多分类以及机器学习实践
如何对多个类别进行分类
Iris数据集是常用的分类实验数据集，由Fisher, 1936收集整理。Iris也称鸢尾花卉数据集，是一类多重变量分析的数据集。数据集包含150个数据样本，分为3类，每类50个数据，每个数据包含4个属性。可通过花萼长度，花萼宽度，花瓣长度，花瓣宽度4个属性预测鸢尾花卉属于（Setosa，Versicolour，Virginica）三个种类中的哪一类。
iris以鸢尾花的特征作为数据来源，常用在分类操作中。该数据集由3种不同类型的鸢尾花的各50个样本数据构成。其中的一个种类与另外两个种类是线性可分离的，后两个种类是非线性可分离的。
该数据集包含了4个属性：
Sepal.Length（花萼长度），单位是cm;
Sepal.Width（花萼宽度），单位是cm;
Petal.Length（花瓣长度），单位是cm;
Petal.Width（花瓣宽度），单位是cm;
种类：Iris Setosa（山鸢尾）、Iris Versicolour（杂色鸢尾），以及Iris Virginica（维吉尼亚鸢尾）。
1.1 数据的预处理
import sklearn.datasets as datasets import pandas as pd import numpy as np
data=datasets.load_iris() data
{'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]), 'frame': None, '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%PLU@io.arc.nasa.gov)\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': 'iris.csv', 'data_module': 'sklearn.datasets.data'}
data_x=data["data"] data_y=data["target"]
data_x.shape,data_y.shape
((150, 4), (150,))
data_y=data_y.reshape([len(data_y),1]) data_y
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]])
#法1 ，用拼接的方法 data=np.hstack([data_x,data_y])
#法二： 用插入的方法 np.insert(data_x,data_x.shape[1],data_y,axis=1)
array([[5.1, 3.5, 1.4, ..., 2. , 2. , 2. ], [4.9, 3. , 1.4, ..., 2. , 2. , 2. ], [4.7, 3.2, 1.3, ..., 2. , 2. , 2. ], ..., [6.5, 3. , 5.2, ..., 2. , 2. , 2. ], [6.2, 3.4, 5.4, ..., 2. , 2. , 2. ], [5.9, 3. , 5.1, ..., 2. , 2. , 2. ]])
data=pd.DataFrame(data,columns=["F1","F2","F3","F4","target"]) data
| F1 | F2 | F3 | F4 | target |
| 0 | 5.1 | 3.5 | 1.4 | 0.2 | 0.0 |
| 1 | 4.9 | 3.0 | 1.4 | 0.2 | 0.0 |
| 2 | 4.7 | 3.2 | 1.3 | 0.2 | 0.0 |
| 3 | 4.6 | 3.1 | 1.5 | 0.2 | 0.0 |
| 4 | 5.0 | 3.6 | 1.4 | 0.2 | 0.0 |
| ... | ... | ... | ... | ... | ... |
| 145 | 6.7 | 3.0 | 5.2 | 2.3 | 2.0 |
| 146 | 6.3 | 2.5 | 5.0 | 1.9 | 2.0 |
| 147 | 6.5 | 3.0 | 5.2 | 2.0 | 2.0 |
| 148 | 6.2 | 3.4 | 5.4 | 2.3 | 2.0 |
| 149 | 5.9 | 3.0 | 5.1 | 1.8 | 2.0 |
150 rows × 5 columns
data.insert(0,"ones",1)
data
ones |
F1 | F2 | F3 | F4 | target | |
| 0 | 1 | 5.1 | 3.5 | 1.4 | 0.2 | 0.0 |
| 1 | 1 | 4.9 | 3.0 | 1.4 | 0.2 | 0.0 |
| 2 | 1 | 4.7 | 3.2 | 1.3 | 0.2 | 0.0 |
| 3 | 1 | 4.6 | 3.1 | 1.5 | 0.2 | 0.0 |
| 4 | 1 | 5.0 | 3.6 | 1.4 | 0.2 | 0.0 |
| ... | ... | ... | ... | ... | ... | ... |
