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 = 5
k_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Array
for 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 observations
for 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 deviation
accuracies_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 = 1
classifier = KNearestNeighbor()
classifier.train(X_train, y_train)
y_test_pred = classifier.predict(X_test, k=best_k)
# Compute and display the accuracy
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)
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。