概述
作业一
作业内容：实现k-NN，SVM分类器，Softmax分类器和两层神经网络，实践一个简单的图像分类流程。
1. KNN分类器
KNN介绍：
KNN分类器其只找最相近的那1个图片的标签，我们找最相似的k个图片的标签，然后让他们针对测试图片进行投票，最后把票数最高的标签作为对测试图片的预测。所以当k=1的时候，k-Nearest Neighbor分类器就是Nearest Neighbor分类器。从直观感受上就可以看到，更高的k值可以让分类的效果更平滑，使得分类器对于异常值更有抵抗力。
KNN常用距离：
- L1距离
- L2距离
图像分类数据集：
CIFAR-10。一个非常流行的图像分类数据集是CIFAR-10。这个数据集包含了60000张32X32的小图像。每张图像都有10种分类标签中的一种。这60000张图像被分为包含50000张图像的训练集和包含10000张图像的测试集。在下图中你可以看见10个类的10张随机图片。
KNN代码
1.导入必要的库
import random
import numpy as np
from cs231n.data_utils import load_CIFAR10
import matplotlib.pyplot as plt
%matplotlib inline
plt.rcParams['figure.figsize'] = (10.0, 8.0) # set default size of plots
plt.rcParams['image.interpolation'] = 'nearest'
plt.rcParams['image.cmap'] = 'gray'
%load_ext autoreload
%autoreload 2
2.加载数据集
cifar10_dir = 'cs231n/datasets/CIFAR10'
X_train, y_train, X_test, y_test = load_CIFAR10(cifar10_dir)
# As a sanity check, we print out the size of the training and test data.
print('Training data shape: ', X_train.shape)
print('Training labels shape: ', y_train.shape)
print('Test data shape: ', X_test.shape)
print('Test labels shape: ', y_test.shape)
# 可视化训练集的一些样本例子
classes = ['plane', 'car', 'bird', 'cat', 'deer', 'dog', 'frog', 'horse', 'ship', 'truck']
num_classes = len(classes)
samples_per_class = 7
# enumerate() 函数用于将一个可遍历的数据对象
for y, cls in enumerate(classes):
# 找出对应标签的样本位置
idxs = np.flatnonzero(y_train == y)
idxs = np.random.choice(idxs, samples_per_class, replace=False)
for i, idx in enumerate(idxs):
# 在子图中所占位置的计算
plt_idx = i * num_classes + y + 1
# print(plt_idx)
plt.subplot(samples_per_class, num_classes, plt_idx)
plt.imshow(X_train[idx].astype('uint8'))
plt.axis('off')
if i == 0:
plt.title(cls)
plt.show()
# 划分训练集和测试集
num_training = 5000
mask = list(range(num_training))
X_train = X_train[mask]
y_train = y_train[mask]
num_test = 500
mask = list(range(num_test))
X_test = X_test[mask]
y_test = y_test[mask]
# 转换shape将图像中的像素变成一行数据 样本*特征
X_train = np.reshape(X_train, (X_train.shape[0], -1))
X_test = np.reshape(X_test, (X_test.shape[0], -1))
print(X_train.shape, X_test.shape)
from cs231n.classifiers import KNearestNeighbor
classifier = KNearestNeighbor()
classifier.train(X_train, y_train)
dists = classifier.compute_distances_two_loops(X_test)
print(dists.shape)
# 可视化距离矩阵
plt.imshow(dists, interpolation='none')
plt.show()
# 测试
y_test_pred = classifier.predict_labels(dists, k=1)
# 准确率
num_correct = np.sum(y_test_pred == y_test)
accuracy = float(num_correct) / num_test
print('Got %d / %d correct => accuracy: %f' % (num_correct, num_test, accuracy))
y_test_pred = classifier.predict_labels(dists, k=5)
num_correct = np.sum(y_test_pred == y_test)
accuracy = float(num_correct) / num_test
print('Got %d / %d correct => accuracy: %f' % (num_correct, num_test, accuracy))
# 循环一次计算L2距离
dists_one = classifier.compute_distances_one_loop(X_test)
difference = np.linalg.norm(dists - dists_one, ord='fro')
print('One loop difference was: %f' % (difference, ))
if difference < 0.001:
print('Good! The distance matrices are the same')
else:
print('Uh-oh! The distance matrices are different')
# 不用循环计算L2距离
dists_two = classifier.compute_distances_no_loops(X_test)
difference = np.linalg.norm(dists - dists_two, ord='fro')
print('No loop difference was: %f' % (difference, ))
if difference < 0.001:
print('Good! The distance matrices are the same')
else:
print('Uh-oh! The distance matrices are different')
# 比较不同循环次数所花费的时间
def time_function(f, *args):
"""
Call a function f with args and return the time (in seconds) that it took to execute.