| 145 | 1 | 6.7 | 3.0 | 5.2 | 2.3 | 2.0 |
| 146 | 1 | 6.3 | 2.5 | 5.0 | 1.9 | 2.0 |
| 147 | 1 | 6.5 | 3.0 | 5.2 | 2.0 | 2.0 |
| 148 | 1 | 6.2 | 3.4 | 5.4 | 2.3 | 2.0 |
| 149 | 1 | 5.9 | 3.0 | 5.1 | 1.8 | 2.0 |
150 rows × 6 columns
data["target"]=data["target"].astype("int32")
data
| ones | F1 | F2 | F3 | F4 | target | |
| 0 | 1 | 5.1 | 3.5 | 1.4 | 0.2 | 0 |
| 1 | 1 | 4.9 | 3.0 | 1.4 | 0.2 | 0 |
| 2 | 1 | 4.7 | 3.2 | 1.3 | 0.2 | 0 |
| 3 | 1 | 4.6 | 3.1 | 1.5 | 0.2 | 0 |
| 4 | 1 | 5.0 | 3.6 | 1.4 | 0.2 | 0 |
| ... | ... | ... | ... | ... | ... | ... |
| 145 | 1 | 6.7 | 3.0 | 5.2 | 2.3 | 2 |
| 146 | 1 | 6.3 | 2.5 | 5.0 | 1.9 | 2 |
| 147 | 1 | 6.5 | 3.0 | 5.2 | 2.0 | 2 |
| 148 | 1 | 6.2 | 3.4 | 5.4 | 2.3 | 2 |
| 149 | 1 | 5.9 | 3.0 | 5.1 | 1.8 | 2 |
150 rows × 6 columns
1.2 训练数据的准备
data_x
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]])
data_x=np.insert(data_x,0,1,axis=1)
data_x.shape,data_y.shape
((150, 5), (150, 1))
#训练数据的特征和标签 data_x,data_y
(array([[1. , 5.1, 3.5, 1.4, 0.2], [1. , 4.9, 3. , 1.4, 0.2], [1. , 4.7, 3.2, 1.3, 0.2], [1. , 4.6, 3.1, 1.5, 0.2], [1. , 5. , 3.6, 1.4, 0.2], [1. , 5.4, 3.9, 1.7, 0.4], [1. , 4.6, 3.4, 1.4, 0.3], [1. , 5. , 3.4, 1.5, 0.2], [1. , 4.4, 2.9, 1.4, 0.2], [1. , 4.9, 3.1, 1.5, 0.1], [1. , 5.4, 3.7, 1.5, 0.2], [1. , 4.8, 3.4, 1.6, 0.2], [1. , 4.8, 3. , 1.4, 0.1], [1. , 4.3, 3. , 1.1, 0.1], [1. , 5.8, 4. , 1.2, 0.2], [1. , 5.7, 4.4, 1.5, 0.4], [1. , 5.4, 3.9, 1.3, 0.4], [1. , 5.1, 3.5, 1.4, 0.3], [1. , 5.7, 3.8, 1.7, 0.3], [1. , 5.1, 3.8, 1.5, 0.3], [1. , 5.4, 3.4, 1.7, 0.2], [1. , 5.1, 3.7, 1.5, 0.4], [1. , 4.6, 3.6, 1. , 0.2], [1. , 5.1, 3.3, 1.7, 0.5], [1. , 4.8, 3.4, 1.9, 0.2], [1. , 5. , 3. , 1.6, 0.2], [1. , 5. , 3.4, 1.6, 0.4], [1. , 5.2, 3.5, 1.5, 0.2], [1. , 5.2, 3.4, 1.4, 0.2], [1. , 4.7, 3.2, 1.6, 0.2], [1. , 4.8, 3.1, 1.6, 0.2], [1. , 5.4, 3.4, 1.5, 0.4], [1. , 5.2, 4.1, 1.5, 0.1], [1. , 5.5, 4.2, 1.4, 0.2], [1. , 4.9, 3.1, 1.5, 0.2], [1. , 5. , 3.2, 1.2, 0.2], [1. , 5.5, 3.5, 1.3, 0.2], [1. , 4.9, 3.6, 1.4, 0.1], [1. , 4.4, 3. , 1.3, 0.2], [1. , 5.1, 3.4, 1.5, 0.2], [1. , 5. , 3.5, 1.3, 0.3], [1. , 4.5, 2.3, 1.3, 0.3], [1. , 4.4, 3.2, 1.3, 0.2], [1. , 5. , 3.5, 1.6, 0.6], [1. , 5.1, 3.8, 1.9, 0.4], [1. , 4.8, 3. , 1.4, 