K-近邻算法（KNN）
0、导引
如何进行电影分类
众所周知，电影可以按照题材分类，然而题材本身是如何定义的?由谁来判定某部电影属于哪个题材?也就是说同一题材的电影具有哪些公共特征?这些都是在进行电影分类时必须要考虑的问题。没有哪个电影人会说自己制作的电影和以前的某部电影类似，但我们确实知道每部电影在风格上的确有可能会和同题材的电影相近。那么动作片具有哪些共有特征，使得动作片之间非常类似，而与爱情片存在着明显的差别呢？动作片中也会存在接吻镜头，爱情片中也会存在打斗场景，我们不能单纯依靠是否存在打斗或者亲吻来判断影片的类型。但是爱情片中的亲吻镜头更多，动作片中的打斗场景也更频繁，基于此类场景在某部电影中出现的次数可以用来进行电影分类。
本章介绍第一个机器学习算法：K-近邻算法，它非常有效而且易于掌握。
1、k-近邻算法原理
简单地说，K-近邻算法采用测量不同特征值之间的距离方法进行分类。
- 优点：精度高(计算距离)、对异常值不敏感（单纯根据距离进行分类，会忽略特殊情况）、无数据输入假定（不会对数据预先进行判定）。
- 缺点：时间复杂度高、空间复杂度高。
- 适用数据范围：数值型和标称型。
工作原理
存在一个样本数据集合，也称作训练样本集，并且样本集中每个数据都存在标签，即我们知道样本集中每一数据 与所属分类的对应关系。输人没有标签的新数据后，将新数据的每个特征与样本集中数据对应的 特征进行比较，然后算法提取样本集中特征最相似数据（最近邻）的分类标签。一般来说，我们 只选择样本数据集中前K个最相似的数据，这就是K-近邻算法中K的出处,通常K是不大于20的整数。 最后 ，选择K个最相似数据中出现次数最多的分类，作为新数据的分类。
回到前面电影分类的例子，使用K-近邻算法分类爱情片和动作片。有人曾经统计过很多电影的打斗镜头和接吻镜头，下图显示了6部电影的打斗和接吻次数。假如有一部未看过的电影，如何确定它是爱情片还是动作片呢？我们可以使用K-近邻算法来解决这个问题。
首先我们需要知道这个未知电影存在多少个打斗镜头和接吻镜头，上图中问号位置是该未知电影出现的镜头数图形化展示，具体数字参见下表。
即使不知道未知电影属于哪种类型，我们也可以通过某种方法计算出来。首先计算未知电影与样本集中其他电影的距离，如图所示。
现在我们得到了样本集中所有电影与未知电影的距离，按照距离递增排序，可以找到K个距 离最近的电影。假定k=3，则三个最靠近的电影依次是California Man、He's Not Really into Dudes、Beautiful Woman。K-近邻算法按照距离最近的三部电影的类型，决定未知电影的类型，而这三部电影全是爱情片，因此我们判定未知电影是爱情片。
欧几里得距离(Euclidean Distance)
欧氏距离是最常见的距离度量，衡量的是多维空间中各个点之间的绝对距离。公式如下：
2、在scikit-learn库中使用k-近邻算法
- 分类问题：from sklearn.neighbors import KNeighborsClassifier
In [2]:
import numpy as np
import pandas as pd
from pandas import DataFrame,Series
E:\Anaconda3\lib\importlib\_bootstrap.py:219: RuntimeWarning: numpy.ufunc size changed, may indicate binary incompatibility. Expected 192 from C header, got 216 from PyObject return f(*args, **kwds) E:\Anaconda3\lib\importlib\_bootstrap.py:219: RuntimeWarning: numpy.ufunc size changed, may indicate binary incompatibility. Expected 192 from C header, got 216 from PyObject return f(*args, **kwds)
In [1]:
from sklearn.neighbors import KNeighborsClassifier
In [7]:
data = pd.read_excel('../my_films.xlsx')
data
Out[7]:
| 0 | 前任3 | 4 | 10 | Action |
|---|---|---|---|---|
| 1 | 西游记 | 16 | 2 | Action |
| 2 | 战狼2 | 18 | 3 | Action |
| 3 | 失恋33天 | 2 | 13 | Love |
| 4 | 宝贝计划 | 4 | 2 | Comedy |
| 5 | 捉妖记 | 10 | 10 | Action |
| 6 | 乡村爱情 | 3 | 4 | Comedy |
| 7 | 阳光的快乐生活 | 2 | 3 | Comedy |
| 8 | 后来的你们 | 2 | 11 | Love |
| 9 | 大话西游 | 18 | 2 | Action |
| 10 | 速度与激情8 | 3 | 19 | Love |
| 11 | 一路向北 | 5 | 17 | Love |
In [8]:
# 实例对象，括号内为k值，k值影响评分，k值小评分高
knn = KNeighborsClassifier(n_neighbors=3)
In [10]:
# 特征数据
feature = data[['Action lens','Love lens']]
# 目标数据
target = data['target']
In [11]:
knn.fit(feature,target)
Out[11]:
KNeighborsClassifier(algorithm='auto', leaf_size=30, metric='minkowski',
metric_params=None, n_jobs=None, n_neighbors=3, p=2,
weights='uniform')In [12]:
# 评分
knn.score(feature,target)
Out[12]:
0.9166666666666666
In [15]:
# 根据特征值进行分类
knn.predict(np.array([[90,333]]))
Out[15]:
array(['Love'], dtype=object)
0）一个最简单的例子
身高、体重、鞋子尺码数据对应性别
In [16]:
import numpy as np
import pandas as pd
from pandas import Series,DataFrame
In [26]:
feature = np.array([[170,75,41],[166,65,38],[177,80,43],[179,80,43],[170,60,40],[160,55,38]])
target = np.array(['男','女','男','男','女','女'])
In [23]:
from sklearn.neighbors import KNeighborsClassifier
knn = KNeighborsClassifier(n_neighbors=3)
In [27]:
knn.fit(feature,target)
knn.score(feature,target)
Out[27]:
1.0
In [28]:
knn.predict(np.array([[176,71,38]]))
Out[28]:
array(['男'], dtype='<U1')
1）用于分类
导包，机器学习的算法KNN、数据蓝蝴蝶
In [30]:
import sklearn.datasets as datasets
In [32]:
iris = datasets.load_iris()
iris
Out[32]:
{'data': array([[5.1, 3.5, 1.4, 0.2],
[4.9, 3. , 1.4, 0.2],
[4.7, 3.2, 1.3, 0.2],
[4.6, 3.1, 1.5, 0.2],
[5. , 3.6, 1.4, 0.2],
[5.4, 3.9, 1.7, 0.4],
[4.6, 3.4, 1.4, 0.3],
[5. , 3.4, 1.5, 0.2],
[4.4, 2.9, 1.4, 0.2],
[4.9, 3.1, 1.5, 0.1],
[5.4, 3.7, 1.5, 0.2],
[4.8, 3.4, 1.6, 0.2],
[4.8, 3. , 1.4, 0.1],
[4.3, 3. , 1.1, 0.1],
[5.8, 4. , 1.2, 0.2],
[5.7, 4.4, 1.5, 0.4],
[5.4, 3.9, 1.3, 0.4],
[5.1, 3.5, 1.4, 0.3],
[5.7, 3.8, 1.7, 0.3],
[5.1, 3.8, 1.5, 0.3],
[5.4, 3.4, 1.7, 0.2],
[5.1, 3.7, 1.5, 0.4],
[4.6, 3.6, 1. , 0.2],
[5.1, 3.3, 1.7, 0.5],
[4.8, 3.4, 1.9, 0.2],
[5. , 3. , 1.6, 0.2],
[5. , 3.4, 1.6, 0.4],
[5.2, 3.5, 1.5, 0.2],
[5.2, 3.4, 1.4, 0.2],
[4.7, 3.2, 1.6, 0.2],
[4.8, 3.1, 1.6, 0.2],
[5.4, 3.4, 1.5, 0.4],
[5.2, 4.1, 1.5, 0.1],
[5.5, 4.2, 1.4, 0.2],
[4.9, 3.1, 1.5, 0.2],
[5. , 3.2, 1.2, 0.2],
[5.5, 3.5, 1.3, 0.2],
[4.9, 3.6, 1.4, 0.1],
[4.4, 3. , 1.3, 0.2],
[5.1, 3.4, 1.5, 0.2],
[5. , 3.5, 1.3, 0.3],
[4.5, 2.3, 1.3, 0.3],
[4.4, 3.2, 1.3, 0.2],
[5. , 3.5, 1.6, 0.6],
[5.1, 3.8, 1.9, 0.4],
[4.8, 3. , 1.4, 0.3],
[5.1, 3.8, 1.6, 0.2],
[4.6, 3.2, 1.4, 0.2],
[5.3, 3.7, 1.5, 0.2],
[5. , 3.3, 1.4, 0.2],
[7. , 3.2, 4.7, 1.4],
[6.4, 3.2, 4.5, 1.5],
[6.9, 3.1, 4.9, 1.5],
[5.5, 2.3, 4. , 1.3],
[6.5, 2.8, 4.6, 1.5],
[5.7, 2.8, 4.5, 1.3],
[6.3, 3.3, 4.7, 1.6],
[4.9, 2.4, 3.3, 1. ],
[6.6, 2.9, 4.6, 1.3],
[5.2, 2.7, 3.9, 1.4],
[5. , 2. , 3.5, 1. ],
[5.9, 3. , 4.2, 1.5],
[6. , 2.2, 4. , 1. ],
[6.1, 2.9, 4.7, 1.4],
[5.6, 2.9, 3.6, 1.3],
[6.7, 3.1, 4.4, 1.4],
[5.6, 3. , 4.5, 1.5],
