一、Numpy知识点

import numpy as np
x = np.arange(10)
x # array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) # 一维向量
X = np.arange(15).reshape((5,3))
X
# array([[ 0,  1,  2], # 二维矩阵 
#        [ 3,  4,  5],
#        [ 6,  7,  8],
#        [ 9, 10, 11],
 #       [12, 13, 14]])

1. 访问

x[2]
# 2
X[1,1]
# 4

2. 切片

格式：[行切片，列切片]

x[5:]
# array([5, 6, 7, 8, 9])
# 行切片，列切片
X[2:4,1:]
# array([[ 7,  8],
#        [10, 11]])
X[2:,:2]
# array([[ 6,  7],
#        [ 9, 10],
#        [12, 13]])

如果说不关心reshape的另外一个参数，我们可以写成-1,numpy自动推导出这个参数

x.reshape(5,-1)
# array([[0, 1],
#        [2, 3],
#        [4, 5],
#        [6, 7],
#        [8, 9]])

3. numpy的运算

numpy's universal function

X
    array([[ 0,  1,  2],
           [ 3,  4,  5],
           [ 6,  7,  8],
           [ 9, 10, 11],
           [12, 13, 14]])
X + 1
    array([[ 1,  2,  3],
           [ 4,  5,  6],
           [ 7,  8,  9],
           [10, 11, 12],
           [13, 14, 15]])
X * 2
    array([[ 0,  2,  4],
           [ 6,  8, 10],
           [12, 14, 16],
           [18, 20, 22],
           [24, 26, 28]])
np.sin(X)
    array([[ 0.        ,  0.84147098,  0.90929743],
           [ 0.14112001, -0.7568025 , -0.95892427],
           [-0.2794155 ,  0.6569866 ,  0.98935825],
           [ 0.41211849, -0.54402111, -0.99999021],
           [-0.53657292,  0.42016704,  0.99060736]])

4. NUMPY中的argsort()

argsort返回排序后的参数的序列

x = np.arange(16)
x
    array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15])
# 随机打乱
# from random import shuffle
np.random.shuffle(x)
x
    array([ 1,  8,  6, 12,  4, 14, 13,  7,  0, 15, 11,  3,  9,  5,  2, 10])
# argsort返回排序后的参数的序列
np.argsort(x)
    array([ 8,  0, 14, 11,  4, 13,  2,  7,  1, 12, 15, 10,  3,  6,  5,  9],
          dtype=int64)

5.Numpy 中的布尔索引

布尔型索引可以应用于数据的筛选
布尔型索引应用于修改值

names = np.array(['Bob','Joe','Will','Bob','Will','Joe','Joe'])
names
    array(['Bob', 'Joe', 'Will', 'Bob', 'Will', 'Joe', 'Joe'], dtype='<U4')
# 使用np.random模块的randn生成一些正态分布的随机数据
data = np.random.randn(7,4)
data
    array([[ 1.8450457 ,  1.91791784, -0.90133072, -0.96715706],
           [ 0.26275727,  1.27134679,  0.33692668, -1.00586409],
           [-0.60143482, -1.41361787,  0.62431237,  0.50040347],
           [ 0.0129754 ,  1.92856064,  1.3711845 , -1.17564517],
           [ 1.43999704, -0.87670553,  0.23952736, -0.64149065],
           [-0.81460157, -1.7537682 , -0.82011688, -0.29424883],
           [-1.00896275, -1.38725507, -1.03945652, -1.19849684]])
# 假设每个名字对应data数组的一行
names == 'Bob'
    array([ True, False, False,  True, False, False, False])
# 布尔型索引可以应用于数据的筛选
data[names =='Bob']
    array([[ 1.8450457 ,  1.91791784, -0.90133072, -0.96715706],
           [ 0.0129754 ,  1.92856064,  1.3711845 , -1.17564517]])
# 布尔型索引应用于修改值
# 选取所有JOE的行，并且全部赋值为 0
data[names == 'Joe'] = 0
data
    array([[ 1.8450457 ,  1.91791784, -0.90133072, -0.96715706],
           [ 0.        ,  0.        ,  0.        ,  0.        ],
           [-0.60143482, -1.41361787,  0.62431237,  0.50040347],
           [ 0.0129754 ,  1.92856064,  1.3711845 , -1.17564517],
           [ 1.43999704, -0.87670553,  0.23952736, -0.64149065],
           [ 0.        ,  0.        ,  0.        ,  0.        ],
           [ 0.        ,  0.        ,  0.        ,  0.        ]])
# 选取所有Will的行，并且将选取的数据的后两列赋值为0
data[names == 'Will',2:] = 0 
data
    array([[ 1.8450457 ,  1.91791784, -0.90133072, -0.96715706],
           [ 0.        ,  0.        ,  0.        ,  0.        ],
           [-0.60143482, -1.41361787,  0.        ,  0.        ],
           [ 0.0129754 ,  1.92856064,  1.3711845 , -1.17564517],
           [ 1.43999704, -0.87670553,  0.        ,  0.        ],
           [ 0.        ,  0.        ,  0.        ,  0.        ],
           [ 0.        ,  0.        ,  0.        ,  0.        ]])