0.3], [1. , 5.1, 3.8, 1.6, 0.2], [1. , 4.6, 3.2, 1.4, 0.2], [1. , 5.3, 3.7, 1.5, 0.2], [1. , 5. , 3.3, 1.4, 0.2], [1. , 7. , 3.2, 4.7, 1.4], [1. , 6.4, 3.2, 4.5, 1.5], [1. , 6.9, 3.1, 4.9, 1.5], [1. , 5.5, 2.3, 4. , 1.3], [1. , 6.5, 2.8, 4.6, 1.5], [1. , 5.7, 2.8, 4.5, 1.3], [1. , 6.3, 3.3, 4.7, 1.6], [1. , 4.9, 2.4, 3.3, 1. ], [1. , 6.6, 2.9, 4.6, 1.3], [1. , 5.2, 2.7, 3.9, 1.4], [1. , 5. , 2. , 3.5, 1. ], [1. , 5.9, 3. , 4.2, 1.5], [1. , 6. , 2.2, 4. , 1. ], [1. , 6.1, 2.9, 4.7, 1.4], [1. , 5.6, 2.9, 3.6, 1.3], [1. , 6.7, 3.1, 4.4, 1.4], [1. , 5.6, 3. , 4.5, 1.5], [1. , 5.8, 2.7, 4.1, 1. ], [1. , 6.2, 2.2, 4.5, 1.5], [1. , 5.6, 2.5, 3.9, 1.1], [1. , 5.9, 3.2, 4.8, 1.8], [1. , 6.1, 2.8, 4. , 1.3], [1. , 6.3, 2.5, 4.9, 1.5], [1. , 6.1, 2.8, 4.7, 1.2], [1. , 6.4, 2.9, 4.3, 1.3], [1. , 6.6, 3. , 4.4, 1.4], [1. , 6.8, 2.8, 4.8, 1.4], [1. , 6.7, 3. , 5. , 1.7], [1. , 6. , 2.9, 4.5, 1.5], [1. , 5.7, 2.6, 3.5, 1. ], [1. , 5.5, 2.4, 3.8, 1.1], [1. , 5.5, 2.4, 3.7, 1. ], [1. , 5.8, 2.7, 3.9, 1.2], [1. , 6. , 2.7, 5.1, 1.6], [1. , 5.4, 3. , 4.5, 1.5], [1. , 6. , 3.4, 4.5, 1.6], [1. , 6.7, 3.1, 4.7, 1.5], [1. , 6.3, 2.3, 4.4, 1.3], [1. , 5.6, 3. , 4.1, 1.3], [1. , 5.5, 2.5, 4. , 1.3], [1. , 5.5, 2.6, 4.4, 1.2], [1. , 6.1, 3. , 4.6, 1.4], [1. , 5.8, 2.6, 4. , 1.2], [1. , 5. , 2.3, 3.3, 1. ], [1. , 5.6, 2.7, 4.2, 1.3], [1. , 5.7, 3. , 4.2, 1.2], [1. , 5.7, 2.9, 4.2, 1.3], [1. , 6.2, 2.9, 4.3, 1.3], [1. , 5.1, 2.5, 3. , 1.1], [1. , 5.7, 2.8, 4.1, 1.3], [1. , 6.3, 3.3, 6. , 2.5], [1. , 5.8, 2.7, 5.1, 1.9], [1. , 7.1, 3. , 5.9, 2.1], [1. , 6.3, 2.9, 5.6, 1.8], [1. , 6.5, 3. , 5.8, 2.2], [1. , 7.6, 3. , 6.6, 2.1], [1. , 4.9, 2.5, 4.5, 1.7], [1. , 7.3, 2.9, 6.3, 1.8], [1. , 6.7, 2.5, 5.8, 1.8], [1. , 7.2, 3.6, 6.1, 2.5], [1. , 6.5, 3.2, 5.1, 2. ], [1. , 6.4, 2.7, 5.3, 1.9], [1. , 6.8, 3. , 5.5, 2.1], [1. , 5.7, 2.5, 5. , 2. ], [1. , 5.8, 2.8, 5.1, 2.4], [1. , 6.4, 3.2, 5.3, 2.3], [1. , 6.5, 3. , 5.5, 1.8], [1. , 7.7, 3.8, 6.7, 2.2], [1. , 7.7, 2.6, 6.9, 2.3], [1. , 6. , 2.2, 5. , 1.5], [1. , 6.9, 3.2, 5.7, 2.3], [1. , 5.6, 2.8, 4.9, 2. ], [1. , 7.7, 2.8, 6.7, 2. ], [1. , 6.3, 2.7, 4.9, 1.8], [1. , 6.7, 3.3, 5.7, 2.1], [1. , 7.2, 3.2, 6. , 1.8], [1. , 6.2, 2.8, 4.8, 1.8], [1. , 6.1, 3. , 4.9, 