[5.8, 2.7, 4.1, 1. ],
[6.2, 2.2, 4.5, 1.5],
[5.6, 2.5, 3.9, 1.1],
[5.9, 3.2, 4.8, 1.8],
[6.1, 2.8, 4. , 1.3],
[6.3, 2.5, 4.9, 1.5],
[6.1, 2.8, 4.7, 1.2],
[6.4, 2.9, 4.3, 1.3],
[6.6, 3. , 4.4, 1.4],
[6.8, 2.8, 4.8, 1.4],
[6.7, 3. , 5. , 1.7],
[6. , 2.9, 4.5, 1.5],
[5.7, 2.6, 3.5, 1. ],
[5.5, 2.4, 3.8, 1.1],
[5.5, 2.4, 3.7, 1. ],
[5.8, 2.7, 3.9, 1.2],
[6. , 2.7, 5.1, 1.6],
[5.4, 3. , 4.5, 1.5],
[6. , 3.4, 4.5, 1.6],
[6.7, 3.1, 4.7, 1.5],
[6.3, 2.3, 4.4, 1.3],
[5.6, 3. , 4.1, 1.3],
[5.5, 2.5, 4. , 1.3],
[5.5, 2.6, 4.4, 1.2],
[6.1, 3. , 4.6, 1.4],
[5.8, 2.6, 4. , 1.2],
[5. , 2.3, 3.3, 1. ],
[5.6, 2.7, 4.2, 1.3],
[5.7, 3. , 4.2, 1.2],
[5.7, 2.9, 4.2, 1.3],
[6.2, 2.9, 4.3, 1.3],
[5.1, 2.5, 3. , 1.1],
[5.7, 2.8, 4.1, 1.3],
[6.3, 3.3, 6. , 2.5],
[5.8, 2.7, 5.1, 1.9],
[7.1, 3. , 5.9, 2.1],
[6.3, 2.9, 5.6, 1.8],
[6.5, 3. , 5.8, 2.2],
[7.6, 3. , 6.6, 2.1],
[4.9, 2.5, 4.5, 1.7],
[7.3, 2.9, 6.3, 1.8],
[6.7, 2.5, 5.8, 1.8],
[7.2, 3.6, 6.1, 2.5],
[6.5, 3.2, 5.1, 2. ],
[6.4, 2.7, 5.3, 1.9],
[6.8, 3. , 5.5, 2.1],
[5.7, 2.5, 5. , 2. ],
[5.8, 2.8, 5.1, 2.4],
[6.4, 3.2, 5.3, 2.3],
[6.5, 3. , 5.5, 1.8],
[7.7, 3.8, 6.7, 2.2],
[7.7, 2.6, 6.9, 2.3],
[6. , 2.2, 5. , 1.5],
[6.9, 3.2, 5.7, 2.3],
[5.6, 2.8, 4.9, 2. ],
[7.7, 2.8, 6.7, 2. ],
[6.3, 2.7, 4.9, 1.8],
[6.7, 3.3, 5.7, 2.1],
[7.2, 3.2, 6. , 1.8],
[6.2, 2.8, 4.8, 1.8],
[6.1, 3. , 4.9, 1.8],
[6.4, 2.8, 5.6, 2.1],
[7.2, 3. , 5.8, 1.6],
[7.4, 2.8, 6.1, 1.9],
[7.9, 3.8, 6.4, 2. ],
[6.4, 2.8, 5.6, 2.2],
[6.3, 2.8, 5.1, 1.5],
[6.1, 2.6, 5.6, 1.4],
[7.7, 3. , 6.1, 2.3],
[6.3, 3.4, 5.6, 2.4],
[6.4, 3.1, 5.5, 1.8],
[6. , 3. , 4.8, 1.8],
[6.9, 3.1, 5.4, 2.1],
[6.7, 3.1, 5.6, 2.4],
[6.9, 3.1, 5.1, 2.3],
[5.8, 2.7, 5.1, 1.9],
[6.8, 3.2, 5.9, 2.3],
[6.7, 3.3, 5.7, 2.5],
[6.7, 3. , 5.2, 2.3],
[6.3, 2.5, 5. , 1.9],
[6.5, 3. , 5.2, 2. ],
[6.2, 3.4, 5.4, 2.3],
[5.9, 3. , 5.1, 1.8]]),
'target': array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]),
'target_names': array(['setosa', 'versicolor', 'virginica'], dtype='<U10'),
'DESCR': '.. _iris_dataset:\n\nIris plants dataset\n--------------------\n\n**Data Set Characteristics:**\n\n :Number of Instances: 150 (50 in each of three classes)\n :Number of Attributes: 4 numeric, predictive attributes and the class\n :Attribute Information:\n - sepal length in cm\n - sepal width in cm\n - petal length in cm\n - petal width in cm\n - class:\n - Iris-Setosa\n - Iris-Versicolour\n - Iris-Virginica\n \n :Summary Statistics:\n\n ============== ==== ==== ======= ===== ====================\n Min Max Mean SD Class Correlation\n ============== ==== ==== ======= ===== ====================\n sepal length: 4.3 7.9 5.84 0.83 0.7826\n sepal width: 2.0 4.4 3.05 0.43 -0.4194\n petal length: 1.0 6.9 3.76 1.76 0.9490 (high!)