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- Multiple classification and machine learning practice
-
- How to classify multiple categories
-
- 1.1 Data preprocessing
- 1.2 Preparation of training data
- 1.3 Define hypothesis function, cost function, gradient descent algorithm (copied from Experiment 3)
- 1.4 Call the gradient descent algorithm to learn the parameters of the three classification models
- 1.5 Using Models to Make Predictions
- 1.6 Evaluation Model
- 1.7 Try sklearn
- Experiment 4(1) Please do your first multi-category problem, good luck! Complete the following code
Multiple classification and machine learning practice
How to classify multiple categories
The Iris data set is a commonly used classification experiment data set, collected by Fisher, 1936. Iris, also known as the iris flower data set, is a data set for multivariate analysis. The data set contains 150 data samples, which are divided into 3 categories, 50 data in each category, and each data contains 4 attributes. Which of the three species (Setosa, Versicolour, Virginica) the iris flower belongs to can be predicted by the four attributes of sepal length, sepal width, petal length and petal width.
iris uses the characteristics of iris as a data source, which is often used in classification operations. The data set consists of 50 sample data of 3 different types of iris flowers. One of the species is linearly separable from the other two, and the latter two are non-linearly separable.
The data set contains 4 attributes:
Sepal.Length (sepal length), the unit is cm;
Sepal.Width (sepal width), the unit is cm;
Petal.Length (petal length), the unit is cm;
Petal.Width (petal width), in cm;
Species: Iris Setosa (Mountain Iris), Iris Versicolour (variegated Iris), and Iris Virginica (Virginia Iris).
1.1 Data preprocessing
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%[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': '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],
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[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 Preparation of training data
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],
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[0],
[0],
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[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]]))
Since there are three categories, the three types of data should be separated during training
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 Define hypothesis function, cost function, gradient descent algorithm (copied from Experiment 3)
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 Call the gradient descent algorithm to learn the parameters of the three classification models
#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 Using Models to Make Predictions
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]])
1.6 Evaluation Model
np.argmax(multi_pred.values,axis=1)==data_y.ravel()
array([ True, True, True, True, True, True, True, True, True,
True, True, True, True, True, True, True, True, True,
True, True, True, True, True, True, True, True, True,
True, True, True, True, True, True, True, True, True,
True, True, True, True, True, True, True, True, True,
True, True, True, True, True, True, True, True, True,
True, True, True, True, True, True, True, True, True,