1.8], [1. , 6.4, 2.8, 5.6, 2.1], [1. , 7.2, 3. , 5.8, 1.6], [1. , 7.4, 2.8, 6.1, 1.9], [1. , 7.9, 3.8, 6.4, 2. ], [1. , 6.4, 2.8, 5.6, 2.2], [1. , 6.3, 2.8, 5.1, 1.5], [1. , 6.1, 2.6, 5.6, 1.4], [1. , 7.7, 3. , 6.1, 2.3], [1. , 6.3, 3.4, 5.6, 2.4], [1. , 6.4, 3.1, 5.5, 1.8], [1. , 6. , 3. , 4.8, 1.8], [1. , 6.9, 3.1, 5.4, 2.1], [1. , 6.7, 3.1, 5.6, 2.4], [1. , 6.9, 3.1, 5.1, 2.3], [1. , 5.8, 2.7, 5.1, 1.9], [1. , 6.8, 3.2, 5.9, 2.3], [1. , 6.7, 3.3, 5.7, 2.5], [1. , 6.7, 3. , 5.2, 2.3], [1. , 6.3, 2.5, 5. , 1.9], [1. , 6.5, 3. , 5.2, 2. ], [1. , 6.2, 3.4, 5.4, 2.3], [1. , 5.9, 3. , 5.1, 1.8]]), 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]]))
由于有三个类别，那么在训练时三类数据要分开
data1=data.copy()
data1
| ones | F1 | F2 | F3 | F4 | target | |
| 0 | 1 | 5.1 | 3.5 | 1.4 | 0.2 | 0 |
| 1 | 1 | 4.9 | 3.0 | 1.4 | 0.2 | 0 |
| 2 | 1 | 4.7 | 3.2 | 1.3 | 0.2 | 0 |
| 3 | 1 | 4.6 | 3.1 | 1.5 | 0.2 | 0 |
| 4 | 1 | 5.0 | 3.6 | 1.4 | 0.2 | 0 |
| ... | ... | ... | ... | ... | ... | ... |
| 145 | 1 | 6.7 | 3.0 | 5.2 | 2.3 | 2 |
| 146 | 1 | 6.3 | 2.5 | 5.0 | 1.9 | 2 |
| 147 | 1 | 6.5 | 3.0 | 5.2 | 2.0 | 2 |
| 148 | 1 | 6.2 | 3.4 | 5.4 | 2.3 | 2 |
| 149 | 1 | 5.9 | 3.0 | 5.1 | 1.8 | 2 |
150 rows × 6 columns
data
data1.loc[data["target"]!=0,"target"]=0 data1.loc[data["target"]==0,"target"]=1
data1
| ones | F1 | F2 | F3 | F4 | target | |
| 0 | 1 | 5.1 | 3.5 | 1.4 | 0.2 | 1 |
| 1 | 1 | 4.9 | 3.0 | 1.4 | 0.2 | 1 |
| 2 | 1 | 4.7 | 3.2 | 1.3 | 0.2 | 1 |
| 3 | 1 | 4.6 | 3.1 | 1.5 | 0.2 | 1 |
| 4 | 1 | 5.0 | 3.6 | 1.4 | 0.2 | 1 |
| ... | ... | ... | ... | ... | ... | ... |
| 145 | 1 | 6.7 | 3.0 | 5.2 | 2.3 | 0 |
| 146 | 1 | 6.3 | 2.5 | 5.0 | 1.9 | 0 |
| 147 | 1 | 6.5 | 3.0 | 5.2 | 2.0 | 0 |
| 148 | 1 | 6.2 | 3.4 | 5.4 | 2.3 | 0 |
| 149 | 1 | 5.9 | 3.0 | 5.1 | 1.8 | 0 |
150 rows × 6 columns
data1_x=data1.iloc[:,:data1.shape[1]-1].values data1_y=data1.iloc[:,data1.shape[1]-1].values data1_x.shape,data1_y.shape
((150, 5), (150,))
#针对第二类，即第二个分类器的数据 data2=data.copy() data2.loc[data["target"]==1,"target"]=1 data2.loc[data["target"]!=1,"target"]=0 data2["target"]==0
0 True 1 True 2 True 3 True 4 True ... 145 True 146 True 147 True 148 True 149 True Name: target, Length: 150, dtype: bool
data2.shape[1]
6