\n petal width: 0.1 2.5 1.20 0.76 0.9565 (high!)\n ============== ==== ==== ======= ===== ====================\n\n :Missing Attribute Values: None\n :Class Distribution: 33.3% for each of 3 classes.\n :Creator: R.A. Fisher\n :Donor: Michael Marshall (MARSHALL%[email protected])\n :Date: July, 1988\n\nThe famous Iris database, first used by Sir R.A. Fisher. The dataset is taken\nfrom Fisher\'s paper. Note that it\'s the same as in R, but not as in the UCI\nMachine Learning Repository, which has two wrong data points.\n\nThis is perhaps the best known database to be found in the\npattern recognition literature. Fisher\'s paper is a classic in the field and\nis referenced frequently to this day. (See Duda & Hart, for example.) The\ndata set contains 3 classes of 50 instances each, where each class refers to a\ntype of iris plant. One class is linearly separable from the other 2; the\nlatter are NOT linearly separable from each other.\n\n.. topic:: References\n\n - Fisher, R.A. "The use of multiple measurements in taxonomic problems"\n Annual Eugenics, 7, Part II, 179-188 (1936); also in "Contributions to\n Mathematical Statistics" (John Wiley, NY, 1950).\n - Duda, R.O., & Hart, P.E. (1973) Pattern Classification and Scene Analysis.\n (Q327.D83) John Wiley & Sons. ISBN 0-471-22361-1. See page 218.\n - Dasarathy, B.V. (1980) "Nosing Around the Neighborhood: A New System\n Structure and Classification Rule for Recognition in Partially Exposed\n Environments". IEEE Transactions on Pattern Analysis and Machine\n Intelligence, Vol. PAMI-2, No. 1, 67-71.\n - Gates, G.W. (1972) "The Reduced Nearest Neighbor Rule". IEEE Transactions\n on Information Theory, May 1972, 431-433.\n - See also: 1988 MLC Proceedings, 54-64. Cheeseman et al"s AUTOCLASS II\n conceptual clustering system finds 3 classes in the data.\n - Many, many more ...',
'feature_names': ['sepal length (cm)',
'sepal width (cm)',
'petal length (cm)',
'petal width (cm)'],
'filename': 'E:\\Anaconda3\\lib\\site-packages\\sklearn\\datasets\\data\\iris.csv'}提取样本数据
In [33]:
feature = iris['data']
target = iris['target']
In [39]:
feature.shape
Out[39]:
(150, 4)
将样本数据进行随机打乱
In [40]:
np.random.seed(1)
np.random.shuffle(feature)
np.random.seed(1)