True, True, True, True, True, True, True, False, True,
True, True, True, True, True, True, True, True, True,
True, True, False, False, True, True, True, True, True,
True, True, True, True, True, True, True, True, True,
True, True, True, True, True, True, True, True, True,
True, True, True, True, True, True, True, True, True,
True, True, True, True, True, True, True, True, True,
True, True, True, False, True, True, True, False, True,
True, True, True, True, True, True, True, True, True,
True, True, True, True, True, True])
np.sum(np.argmax(multi_pred.values,axis=1)==data_y.ravel())
145
np.sum(np.argmax(multi_pred.values,axis=1)==data_y.ravel())/len(data)
0.9666666666666667
1.7 Try sklearn
from sklearn.linear_model import LogisticRegression
#建立第一个模型
clf1=LogisticRegression()
clf1.fit(data1_x,data1_y)
#建立第二个模型
clf2=LogisticRegression()
clf2.fit(data2_x,data2_y)
#建立第三个模型
clf3=LogisticRegression()
clf3.fit(data3_x,data3_y)
LogisticRegression()
y_pred1=clf1.predict(data_x)
y_pred2=clf2.predict(data_x)
y_pred3=clf3.predict(data_x)
#可视化各模型的预测结果
multi_pred=pd.DataFrame(zip(y_pred1,y_pred2,y_pred3),columns=["模型1","模糊2","模型3"])
multi_pred
| model 1 | Blur 2 | model 3 | |
|---|---|---|---|
| 0 | 1 | 0 | 0 |
| 1 | 1 | 0 | 0 |
| 2 | 1 | 0 | 0 |
| 3 | 1 | 0 | 0 |
| 4 | 1 | 0 | 0 |
| ... | ... | ... | ... |
| 145 | 0 | 0 | 1 |
| 146 | 0 | 1 | 1 |
| 147 | 0 | 0 | 1 |
| 148 | 0 | 0 | 1 |
| 149 | 0 | 0 | 1 |
150 rows × 3 columns
#判断预测结果
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, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0,
0, 1, 1, 1, 2, 0, 1, 1, 0, 0, 0, 2, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1,
0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2, 1, 1, 1, 2,
2, 2, 2, 1, 2, 2, 2, 2, 1, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2,
2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2], dtype=int64)
data_y.ravel()
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])
#计算准确率
np.sum(np.argmax(multi_pred.values,axis=1)==data_y.ravel())/data.shape[0]
0.7333333333333333
Experiment 4(1) Please do your first multi-category problem, good luck! Complete the following code
2.1 Data reading
data_x,data_y=datasets.make_blobs(n_samples=200, n_features=6, centers=4,random_state=0)
data_x.shape,data_y.shape
((200, 6), (200,))
2.2 Preparation of training data
data=np.insert(data_x,data_x.shape[1],data_y,axis=1)
data=pd.DataFrame(data,columns=["F1","F2","F3","F4","F5","F6","target"])
data
| F1 | F2 | F3 | F4 | F5 | F6 | target | |
|---|---|---|---|---|---|---|---|
| 0 | 2.116632 | 7.972800 | -9.328969 | -8.224605 | -12.178429 | 5.498447 | 2.0 |
| 1 | 1.886449 | 4.621006 | 2.841595 | 0.431245 | -2.471350 | 2.507833 | 0.0 |
| 2 | 2.391329 | 6.464609 | -9.805900 | -7.289968 | -9.650985 | 6.388460 | 2.0 |
| 3 | -1.034776 | 6.626886 | 9.031235 | -0.812908 | 5.449855 | 0.134062 | 1.0 |
| 4 | -0.481593 | 8.191753 | 7.504717 | -1.975688 | 6.649021 | 0.636824 | 1.0 |
| ... | ... | ... | ... | ... | ... | ... | ... |
| 195 | 5.434893 | 7.128471 | 9.789546 | 6.061382 | 0.634133 | 5.757024 | 3.0 |
| 196 | -0.406625 | 7.586001 | 9.322750 | -1.837333 | 6.477815 | -0.992725 | 1.0 |
| 197 | 2.031462 | 7.804427 | -8.539512 | -9.824409 | -10.046935 | 6.918085 | 2.0 |
| 198 | 4.081889 | 6.127685 | 11.091126 | 4.812011 | -0.005915 | 5.342211 | 3.0 |
| 199 | 0.985744 | 7.285737 | -8.395940 | -6.586471 | -9.651765 | 6.651012 | 2.0 |