data2.iloc[50:55,:]
| ones | F1 | F2 | F3 | F4 | target | |
| 50 | 1 | 7.0 | 3.2 | 4.7 | 1.4 | 1 |
| 51 | 1 | 6.4 | 3.2 | 4.5 | 1.5 | 1 |
| 52 | 1 | 6.9 | 3.1 | 4.9 | 1.5 | 1 |
| 53 | 1 | 5.5 | 2.3 | 4.0 | 1.3 | 1 |
| 54 | 1 | 6.5 | 2.8 | 4.6 | 1.5 | 1 |
data2_x=data2.iloc[:,:data2.shape[1]-1].values data2_y=data2.iloc[:,data2.shape[1]-1].values
#针对第三类，即第三个分类器的数据 data3=data.copy() data3.loc[data["target"]==2,"target"]=1 data3.loc[data["target"]!=2,"target"]=0 data3
ones |
F1 | F2 | F3 | F4 | target | |
| 0 | 1 | 5.1 | 3.5 | 1.4 | 0.2 | 0 |
| 1 | 1 | 4.9 | 3.0 | 1.4 | 0.2 | 0 |
| 2 | 1 | 4.7 | 3.2 | 1.3 | 0.2 | 0 |
| 3 | 1 | 4.6 | 3.1 | 1.5 | 0.2 | 0 |
| 4 | 1 | 5.0 | 3.6 | 1.4 | 0.2 | 0 |
| ... | ... | ... | ... | ... | ... | ... |
| 145 | 1 | 6.7 | 3.0 | 5.2 | 2.3 | 1 |
| 146 | 1 | 6.3 | 2.5 | 5.0 | 1.9 | 1 |
| 147 | 1 | 6.5 | 3.0 | 5.2 | 2.0 | 1 |
| 148 | 1 | 6.2 | 3.4 | 5.4 | 2.3 | 1 |
| 149 | 1 | 5.9 | 3.0 | 5.1 | 1.8 | 1 |
150 rows × 6 columns
data3_x=data3.iloc[:,:data3.shape[1]-1].values data3_y=data3.iloc[:,data3.shape[1]-1].values
1.3 定义假设函数，代价函数，梯度下降算法（从实验3复制过来）
def sigmoid(z): return 1 / (1 + np.exp(-z))
def h(X,w): z=X@w h=sigmoid(z) return h
#代价函数构造 def cost(X,w,y): #当X(m,n+1),y(m,),w(n+1,1) y_hat=sigmoid(X@w) right=np.multiply(y.ravel(),np.log(y_hat).ravel())+np.multiply((1-y).ravel(),np.log(1-y_hat).ravel()) cost=-np.sum(right)/X.shape[0] return cost
def sigmoid(z): return 1 / (1 + np.exp(-z)) def h(X,w): z=X@w h=sigmoid(z) return h #代价函数构造 def cost(X,w,y): #当X(m,n+1),y(m,),w(n+1,1) y_hat=sigmoid(X@w) right=np.multiply(y.ravel(),np.log(y_hat).ravel())+np.multiply((1-y).ravel(),np.log(1-y_hat).ravel()) cost=-np.sum(right)/X.shape[0] return cost def grandient(X,y,iter_num,alpha): y=y.reshape((X.shape[0],1)) w=np.zeros((X.shape[1],1)) cost_lst=[] for i in range(iter_num): y_pred=h(X,w)-y temp=np.zeros((X.shape[1],1)) for j in range(X.shape[1]): right=np.multiply(y_pred.ravel(),X[:,j]) gradient=1/(X.shape[0])*(np.sum(right)) temp[j,0]=w[j,0]-alpha*gradient w=temp cost_lst.append(cost(X,w,y.ravel())) return w,cost_lst
1.4 调用梯度下降算法来学习三个分类模型的参数
#初始化超参数 iter_num,alpha=600000,0.001
#训练第一个模型 w1,cost_lst1=grandient(data1_x,data1_y,iter_num,alpha)
import matplotlib.pyplot as plt plt.plot(range(iter_num),cost_lst1,"b-o")
[<matplotlib.lines.Line2D at 0x2562630b100>]
#训练第二个模型 w2,cost_lst2=grandient(data2_x,data2_y,iter_num,alpha)
import matplotlib.pyplot as plt plt.plot(range(iter_num),cost_lst2,"b-o")
[<matplotlib.lines.Line2D at 0x25628114280>]
#训练第三个模型 w3,cost_lst3=grandient(data3_x,data3_y,iter_num,alpha)
w3
array([[-3.22437049], [-3.50214058], [-3.50286355], [ 5.16580317], [ 5.89898368]])
import matplotlib.pyplot as plt plt.plot(range(iter_num),cost_lst3,"b-o")
[<matplotlib.lines.Line2D at 0x2562e0f81c0>]
1.5 利用模型进行预测
h(data_x,w3)
array([[1.48445441e-11], [1.72343968e-10], [1.02798153e-10], [5.81975546e-10], [1.48434710e-11], [1.95971176e-11], [2.18959639e-10], [5.01346874e-11], [1.40930075e-09], [1.12830635e-10], [4.31888744e-12], [1.69308343e-10], [1.35613372e-10], [1.65858883e-10], [7.89880725e-14], [4.23224675e-13], [2.48199140e-12], [2.67766642e-11], [5.39314286e-12], [1.56935848e-11], [3.47096426e-11], [4.01827075e-11], [7.63005509e-12], [8.26864773e-10], [7.97484594e-10], [3.41189783e-10], [2.73442178e-10], [1.75314894e-11], [1.48456174e-11], [4.84204982e-10], [4.84239990e-10], [4.01914238e-11], [1.18813180e-12], [3.14985611e-13], [2.03524473e-10], [2.14461446e-11], [2.18189955e-12], [1.16799745e-11], [5.92281641e-10], [3.53217554e-11], [2.26727669e-11], [8.74004884e-09], [2.93949962e-10], [6.26783110e-10], [2.23513465e-10], [4.41246960e-10], [1.45841303e-11], [2.44584721e-10], [6.13010507e-12], [4.24539165e-11], [1.64123143e-03], [8.55503211e-03], [1.65105645e-02], [9.87814122e-02], [3.97290777e-02], [1.11076040e-01], [4.19003715e-02], [2.88426221e-03], [6.27161978e-03], [7.67020481e-02], [2.27204861e-02], [2.08212169e-02], [4.58067633e-03], [9.90450665e-02], [1.19419048e-03], [1.41462060e-03], [2.22638069e-01], [2.68940904e-03], [3.66014737e-01], [6.97791873e-03], [5.78803255e-01], [2.32071970e-03], [5.28941621e-01], [4.57649874e-02], [2.69208900e-03], [2.84603646e-03], [2.20421076e-02], [2.07507605e-01], [9.10460936e-02], [2.44824946e-04], [8.37509821e-03], [2.78543808e-03], [3.11283202e-03], [8.89831833e-01], [3.65880536e-01], [3.03993844e-02], [1.18930239e-02], [4.99150151e-02], [1.10252946e-02], [5.15923462e-02], [1.43653056e-01], [4