CS231n----assignment1 -notes for KNN

前言

自学了一段时间的cs231n的课程，但是由于python工具掌握并不熟练，暂时无法独自完成作业任务，将有借鉴代码。

k-Nearest Neighbor

1、Knn：k-Nearest Neighbor（K邻近分类），计算已知标签的训练集和测试集的距离（距离算法有很多种如：将两张图片先转化为两个向量I_1和I_2，然后让他们相减取绝对值为L1），统计距离最近的k个测试数据的标签，将投票数最高的标签赋给测试集。更高的k值可以使算法对异常数据更有鲁棒性。下面介绍处理数据时各个模块具体代码

• 数据导入函数

 #自定义访问数据函数def load_CIFAR_batch(filename):  """ load single batch of cifar """  with open(filename, 'rb') as f:                                                                                       #二进制方式读取文件    datadict = pickle.load(f)                                                                                           #pickle读取文件得到一个类似于excel表的表格    X = datadict['data']    Y = datadict['labels']    X = X.reshape(10000, 3, 32,32).transpose(0,2,3,1).astype("float")                                                   #每个文件里有10000个训练数据，每个数据是32*32像素的彩色图片,改变了数据的shape和索引顺序    Y = np.array(Y)    return X, Y#访问文件，整合文件中的所有数据def load_CIFAR10(ROOT):  """ load all of cifar """  xs = []  ys = []  for b in range(1,6):    f = os.path.join(ROOT, 'data_batch_%d' % (b, ))                                                                     #将多个路径组合后返回，循环访问五个训练数据文件    X, Y = load_CIFAR_batch(f)    xs.append(X)    ys.append(Y)  Xtr = np.concatenate(xs)                                                                                              #使变成行向量  Ytr = np.concatenate(ys)  del X, Y  Xte, Yte = load_CIFAR_batch(os.path.join(ROOT, 'test_batch'))  return Xtr, Ytr, Xte, Yte

• KNN分类器代码

 #自定义Knn分类器class KNearestNeighbor(object):  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.（参与投票的数据个数）    - num_loops: Determines which implementation to use to compute distances（用于选择计算测试数据和训练数据的距离公式）      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))#每个测试数据分别与每个训练数据做计算得到距离，所以距离个数有num_test*num_train个    for i in xrange(num_test):      for j in xrange(num_train):        train = self.X_train[j,:]        test =  X[i,:]        distence = np.sqrt(np.sum((test-train)**2))#Calculate the eyclidean distance        dists[i,j]=distence#第i个测试数据与第j个训练数据的计算结果放在第i行第j列    return dists  def compute_distances_one_loop(self, X):#用一个循环完成计算    """    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):      dis_array = X[i,:]-self.X_train      dists[i,:] = np.sqrt(np.sum(dis_array**2))    return dists  def compute_distances_no_loops(self, X):    #不使用循环计算距离，使用矩阵运算的方式    """    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))    M = np.dot(X, self.X_train.T)    te = np.square(X).sum(axis = 1)    tr = np.square(self.X_train).sum(axis = 1)    dists = np.sqrt(-2*M+tr+np.matrix(te).T)#表达式：根号（te-tr）^2    dists = np.array(dists)    return dists#预测标签函数  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)    #针对每个测试数据而言标签如何去贴    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 = []      idx = np.argsort(dists[i,:],-1)#argsort函数返回的是数组值从小到大的索引值，关于argsort()函数在后面有详细描述      closest_y = self.y_train[idx[:k]]#取出前K个项对应的索引，找到索引对应的训练数据的标签      closest_set = set(closest_y)#find max label返回集合，重复次数最多的排列在第一个，其余的按原顺序排列      for idx,item in enumerate(closest_set):#enumerate常用语for循环中利用它可以同时获得索引和值        y_pred[i]= item        if idx == 0:          break    return y_pred

关于argsort

numpy.argsort(a, axis=-1, kind=’quicksort’, order=None）
a:待排序的array
axis：待排序的维度，-1表示最后一个维度
quicksort：排序方式（比如排序时用的算法）
order：排序顺序

• 交叉验证代码
  交叉验证是为了找到合适的k值，交叉验证在训练集内部进行，选择出最佳k值之后再使用测试集进行最终的分类精准度的检测。

num_folds = 5k_choices = [1, 3, 5, 8, 10, 12, 15, 20, 50, 100]X_train_folds = []y_train_folds = []X_train_folds = np.array_split(X_train, num_folds);#split the array把训练数据分成五份y_train_folds = np.array_split(y_train, num_folds);k_to_accuracies = {}for k in k_choices:    k_to_accuracies[k] = []for k in k_choices:#find the best k-value#设置交叉验证中的训练集和测试集    for i in range(num_folds):        X_train_cv = np.vstack(X_train_folds[:i]+X_train_folds[i+1:])        X_test_cv = X_train_folds[i]        y_train_cv = np.hstack(y_train_folds[:i]+y_train_folds[i+1:])  #size:4000        y_test_cv = y_train_folds[i]        classifier.train(X_train_cv, y_train_cv)#进行训练        dists_cv = classifier.compute_distances_no_loops(X_test_cv)#选择距离计算公式        y_test_pred = classifier.predict_labels(dists_cv, k)#获得预测结果，给测试数据上了标签        num_correct = np.sum(y_test_pred == y_test_cv)#计算正确贴标签的测试数据个数        accuracy = float(num_correct) / y_test_cv.shape[0]#计算准确度        k_to_accuracies[k].append(accuracy)#准确度结果填入Arrayfor k in sorted(k_to_accuracies):    for accuracy in k_to_accuracies[k]:        print 'k = %d, accuracy = %f' % (k, accuracy)#打印不同k值下的准确度        # plot the raw observationsfor k in k_choices:  accuracies = k_to_accuracies[k]  #设置输入数据  plt.scatter([k] * len(accuracies), accuracies)# plot the trend line with error bars that correspond to standard deviationaccuracies_mean = np.array([np.mean(v) for k,v in sorted(k_to_accuracies.items())])#计算每个K对应的平均精准度accuracies_std = np.array([np.std(v) for k,v in sorted(k_to_accuracies.items())])#计算标准误差plt.errorbar(k_choices, accuracies_mean, yerr=accuracies_std)plt.title('Cross-validation on k')plt.xlabel('k')plt.ylabel('Cross-validation accuracy')plt.show()

由此可判断，K=1时分类结果最佳，选用该k值进行真正的分类即完成了整个knn分类

best_k = 1classifier = KNearestNeighbor()classifier.train(X_train, y_train)y_test_pred = classifier.predict(X_test, k=best_k)# Compute and display the accuracynum_correct = np.sum(y_test_pred == y_test)accuracy = float(num_correct) / num_testprint 'Got %d / %d correct => accuracy: %f' % (num_correct, num_test, accuracy)print accuracy

注意：跑代码的时候我只用了一部分训练数据和测试数据以减少训练时间，分类精确度在27%左右。

总结

第一次写这种类型的博客，再加之自己对python工具掌握并不熟练，会出现许多用于偏差，另外，以上代码并非原创，只是整合了大家的成果，但是比较完整的。学习过程中要勤于积累才能进步。