200 rows × 7 columns
data["target"]=data["target"].astype("int32")
data
| F1 | F2 | F3 | F4 | F5 | F6 | target | |
|---|---|---|---|---|---|---|---|
| 0 | 2.116632 | 7.972800 | -9.328969 | -8.224605 | -12.178429 | 5.498447 | 2 |
| 1 | 1.886449 | 4.621006 | 2.841595 | 0.431245 | -2.471350 | 2.507833 | 0 |
| 2 | 2.391329 | 6.464609 | -9.805900 | -7.289968 | -9.650985 | 6.388460 | 2 |
| 3 | -1.034776 | 6.626886 | 9.031235 | -0.812908 | 5.449855 | 0.134062 | 1 |
| 4 | -0.481593 | 8.191753 | 7.504717 | -1.975688 | 6.649021 | 0.636824 | 1 |
| ... | ... | ... | ... | ... | ... | ... | ... |
| 195 | 5.434893 | 7.128471 | 9.789546 | 6.061382 | 0.634133 | 5.757024 | 3 |
| 196 | -0.406625 | 7.586001 | 9.322750 | -1.837333 | 6.477815 | -0.992725 | 1 |
| 197 | 2.031462 | 7.804427 | -8.539512 | -9.824409 | -10.046935 | 6.918085 | 2 |
| 198 | 4.081889 | 6.127685 | 11.091126 | 4.812011 | -0.005915 | 5.342211 | 3 |
| 199 | 0.985744 | 7.285737 | -8.395940 | -6.586471 | -9.651765 | 6.651012 | 2 |
200 rows × 7 columns
data.insert(0,"ones",1)
data
| ones | F1 | F2 | F3 | F4 | F5 | F6 | target | |
|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2.116632 | 7.972800 | -9.328969 | -8.224605 | -12.178429 | 5.498447 | 2 |
| 1 | 1 | 1.886449 | 4.621006 | 2.841595 | 0.431245 | -2.471350 | 2.507833 | 0 |
| 2 | 1 | 2.391329 | 6.464609 | -9.805900 | -7.289968 | -9.650985 | 6.388460 | 2 |
| 3 | 1 | -1.034776 | 6.626886 | 9.031235 | -0.812908 | 5.449855 | 0.134062 | 1 |
| 4 | 1 | -0.481593 | 8.191753 | 7.504717 | -1.975688 | 6.649021 | 0.636824 | 1 |
| ... | ... | ... | ... | ... | ... | ... | ... | ... |
| 195 | 1 | 5.434893 | 7.128471 | 9.789546 | 6.061382 | 0.634133 | 5.757024 | 3 |
| 196 | 1 | -0.406625 | 7.586001 | 9.322750 | -1.837333 | 6.477815 | -0.992725 | 1 |
| 197 | 1 | 2.031462 | 7.804427 | -8.539512 | -9.824409 | -10.046935 | 6.918085 | 2 |
| 198 | 1 | 4.081889 | 6.127685 | 11.091126 | 4.812011 | -0.005915 | 5.342211 | 3 |
| 199 | 1 | 0.985744 | 7.285737 | -8.395940 | -6.586471 | -9.651765 | 6.651012 | 2 |
200 rows × 8 columns
#第一个类别的数据
data1=data.copy()
data1.loc[data["target"]==0,"target"]=1
data1.loc[data["target"]!=0,"target"]=0
data1
| ones | F1 | F2 | F3 | F4 | F5 | F6 | target | |
|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2.116632 | 7.972800 | -9.328969 | -8.224605 | -12.178429 | 5.498447 | 0 |
| 1 | 1 | 1.886449 | 4.621006 | 2.841595 | 0.431245 | -2.471350 | 2.507833 | 1 |
| 2 | 1 | 2.391329 | 6.464609 | -9.805900 | -7.289968 | -9.650985 | 6.388460 | 0 |
| 3 | 1 | -1.034776 | 6.626886 | 9.031235 | -0.812908 | 5.449855 | 0.134062 | 0 |
| 4 | 1 | -0.481593 | 8.191753 | 7.504717 | -1.975688 | 6.649021 | 0.636824 | 0 |
| ... | ... | ... | ... | ... | ... | ... | ... | ... |
| 195 | 1 | 5.434893 | 7.128471 | 9.789546 | 6.061382 | 0.634133 | 5.757024 | 0 |
| 196 | 1 | -0.406625 | 7.586001 | 9.322750 | -1.837333 | 6.477815 | -0.992725 | 0 |
| 197 | 1 | 2.031462 | 7.804427 | -8.539512 | -9.824409 | -10.046935 | 6.918085 | 0 |
| 198 | 1 | 4.081889 | 6.127685 | 11.091126 | 4.812011 | -0.005915 | 5.342211 | 0 |
| 199 | 1 | 0.985744 | 7.285737 | -8.395940 | -6.586471 | -9.651765 | 6.651012 | 0 |
200 rows × 8 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
((200, 7), (200,))
#第二个类别的数据
data2=data.copy()
data2.loc[data["target"]==1,"target"]=1
data2.loc[data["target"]!=1,"target"]=0
