【cs231n学习笔记（2017）】——— KNN

好久没写博客了，最近有点忙，然后自己也有点懒。。。。。。
最近确定自己要搞计算机视觉方向，然后就开始看斯坦福的cs231n课程，准备写系列博客记录自己的学习过程及心得。
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KNN(K-邻近算法)

L1 distance: 曼哈顿距离

表达式：

d1(I1,I2)=∑p|Ip1−Ip2| d 1 ( I 1 , I 2 ) = ∑ p | I 1 p − I 2 p |

示例：（自己简单画的，略潦草）
python实现：

import numpy as np


class KNN_L1:
    def __init__(self):
        pass

    def train(self, x, y):
        self.x_train = x
        self.y_train = y

    def predict(self, x):
        num_test = x.shape[0]
        Ypred = np.zeros(num_test, dtype=self.y_train.dtype)
            # 求和
            distances = np.sum(np.abs(self.x_train-x[i, :]), axis=1)
            # 求最小索引
            min_index = np.argmin(distances)
            # 排序
            Ypred[i] = self.y_train[min_index]
        return Ypred

L2 distance: 欧式距离

表达式：

d2(I1,I2)=∑p(Ip1−Ip2)2−−−−−−−−−−−√ d 2 ( I 1 , I 2 ) = ∑ p ( I 1 p − I 2 p ) 2

示例：

python代码实现

import numpy as np


class KNN_L2:

    def __init__(self):
        pass

    def train(self,X,y):
        self.X_train=X
        self.y_train=y

    def predict(self,X,k=1,num_loops=0):
        if num_loops==0:
            dists=self.compute_distances_no_loops(X)
        elif num_loops==1:
            dists=self.compute_distances_one_loops(X)
        elif num_loops==2:
            dists=self.compute_distances_one_loops(X)
        return self.predict_labels(dists,k=k)

    #双重循环
    def compute_distances_two_loops(self,X):
        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):
                dists[i,j]=np.sqrt(np.sum(X[i,:]-self.X_train[j,:])**2))
        return dists

    # 一层循环
    def compute_distances_one_loop(self, X):
        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):
            dists[i, :] = np.sqrt(np.sum(np.square(self.X_train - X[i, :]), axis=1))
        return dists

    #无循环
    def compute_distances_no_loops(self, X):
        num_test = X.shape[0]
        num_train = self.X_train.shape[0]
        dists = np.zeros((num_test, num_train))
        test_sum = np.sum(np.square(X), axis=1)
        train_sum = np.sum(np.square(self.X_train), axis=1)
        inner_product = np.dot(X, self.X_train.T)
        dists = np.sqrt(-2 * inner_product + test_sum.reshape(-1, 1) + train_sum)
        return dists

    def predict_labels(self, dists, k=1):  # 2
        num_test = dists.shape[0]
        y_pred = np.zeros(num_test)
        for i in range(num_test):
            closest_y = []
            y_indicies = np.argsort(dists[i, :], axis=0)
            closest_y = self.y_train[y_indicies[: k]]  
            y_pred[i] = np.argmax(np.bincount(closest_y))  
        return y_pred

L1与L2区别

1.L1与坐标轴有关，会随着坐标轴改变而改变，L2不会随着坐标轴的改变而改变
2.L1适用于某个有重要意义的特征向量，L2适用于某个空间通用量，不知道其实际意义