The python implementation of knn (numpy matrix operation)

The content of knn is very simple, assuming that m points and a center point are given, find the k points closest to the center point among the given points.

Therefore, the code idea is to first calculate the distance between all points and the center point, sort them in ascending order, and take the first k points.

In machine learning, when the amount of data is large, the use of loops will make the code operation efficiency very low, so the code is completed by matrix operations.

Matrix operation of Euclidean distance

code show as below

def euclidean_dist(x, y):
    """
    矩阵计算欧式距离
    :param x: Ndarray Variable, with shape [m, d]
    :param y: Ndarray Variable, with shape [n, d]
    :return: dist: Ndarray Variable, with shape [n, m]
    """

    m, n = x.shape[0], y.shape[0]
    # x先对每个数据取平方，后按行求和，再将得到的重复扩展n个，得到m*n的数据
    xx = np.expand_dims(np.sum((x**2), axis=1), axis=1).repeat(n, axis=1)
    # x先对每个数据取平方，后按行求和，再将得到的重复扩展m个，转置后得到m*n的数据
    yy = np.expand_dims(np.sum((y**2), axis=1), axis=1).repeat(m, axis=1).T
    dist = xx + yy - 2 * x @ y.T
    # np.clip()函数可以限定dist内元素的最大最小范围，然后用np.sqrt()开方，得到样本之间的距离矩阵
    dist = np.sqrt(np.clip(dist, a_min=1e-12, a_max=None))

    return dist.T

Knn

def knn(data_support, center_data, k):
    """
    根据给定的center_data, 在data_support中找到最近的k个数据的idx
    :param data_support:[M, D], M个D维的数据
    :param center_data:[N, D], N个D维的数据
    :param k:
    :return:res:[N, k, D]
            res[0]为[k, D]，即第一个center_data的k个最近数据
    """
    # 计算距离矩阵，(i, j)处的数据表示center_data[j]与data_support[i]的距离
    dist = euclidean_dist(data_support, center_data)
    # 对每一列进行排序，找到center_data[]最近的k个data_support
    sorted_idxs = dist.argsort(axis=1)
    res = []
    for idxs in sorted_idxs:
        res.append([data_support[idx] for idx in idxs[:k]])

    return np.array(res)

full code

# -*- coding: utf-8 -*-
"""
Time:     2023/3/13 13:56
Author:   cjn
Version:  1.0.0
File:     knn.py
Describe: 
"""
import numpy as np


def euclidean_dist(x, y):
    """
    矩阵计算欧式距离
    :param x: Ndarray Variable, with shape [m, d]
    :param y: Ndarray Variable, with shape [n, d]
    :return: dist: Ndarray Variable, with shape [n, m]
    """

    m, n = x.shape[0], y.shape[0]
    # x先对每个数据取平方，后按行求和，再将得到的重复扩展n个，得到m*n的数据
    xx = np.expand_dims(np.sum((x**2), axis=1), axis=1).repeat(n, axis=1)
    # x先对每个数据取平方，后按行求和，再将得到的重复扩展m个，转置后得到m*n的数据
    yy = np.expand_dims(np.sum((y**2), axis=1), axis=1).repeat(m, axis=1).T
    dist = xx + yy - 2 * x @ y.T
    # np.clip()函数可以限定dist内元素的最大最小范围，然后用np.sqrt()开方，得到样本之间的距离矩阵
    dist = np.sqrt(np.clip(dist, a_min=1e-12, a_max=None))

    return dist.T


def knn(data_support, center_data, k):
    """
    根据给定的center_data, 在data_support中找到最近的k个数据的idx
    :param data_support:[M, D], M个D维的数据
    :param center_data:[N, D], N个D维的数据
    :param k:
    :return:res:[N, k, D]
            res[0]为[k, D]，即第一个center_data的k个最近数据
    """
    # 计算距离矩阵，(i, j)处的数据表示center_data[j]与data_support[i]的距离
    dist = euclidean_dist(data_support, center_data)
    # 对每一列进行排序，找到center_data[]最近的k个data_support
    sorted_idxs = dist.argsort(axis=1)
    res = []
    for idxs in sorted_idxs:
        res.append([data_support[idx] for idx in idxs[:k]])

    return np.array(res)


if __name__ == "__main__":
    dataset = np.array([[1, 2, 3, 4], [2, 5, 1, 3], [7, 7, 2, 1], [4, 2, 5, 2]])
    center = np.array([[2, 2, 1, 4], [7, 3, 2, 4]])

    k = 2
    res = knn(dataset, center, k)
    print(res)

operation result: