图像分类

目标

给一张输入图片赋予一个标签，这个标签属于事先定义好的类别集合中

地位

计算机视觉的核心问题

例子

难点

拍摄点的视角多样
拍摄点的远近距离多样
物体的变形
物体部分遮挡
光线
背景相似
品种多样

方法

数据驱动（即包含训练数据）

pipeline

输入 -> 学习 -> 评估

最近邻分类器

距离度量

L1 distance

$$d_1 (I_1, I_2) = \sum_{p} \left| I^p_1 - I^p_2 \right|$$

L2 distance

$$d_2 (I_1, I_2) = \sqrt{\sum_{p} \left( I^p_1 - I^p_2 \right)^2}$$

示例代码

数据读取

Xtr, Ytr, Xte, Yte = load_CIFAR10('data/cifar10/') # a magic function we provide
# flatten out all images to be one-dimensional
Xtr_rows = Xtr.reshape(Xtr.shape[0], 32 * 32 * 3) # Xtr_rows becomes 50000 x 3072
Xte_rows = Xte.reshape(Xte.shape[0], 32 * 32 * 3) # Xte_rows becomes 10000 x 3072

预测及评估

nn = NearestNeighbor() # create a Nearest Neighbor classifier class
nn.train(Xtr_rows, Ytr) # train the classifier on the training images and labels
Yte_predict = nn.predict(Xte_rows) # predict labels on the test images
# and now print the classification accuracy, which is the average number
# of examples that are correctly predicted (i.e. label matches)
print 'accuracy: %f' % ( np.mean(Yte_predict == Yte) )

基本方法

import numpy as np
class NearestNeighbor(object):
  def __init__(self):
    pass
  def train(self, X, y):
    """ X is N x D where each row is an example. Y is 1-dimension of size N """
    # the nearest neighbor classifier simply remembers all the training data
    self.Xtr = X
    self.ytr = y
  def predict(self, X):
    """ X is N x D where each row is an example we wish to predict label for """
    num_test = X.shape[0]
    # lets make sure that the output type matches the input type
    Ypred = np.zeros(num_test, dtype = self.ytr.dtype)
    # loop over all test rows
    for i in xrange(num_test):
      # find the nearest training image to the i'th test image
      # using the L1 distance (sum of absolute value differences)
      distances = np.sum(np.abs(self.Xtr - X[i,:]), axis = 1)
      min_index = np.argmin(distances) # get the index with smallest distance
      Ypred[i] = self.ytr[min_index] # predict the label of the nearest example
    return Ypred

实验结果

L1-distance 38.6% on CIFAR-10

L2-distance 35.4% on CIFAR-10

L1 vs. L2 L2比L1的差异容忍度更小

K近邻分类器

采用验证集进行超参调参

实例代码

# assume we have Xtr_rows, Ytr, Xte_rows, Yte as before
# recall Xtr_rows is 50,000 x 3072 matrix
Xval_rows = Xtr_rows[:1000, :] # take first 1000 for validation
Yval = Ytr[:1000]
Xtr_rows = Xtr_rows[1000:, :] # keep last 49,000 for train
Ytr = Ytr[1000:]
# find hyperparameters that work best on the validation set
validation_accuracies = []
for k in [1, 3, 5, 10, 20, 50, 100]:
  
  # use a particular value of k and evaluation on validation data
  nn = NearestNeighbor()
  nn.train(Xtr_rows, Ytr)
  # here we assume a modified NearestNeighbor class that can take a k as input
  Yval_predict = nn.predict(Xval_rows, k = k)
  acc = np.mean(Yval_predict == Yval)
  print 'accuracy: %f' % (acc,)
  # keep track of what works on the validation set
  validation_accuracies.append((k, acc))