二、绘制散点图

散点图
散点图

三、鸢尾花数据集散点图绘制

sklearn库封装了很多机器学习算法

1
2
3

四、机器学习初识

监督学习(supervised learning)，无监督学习(unsupervised learning)，半监督学习(Semi-Supervised Learning)，强化学习（reinforcement Learning ）

• 监督学习(supervised learning)和无监督学习(unsupervised learning)的判断：是否有监督（supervised），就看输入数据是否有标签（label）。输入数据有标签，则为有监督学习，没标签则为无监督学习。
• 监督学习：回归(Regression，连续）、分类（Classification，离散)
• 无监督学习：聚类（clustering）

分类算法KNN：

K近邻算法，即K-Nearest Neighbor algorithm，简称KNN算法。
可认为是：找最接近K的那个邻居。
实例：肿瘤良，恶性判断(手动实现)

自己实现KNN算法

数据集

import numpy as np
from matplotlib import pyplot as plt
from math import sqrt   # 开平方
from collections import Counter  #collections库非常有用
raw_data_X = [[3.393533211, 2.331273381],
              [3.110073483, 1.781539638],
              [1.343808831, 3.368360954],
              [3.582294042, 4.679179110],
              [2.280362439, 2.866990263],
              [7.423436942, 4.696522875],
              [5.745051997, 3.533989803],
              [9.172168622, 2.511101045],
              [7.792783481, 3.424088941],
              [7.939820817, 0.791637231]
             ]
raw_data_y = [0, 0, 0, 0, 0, 1, 1, 1, 1, 1]
# 转化成ndarray类型
X_train = np.array(raw_data_X)
y_train = np.array(raw_data_y)

对数据进行可视化

plt.scatter(X_train[y_train==0,0],X_train[y_train==0,1],color='g')
plt.scatter(X_train[y_train==1,0],X_train[y_train==1,1],color='r')
plt.show()

数据可视化

预测

# 假设新来一个样本数据判断x是恶性还是良性
x = np.array([8.093607318, 3.365731514])
plt.scatter(X_train[y_train==0,0],X_train[y_train==0,1],color='g')
plt.scatter(X_train[y_train==1,0],X_train[y_train==1,1],color='r')
plt.scatter(x[0],x[1],color='b')
plt.show()

预测

通过knn算法来预测

# 计算x距离所有的十个点的距离，然后选距离最近的前k个
# distances = []
# for x_train in X_train:
#     d = sqrt(np.sum((x_train-x)**2))
#     distances.append(d)
distances = [sqrt(np.sum((x_train-x)**2)) for x_train in X_train] # 欧式距离
distances
'''
[4.812566907609877,
 5.229270827235305,
 6.749798999160064,
 4.6986266144110695,
 5.83460014556857,
 1.4900114024329525,
 2.354574897431513,
 1.3761132675144652,
 0.3064319992975,
 2.5786840957478887]
'''
nearst = np.argsort(distances)
nearst
# array([8, 7, 5, 6, 9, 3, 0, 1, 4, 2], dtype=int64)
# 假设我们制定K的值是6
k = 6
top_k_y = [y_train[i] for i in nearst[:6]]
top_k_y
# [1, 1, 1, 1, 1, 0]

数据统计量大的话使用的统计办法

votes = Counter(top_k_y)
votes
# Counter({1: 5, 0: 1})
# 返回数量前i的数据信息
votes.most_common(1)
predict_y = votes.most_common(1)[0][0]
predict_y
1
# 结论：x恶