[KNN]基於numpy的曼哈頓距離實現

出租車幾何或曼哈頓距離（Manhattan Distance）是由十九世紀的赫爾曼·閔可夫斯基所創詞彙 ，是種使用在幾何度量空間的幾何學用語，用以標明兩個點在標準座標系上的絕對軸距總和。

在numpy中，曼哈頓距離可以這樣表述

distances = np.sum(np.abs(X_train[-1,1] - Y_test[-1,1]) + np.abs(X_train[-1,0] - Y_test[-1,1]))

當然，numpy本身也提供了通過閔氏距離修改p值來直接實現包括曼哈頓距離在內的多種距離計算方式，具體如下

def minkowski_distance(vec1, vec2, p=3):
    """
    閔氏距離
    當p=1時，就是曼哈頓距離
    當p=2時，就是歐氏距離
    當p→∞時，就是切比雪夫距離
    :param vec1:
    :param vec2:
    :param p:
    :return:
    """
    # return sum([(x - y) ** p for (x, y) in zip(vec1, vec2)]) ** (1 / p)
    return np.linalg.norm(vec1 - vec2, ord=p)

def cosine_distance(vec1, vec2):
    """
    夾角餘弦
    :param vec1:
    :param vec2:
    :return:
    """
    vec1_norm = np.linalg.norm(vec1)
    vec2_norm = np.linalg.norm(vec2)
    return vec1.dot(vec2) / (vec1_norm * vec2_norm)

def euclidean_distance(vec1, vec2):
    """
    歐氏距離
    :param vec1:
    :param vec2:
    :return:
    """
    # return np.sqrt(np.sum(np.square(vec1 - vec2)))
    # return sum([(x - y) ** 2 for (x, y) in zip(vec1, vec2)]) ** 0.5
    return np.linalg.norm(vec1 - vec2, ord=2)

def manhattan_distance(vec1, vec2):
    """
    曼哈頓距離
    :param vec1:
    :param vec2:
    :return:
    """
    # return np.sum(np.abs(vec1 - vec1))
    return np.linalg.norm(vec1 - vec2, ord=1)

def chebyshev_distance(vec1, vec2):
    """
    切比雪夫距離
    :param vec1:
    :param vec2:
    :return:
    """
    # return np.abs(vec1 - vec2).max()
    return np.linalg.norm(vec1 - vec2, ord=np.inf)

def hamming_distance(vec1, vec2):
    """
    漢明距離
    :param vec1:
    :param vec2:
    :return:
    """
    return np.shape(np.nonzero(vec1 - vec2)[0])[0]

def jaccard_similarity_coefficient(vec1, vec2):
    """
    傑卡德距離
    :param vec1:
    :param vec2:
    :return:
    """
    return dist.pdist(np.array([vec1, vec2]), 'jaccard')

這是我學習KNN的第一個習題中遇到的問題，即通過曼哈頓距離或者歐拉距離對輸入的測試集進行分類，項目整體代碼如下

import numpy as np
import matplotlib.pyplot as plt
import operator

def creatDataSet():
    group = np.array([[1.0,2.0],
                      [1.2,0.1],
                      [0.1,1.4],
                      [0.3,3.5],
                      [1.1,1.0],
                      [0.5,1.5]])
    lebals = np.array(['A','A','B','B','A','B'])
    return group,lebals

def KNN_classify(k,dis,X_train,x_train,Y_test):
    assert dis == 'E' or dis =='M','dis must E or M,E爲歐拉距離，M爲曼哈頓距離'
    num_test = Y_test.shape[0]
    leballist = []
    if dis == 'E':
        for i in range(num_test):
            distances = np.sqrt(np.sum(((X_train - np.tile(Y_test[i],(X_train.shape[0],1))) ** 2 ),axis = 1))
            nearest_k = np.argsort(distances)
            topK = nearest_k[:k]
            classCount = {}
            for i in topK:
                classCount[x_train[i]] = classCount.get(x_train[i],0) + 1
            sortedClassCount = sorted(classCount.items(),key=operator.itemgetter(1),reverse=True)
            leballist.append (sortedClassCount[0][0])
        return np.array(leballist)
    else:
        for i in range(num_test):
            distances = np.sum(np.abs(X_train[-1,1] - Y_test[-1,1]) + np.abs(X_train[-1,0] - Y_test[-1,1]))
            nearest_k = np.argsort(distances)
            topK = nearest_k[:k]
            classCount = {}
            for i in topK:
                classCount[x_train[i]] = classCount.get(x_train[i],0) + 1
            sortedClassCount = sorted(classCount.items(),key=operator.itemgetter(1),reverse=True)
            leballist.append (sortedClassCount[0][0])
        return np.array(leballist)

if __name__ == "__main__":
    group,lebals = creatDataSet()
    y_test_res = KNN_classify(1,'M',group,lebals,np.array([[1.0,2.1],[0.4,2.0]]))
    print(y_test_res)
    plt.show()