"""
import time
tic = time.time()
f(*args)
toc = time.time()
return toc - tic
two_loop_time = time_function(classifier.compute_distances_two_loops, X_test)
print('Two loop version took %f seconds' % two_loop_time)
one_loop_time = time_function(classifier.compute_distances_one_loop, X_test)
print('One loop version took %f seconds' % one_loop_time)
no_loop_time = time_function(classifier.compute_distances_no_loops, X_test)
print('No loop version took %f seconds' % no_loop_time)
进行交叉验证，选取最好的K
num_folds = 5
k_choices = [1, 3, 5, 8, 10, 12, 15, 20, 50, 100]
X_train_folds = []
y_train_folds = []
# 我们将要通过交叉验证来得出最好的k系数
# 将训练数据分成几份，在分完后X_train_folds和y_train_folds应该为长度为num_folds
X_train_folds = np.array_split(X_train, num_folds)
y_train_folds = np.array_split(y_train, num_folds)
k_to_accuracies = {}
step = int(num_training/num_folds)
for k in k_choices:
acc = []
# 一共num_folds叠中，用除了其中一叠的所有叠当做训练集进行训练，然后用剩余的一叠当做验证集
for i in range(num_folds):
# 训练 / 验证集 比例 (80% 20%)
train_data = np.concatenate([X_train[:i*step], X_train[(i+1)*step:]], axis = 0)
test_data = X_train[i*step:(i+1)*step]
train_label = np.concatenate([y_train[:i*step], y_train[(i+1)*step:]], axis = 0)
test_label = y_train[i*step:(i+1)*step]
classifier = KNearestNeighbor()
classifier.train(train_data, train_label)
dists = classifier.compute_distances_no_loops(test_data)
label_test_pred = classifier.predict_labels(dists, k=k)
num_correct = np.sum(label_test_pred == test_label)
acc.append(float(num_correct) / num_test)
k_to_accuracies[k] = acc
# 打印出计算好的准确度
for k in sorted(k_to_accuracies):
for accuracy in k_to_accuracies[k]:
print('k = %d, accuracy = %f' % (k, accuracy))
# 可视化交叉验证的K选择
for k in k_choices:
accuracies = k_to_accuracies[k]
plt.scatter([k] * len(accuracies), accuracies)
accuracies_mean = np.array([np.mean(v) for k,v in sorted(k_to_accuracies.items())])
accuracies_std = np.array([np.std(v) for k,v in sorted(k_to_accuracies.items())])
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()
# 在交叉验证的结果中，选择最合适的k，重新操作一遍，你能得到大概28%的准确率
best_k = 10
classifier = KNearestNeighbor()
classifier.train(X_train, y_train)
y_test_pred = classifier.predict(X_test, k=best_k)
# 计算准确率
num_correct = np.sum(y_test_pred == y_test)
accuracy = float(num_correct) / num_test
print('Got %d / %d correct => accuracy: %f' % (num_correct, num_test, accuracy))
k_nearest_neighbor.py文件的相关代码
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: #
# Compute the l2 distance between the ith test point and the jth #
# training point, and store the result in dists[i, j]. You should #
# not use a loop over dimension, nor use np.linalg.norm(). #
#####################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
dists[i, j] = np.sqrt(np.sum(np.square((X[i] - self.X_train[j]))))
# *****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: #
# Compute the l2 distance between the ith test point and all training #
# points, and store the result in dists[i, :]. #
# Do not use np.linalg.norm(). #
#######################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
dists[i, :] = np.sqrt(np.sum(np.square((X[i]-self.X_train)), axis = 1))
# *****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: #
# Compute the l2 distance between all test points and all training #
# points without using any explicit loops, and store the result in #
# dists. #
# #
# You should implement this function using only basic array operations; #
# in particular you should not use functions from scipy, #
# nor use np.linalg.norm(). #
# #
# HINT: Try to formulate the l2 distance using matrix multiplication #
# and two broadcast sums. #
#########################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
num_test = X.shape[0]
num_train = self.X_train.shape[0]
dists = np.zeros((num_test, num_train))
dists = np.sqrt(
np.sum(X**2, axis = 1, keepdims = True)
+ np.sum(self.X_train**2, axis = 1, keepdims = True).T
- 2*np.dot(X, self.X_train.T)
)
# *****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: #
# Use the distance matrix to find the k nearest neighbors of the ith #
# testing 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. #
#########################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
max_index = np.argsort(dists[i])
for j in range(k):
index = max_index[j]
closest_y.append(self.y_train[index])
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
#########################################################################
# 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. #
#########################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
maxdir = {}
sy = set(closest_y)
for s in sy:
count = closest_y.count(s)
maxdir[s] = count
y_pred[i] = int(max(maxdir, key = maxdir.get))
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
return y_pred
参考资料
https://zhuanlan.zhihu.com/p/21930884
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