from builtins import range from builtins import object import numpy as np from past.builtins import xrange class KNearestNeighbor(object): """ 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. Inputs: - X: A numpy array of shape (num_train, D) containing the training data consisting of num_train samples each of dimension D. - y: A numpy array of shape (N,) containing the training labels, 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. Inputs: - X: A numpy array of shape (num_test, D) containing test data consisting of num_test samples each of dimension D. - k: The number of nearest neighbors that vote for the predicted labels. - num_loops: Determines which implementation to use to compute distances between training points and testing points. Returns: - y: A numpy array of shape (num_test,) containing predicted labels for the test data, 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. Inputs: - X: A numpy array of shape (num_test, D) containing test data. Returns: - dists: A numpy array of shape (num_test, num_train) where dists[i, j] is the Euclidean 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 range(num_test): for j in range(num_train): ##################################################################### # TODO: #计算第i个测试点与第j个训练点之间的l2距离,并将结果存储在dists[i,j]中。 #你不应使用循环和np.linalg.norm()函数。 ##################################################################### # *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)***** pass # *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)***** 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 range(num_test): ####################################################################### # TODO: #计算第i个测试点与所有训练点之间的l2距离,并将结果存储在dists[i,:]中。 #不要使用np.linalg.norm()。 ####################################################################### # *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)***** # 注意np.sum中要加上维度axis=1才能得出正确的结果 # 关于axis的介绍 # https://zhuanlan.zhihu.com/p/30960190 # 以及np.sum的介绍 # https://docs.scipy.org/doc/numpy/reference/generated/numpy.sum.html # self.X_train (5000,3072) X[i] (1,3072) (self.X_train - X[i]) (5000,3072) pass # *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)***** 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: #在不使用任何显式循环的情况下,计算所有测试点和所有训练点之间的l2距离, #并将结果存储在dists中。 #您应该仅使用基本的数组操作来实现此功能。 #不可以使用scipy中的函数以及函数np.linalg.norm()。 # #提示:尝试使用矩阵乘法和广播总和来计算l2距离。 ######################################################################### # *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)***** # (x-y)^2 = x^2 + y^2 - 2xy # reshape是为了让两个矩阵有个维度为1,这样子便可进行广播 pass # *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)***** 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. Inputs: - dists: A numpy array of shape (num_test, num_train) where dists[i, j] gives the distance betwen the ith test point and the jth training point. Returns: - y: A numpy array of shape (num_test,) containing predicted labels for the test data, where y[i] is the predicted label for the test point X[i]. """ num_test = dists.shape[0] y_pred = np.zeros(num_test) for i in range(num_test): # A list of length k storing the labels of the k nearest neighbors to # the ith test point. closest_y = [] ######################################################################### # TODO: #使用距离矩阵查找第i个测试点的k个最近邻居, #并使用self.y_train查找这些邻居的标签。 #将这些标签存储在closest_y中。 # #提示:查阅函数numpy.argsort。 ######################################################################### # *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)***** # numpy.argsort 返回排序好的数列的索引 pass # *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)***** ######################################################################### # TODO: # #现在,你已经找到了k个最近邻的标签,接着需要在closest_y中找到最可能的标签。 #将此标签存储在y_pred [i]中。如果有两个标签可能性一样的话选择索引更小的那个。 ######################################################################### # *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)***** y_pred[i] = np.bincount(closest_y).argmax() # *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)***** return y_pred