np.random.shuffle(target)
In [41]:
feature.shape
Out[41]:
(150, 4)
获取训练样本数据和测试样本数据
In [46]:
#训练数据
x_train = feature[:140]
y_train = target[:140]
#测试数据
x_test = feature[-10:]
y_test =target[-10:]
In [47]:
x_test.shape
Out[47]:
(10, 4)
实例化模型对象&训练模型
In [67]:
knn = KNeighborsClassifier(n_neighbors=10)
knn.fit(x_train,y_train)
Out[67]:
KNeighborsClassifier(algorithm='auto', leaf_size=30, metric='minkowski',
metric_params=None, n_jobs=None, n_neighbors=10, p=2,
weights='uniform')In [68]:
knn.score(x_train,y_train)
Out[68]:
0.9785714285714285
In [60]:
print('模型分类结果：',knn.predict(x_test))
print('真实分类结果：',y_test)
模型分类结果： [0 2 1 2 1 2 2 1 2 0] 真实分类结果： [0 2 1 2 1 2 2 1 2 0]
如何选中最有的k值
In [62]:
k_list = []
s_list = []
for k in range(1,61):
knn = KNeighborsClassifier(n_neighbors=k)
knn.fit(x_train,y_train)
s = knn.score(x_train,y_train)
s_list.append(s)
k_list.append(k)
In [63]:
import matplotlib.pyplot as plt
In [64]:
plt.plot(k_list,s_list)
Out[64]:
[<matplotlib.lines.Line2D at 0x1a153b9c198>]
3、作业
1、预测年收入是否大于50K美元
读取adult.txt文件，最后一列是年收入，并使用KNN算法训练模型，然后使用模型预测一个人的年收入是否大于50
In [69]:
df = pd.read_csv('../data/adults.txt')
df.head()
Out[69]:
| 0 | 39 | State-gov | 77516 | Bachelors | 13 | Never-married | Adm-clerical | Not-in-family | White | Male | 2174 | 0 | 40 | United-States | <=50K |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 50 | Self-emp-not-inc | 83311 | Bachelors | 13 | Married-civ-spouse | Exec-managerial | Husband | White | Male | 0 | 0 | 13 | United-States | <=50K |
| 2 | 38 | Private | 215646 | HS-grad | 9 | Divorced | Handlers-cleaners | Not-in-family | White | Male | 0 | 0 | 40 | United-States | <=50K |
| 3 | 53 | Private | 234721 | 11th | 7 | Married-civ-spouse | Handlers-cleaners | Husband | Black | Male | 0 | 0 | 40 | United-States | <=50K |
| 4 | 28 | Private | 338409 | Bachelors | 13 | Married-civ-spouse | Prof-specialty | Wife | Black | Female | 0 | 0 | 40 | Cuba | <=50K |
In [70]:
df.shape
Out[70]:
(32561, 15)
获取年龄、教育程度、职位、每周工作时间作为机器学习数据
获取薪水作为对应结果
In [61]:
job_array = df['occupation'].unique()
job_array
Out[61]:
array(['Adm-clerical', 'Exec-managerial', 'Handlers-cleaners',
'Prof-specialty', 'Other-service', 'Sales', 'Craft-repair',
'Transport-moving', 'Farming-fishing', 'Machine-op-inspct',
'Tech-support', '?', 'Protective-serv', 'Armed-Forces',
'Priv-house-serv'], dtype=object)In [62]:
dic = {}
for i in range(15):
key = job_array[i]
value = i
dic[key] = value
In [64]:
df['occupation'] = df['occupation'].map(dic)
