积跬步至千里 || 生成测试数据集及k近邻计算

生成测试数据集及k近邻计算

1. 生成测试数据集

在设计算法或对算法进行改进时,不可避免地要对新算法进行测试,则会用到toy类型的数据进行直观展示. 最常用的数据类型是高斯类型数据或者直线型数据, 同时要对数据点的顺序进行标注, 然后看相互之间的关系. 样本点相互之间的关系以近邻关系最为常用, 它是很多算法优秀效果的保障.

1.1 生成高斯型测试数据

import numpy as np
import matplotlib.pyplot as plt

def gaussian2d2c(n1,n2):
    mean1 = [0,0]
    cov1 = [[1,0],[0,1]]
    x1 = np.random.multivariate_normal(mean1,cov1,n1,'raise')# 100表示样本数,每个样本的维数等同于均值的长度
    print(x1.shape)
    
    mean2 = [10,10]
    cov2 = [[1,0],[0,1]]
    x2 = np.random.multivariate_normal(mean2,cov2,n2,'raise')
    print(x2.shape)
    
    X = np.vstack((x1,x2))
    print(X.shape)
    return X.T

data = gaussian2d2c(10,10)
plt.scatter(data[0,:],data[1,:])
epsilon = 0.01
for i in range(data.shape[1]):
    plt.text(data[0,i]+epsilon, data[1,i]+epsilon, str(i))

plt.show()

1.2 生成直线型测试数据集

import numpy as np
import matplotlib.pyplot as plt

def line2d2c(n):
    t = np.linspace(0, 1, n)
    q1t = 2 * t + 1 + 0.1 * np.random.randn(n)
    x1 = np.vstack((t, q1t))
    q2t = 2 * t + 5 + 0.1 * np.random.randn(n)
    x2 = np.vstack((t, q2t))
    x = np.hstack((x1, x2))
    return x

data = line2d2c(10)
plt.scatter(data[0,:],data[1,:])
for i in range(data.shape[1]):
    plt.text(data[0,i]+epsilon, data[1,i]+epsilon, str(i))
plt.show()

2. 计算直线型分类数据的近邻点

def kneightbors(X, k):
    D, N = X.shape
    print('LLE running on {} points in {} dimensions\n'.format(N,D))
 
    # Step1: compute pairwise distances & find neighbors
    print('-->Finding {} nearest neighbours.\n'.format(k))
 
    X2 = np.sum(X**2,axis = 0).reshape(1,-1) # 1xN
    distance = np.tile(X2,(N,1)) + np.tile(X2.T, (1, N)) - 2 * np.dot(X.T,X) # NxN
 
    index = np.argsort(distance,axis=0)
    neighborhood = index[1:1+k,:] # kxN filter itself
    
    return neighborhood

kfield = kneightbors(data, 3)
print(kfield[:,:10])