.41610209e-02], [7.37513950e-03], [2.88447014e-03], [5.07366744e-02], [7.24617687e-03], [1.83460602e-02], [5.40874928e-03], [3.87210511e-04], [1.55791816e-02], [9.99862942e-01], [9.89637526e-01], [9.86183040e-01], [9.83705644e-01], [9.98410187e-01], [9.97834502e-01], [9.84208537e-01], [9.85434538e-01], [9.94141336e-01], [9.94561329e-01], [7.20333384e-01], [9.70431293e-01], [9.62754456e-01], [9.96609064e-01], [9.99222270e-01], [9.83684437e-01], [9.26437633e-01], [9.83486260e-01], [9.99950496e-01], [9.39002061e-01], [9.88043323e-01], [9.88637702e-01], [9.98357641e-01], [7.65848930e-01], [9.73006160e-01], [8.76969899e-01], [6.61137141e-01], [6.97324053e-01], [9.97185846e-01], [6.11033594e-01], [9.77494647e-01], [6.58573810e-01], [9.98437920e-01], [5.24529693e-01], [9.70465066e-01], [9.87624920e-01], [9.97236435e-01], [9.26432706e-01], [6.61104746e-01], [8.84442100e-01], [9.96082862e-01], [8.40940308e-01], [9.89637526e-01], [9.96974990e-01], [9.97386310e-01], [9.62040470e-01], [9.52214579e-01], [8.96902215e-01], [9.90200940e-01], [9.28785160e-01]])
#将数据输入三个模型的看看结果 multi_pred=pd.DataFrame(zip(h(data_x,w1).ravel(),h(data_x,w2).ravel(),h(data_x,w3).ravel())) multi_pred
0 |
1 | 2 | |
| 0 | 0.999297 | 0.108037 | 1.484454e-11 |
| 1 | 0.997061 | 0.270814 | 1.723440e-10 |
| 2 | 0.998633 | 0.164710 | 1.027982e-10 |
| 3 | 0.995774 | 0.231910 | 5.819755e-10 |
| 4 | 0.999415 | 0.085259 | 1.484347e-11 |
| ... | ... | ... | ... |
| 145 | 0.000007 | 0.127574 | 9.620405e-01 |
| 146 | 0.000006 | 0.496389 | 9.522146e-01 |
| 147 | 0.000010 | 0.234745 | 8.969022e-01 |
| 148 | 0.000006 | 0.058444 | 9.902009e-01 |
| 149 | 0.000014 | 0.284295 | 9.287852e-01 |
150 rows × 3 columns
multi_pred.values[:3]
array([[9.99297209e-01, 1.08037473e-01, 1.48445441e-11], [9.97060801e-01, 2.70813780e-01, 1.72343968e-10], [9.98632728e-01, 1.64709623e-01, 1.02798153e-10]])
#每个样本的预测值 np.argmax(multi_pred.values,axis=1)
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, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 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, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], dtype=int64)
#每个样本的真实值 data_y
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]])
