label
    num_loops - Determines which method to use to compute distances
                between training points and test points.

    Output:
    y - A vector of length num_test, where y[i] is the predicted label for the
        test point X[i, :].
    """
    if num_loops == 0:
      dists = self.compute_distances_no_loops(X)
    elif num_loops == 1:
      dists = self.compute_distances_one_loop(X)
    elif num_loops == 2:
      dists = self.compute_distances_two_loops(X)
    else:
      raise ValueError('Invalid value %d for num_loops' % num_loops)

    return self.predict_labels(dists, k=k)

  def compute_distances_two_loops(self, X):
    """
    Compute the distance between each test point in X and each training point
    in self.X_train using a nested loop over both the training data and the 
    test data.

    Input:
    X - An num_test x dimension array where each row is a test point.

    Output:
    dists - A num_test x num_train array where dists[i, j] is the distance
            between the ith test 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))
    for i in xrange(num_test):
      for j in xrange(num_train):
        #####################################################################
        # TODO:                                                             #
        # Compute the l2 distance between the ith test point and the jth    #
        # training point, and store the result in dists[i, j]               #
        #####################################################################
        dists[i,j] = np.sqrt(np.sum(np.square(X[i,:] - self.X_train[j,:])))
        #####################################################################
        #                       END OF YOUR CODE                            #
        #####################################################################
    return dists

  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))
      #######################################################################
      #                         END OF YOUR CODE                            #
      #######################################################################
    return dists

  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.                                                                #
    # HINT: Try to formulate the l2 distance using matrix multiplication    #
    #       and two broadcast sums.                                         #
    #########################################################################
    tDot = np.multiply(np.dot(X, self.X_train.T), -2)
    t1 = np.sum(np.square(X), axis=1, keepdims=True)
    t2 = np.sum(np.square(self.X_train), axis=1)
    tDot = np.add(t1, tDot)
    tDot = np.add(tDot, t2)
    dists = np.sqrt(tDot)
    #########################################################################
    #                         END OF YOUR CODE                              #
    #########################################################################
    return dists

  def predict_labels(self, dists, k=1):
    """
    Given a matrix of distances between test points and training points,
    predict a label for each test point.

    Input:
    dists - A num_test x num_train array where dists[i, j] gives the distance
            between the ith test point and the jth training point.

    Output:
    y - A vector of length num_test where y[i] is the predicted label for the
        ith test point.
    """
    num_test = dists.shape[0]
    y_pred = np.zeros(num_test)
    for i in xrange(num_test):
      # A list of length k storing the labels of the k nearest neighbors to
      # the ith test point.
      closest_y = []
      #########################################################################
      # TODO:                                                                 #
      # Use the distance matrix to find the k nearest neighbors of the ith    #
      # training point, and use self.y_train to find the labels of these      #
      # neighbors. Store these labels in closest_y.                           #
      # Hint: Look up the function numpy.argsort.                             #
      #########################################################################
      # pass
      closest_y = self.y_train[np.argsort(dists[i, :])[:k]]
      #########################################################################
      # TODO:                                                                 #
      # Now that you have found the labels of the k nearest neighbors, you    #
      # need to find the most common label in the list closest_y of labels.   #
      # Store this label in y_pred[i]. Break ties by choosing the smaller     #
      # label.                                                                #
      #########################################################################
      
      y_pred[i] = np.argmax(np.bincount(closest_y))
      #########################################################################
      #                           END OF YOUR CODE                            # 
      #########################################################################

    return y_pred

 

输出：

Two loop version took 55.817642 seconds
One loop version took 49.692089 seconds
No loop version took 1.267753 seconds