In [66]:
feature = df[['occupation','age','education_num','hours_per_week']]
target = df['salary']
数据转换，将String类型数据转换为int
【知识点】map方法，进行数据转换
切片：训练数据和预测数据
In [67]:
feature.shape
Out[67]:
(32561, 4)
In [70]:
x_train = feature[:32551]
y_train = target[:32551]
x_test = feature[-10:]
y_test = target[-10:]
生成算法
In [75]:
knn = KNeighborsClassifier(n_neighbors=10)
knn.fit(x_train,y_train)
knn.score(x_train,y_train)
Out[75]:
0.8192375042241405
In [76]:
print('预测值:',knn.predict(x_test))
print('真实值：',y_test)
预测值: ['<=50K' '<=50K' '<=50K' '<=50K' '<=50K' '<=50K' '<=50K' '<=50K' '<=50K' '<=50K'] 真实值： 32551 <=50K 32552 <=50K 32553 <=50K 32554 >50K 32555 <=50K 32556 <=50K 32557 >50K 32558 <=50K 32559 <=50K 32560 >50K Name: salary, dtype: object
第一步：训练数据
第二步：预测数据
保存训练模型
from sklearn.externals import joblib
In [77]:
from sklearn.externals import joblib
In [78]:
joblib.dump(knn,'./job_knn.m')
Out[78]:
['./job_knn.m']
In [80]:
k = joblib.load('./job_knn.m')
k
Out[80]:
KNeighborsClassifier(algorithm='auto', leaf_size=30, metric='minkowski',
metric_params=None, n_jobs=1, n_neighbors=10, p=2,
weights='uniform')2、小麦种类预测
读取seeds.tsv文件，最后一列是小麦品种，其他列是小麦特征
3、改进约会网站的匹配效果
读取datingTestSet.txt文件，最后一列是喜欢程度。模型：根据前几列的信息，预测喜欢程度
In [ ]:
归一化处理（特征数据）
In [82]:
x = [1,2,3,4,5]
y = [3,6,8,9,11]
In [83]:
import matplotlib.pyplot as plt
plt.scatter(x,y)
Out[83]:
<matplotlib.collections.PathCollection at 0x2c9cf754d30>
In [91]:
x1 = np.array([1,2,3,4,5])
y1 = np.array([6,7,8,9,10])
xx1,yy1 = np.meshgrid(x1,y1)
display(xx1,yy1)
array([[1, 2, 3, 4, 5],
[1, 2, 3, 4, 5],
[1, 2, 3, 4, 5],
[1, 2, 3, 4, 5],
[1, 2, 3, 4, 5]])array([[ 6, 6, 6, 6, 6],
[ 7, 7, 7, 7, 7],
[ 8, 8, 8, 8, 8],
[ 9, 9, 9, 9, 9],
[10, 10, 10, 10, 10]])In [93]:
np.c_[xx1.reshape(-1,1),yy1.reshape(-1,1)]
Out[93]:
array([[ 1, 6],
[ 2, 6],
[ 3, 6],
[ 4, 6],
[ 5, 6],
[ 1, 7],
[ 2, 7],
[ 3, 7],
[ 4, 7],
[ 5, 7],
[ 1, 8],
[ 2, 8],
[ 3, 8],
[ 4, 8],
[ 5, 8],
[ 1, 9],
[ 2, 9],
[ 3, 9],
[ 4, 9],
[ 5, 9],
[ 1, 10],
[ 2, 10],
[ 3, 10],
[ 4, 10],
[ 5, 10]])In [84]:
x = np.linspace(1,5,num=200)
y = np.linspace(3,11,num=200)
In [98]:
#返回一个网格矩阵
xx,yy = np.meshgrid(x,y)
xy = np.c_[xx.reshape(-1,1),yy.reshape(-1,1)]
xy.shape
Out[98]:
(40000, 2)
In [107]:
xa = [1,2,3,4,5]
xb = [3,4,5,6,7]
In [108]:
plt.scatter(xy[:,0],xy[:,1])
plt.scatter(xa,xb)
Out[108]:
<matplotlib.collections.PathCollection at 0x2c9cfa1f400>
In [99]:
xy[:,0]
Out[99]:
array([1. , 1.0201005 , 1.04020101, ..., 4.95979899, 4.9798995 ,
5. ])