data2
| ones | F1 | F2 | F3 | F4 | F5 | F6 | target | |
|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2.116632 | 7.972800 | -9.328969 | -8.224605 | -12.178429 | 5.498447 | 0 |
| 1 | 1 | 1.886449 | 4.621006 | 2.841595 | 0.431245 | -2.471350 | 2.507833 | 0 |
| 2 | 1 | 2.391329 | 6.464609 | -9.805900 | -7.289968 | -9.650985 | 6.388460 | 0 |
| 3 | 1 | -1.034776 | 6.626886 | 9.031235 | -0.812908 | 5.449855 | 0.134062 | 1 |
| 4 | 1 | -0.481593 | 8.191753 | 7.504717 | -1.975688 | 6.649021 | 0.636824 | 1 |
| ... | ... | ... | ... | ... | ... | ... | ... | ... |
| 195 | 1 | 5.434893 | 7.128471 | 9.789546 | 6.061382 | 0.634133 | 5.757024 | 0 |
| 196 | 1 | -0.406625 | 7.586001 | 9.322750 | -1.837333 | 6.477815 | -0.992725 | 1 |
| 197 | 1 | 2.031462 | 7.804427 | -8.539512 | -9.824409 | -10.046935 | 6.918085 | 0 |
| 198 | 1 | 4.081889 | 6.127685 | 11.091126 | 4.812011 | -0.005915 | 5.342211 | 0 |
| 199 | 1 | 0.985744 | 7.285737 | -8.395940 | -6.586471 | -9.651765 | 6.651012 | 0 |
200 rows × 8 columns
data2_x=data2.iloc[:,:data2.shape[1]-1].values
data2_y=data2.iloc[:,data2.shape[1]-1].values
#第三个类别的数据
data3=data.copy()
data3.loc[data["target"]==2,"target"]=1
data3.loc[data["target"]!=2,"target"]=0
data3
| ones | F1 | F2 | F3 | F4 | F5 | F6 | target | |
|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2.116632 | 7.972800 | -9.328969 | -8.224605 | -12.178429 | 5.498447 | 1 |
| 1 | 1 | 1.886449 | 4.621006 | 2.841595 | 0.431245 | -2.471350 | 2.507833 | 0 |
| 2 | 1 | 2.391329 | 6.464609 | -9.805900 | -7.289968 | -9.650985 | 6.388460 | 1 |
| 3 | 1 | -1.034776 | 6.626886 | 9.031235 | -0.812908 | 5.449855 | 0.134062 | 0 |
| 4 | 1 | -0.481593 | 8.191753 | 7.504717 | -1.975688 | 6.649021 | 0.636824 | 0 |
| ... | ... | ... | ... | ... | ... | ... | ... | ... |
| 195 | 1 | 5.434893 | 7.128471 | 9.789546 | 6.061382 | 0.634133 | 5.757024 | 0 |
| 196 | 1 | -0.406625 | 7.586001 | 9.322750 | -1.837333 | 6.477815 | -0.992725 | 0 |
| 197 | 1 | 2.031462 | 7.804427 | -8.539512 | -9.824409 | -10.046935 | 6.918085 | 1 |
| 198 | 1 | 4.081889 | 6.127685 | 11.091126 | 4.812011 | -0.005915 | 5.342211 | 0 |
| 199 | 1 | 0.985744 | 7.285737 | -8.395940 | -6.586471 | -9.651765 | 6.651012 | 1 |
200 rows × 8 columns
data3_x=data3.iloc[:,:data3.shape[1]-1].values
data3_y=data3.iloc[:,data3.shape[1]-1].values
#第四个类别的数据
data4=data.copy()
data4.loc[data["target"]==3,"target"]=1
data4.loc[data["target"]!=3,"target"]=0
data4
| ones | F1 | F2 | F3 | F4 | F5 | F6 | target | |
|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2.116632 | 7.972800 | -9.328969 | -8.224605 | -12.178429 | 5.498447 | 0 |
| 1 | 1 | 1.886449 | 4.621006 | 2.841595 | 0.431245 | -2.471350 | 2.507833 | 0 |
| 2 | 1 | 2.391329 | 6.464609 | -9.805900 | -7.289968 | -9.650985 | 6.388460 | 0 |
| 3 | 1 | -1.034776 | 6.626886 | 9.031235 | -0.812908 | 5.449855 | 0.134062 | 0 |
| 4 | 1 | -0.481593 | 8.191753 | 7.504717 | -1.975688 | 6.649021 | 0.636824 | 0 |
| ... | ... | ... | ... | ... | ... | ... | ... | ... |
| 195 | 1 | 5.434893 | 7.128471 | 9.789546 | 6.061382 | 0.634133 | 5.757024 | 1 |
| 196 | 1 | -0.406625 | 7.586001 | 9.322750 | -1.837333 | 6.477815 | -0.992725 | 0 |
| 197 | 1 | 2.031462 | 7.804427 | -8.539512 | -9.824409 | -10.046935 | 6.918085 | 0 |
| 198 | 1 | 4.081889 | 6.127685 | 11.091126 | 4.812011 | -0.005915 | 5.342211 | 1 |
| 199 | 1 | 0.985744 | 7.285737 | -8.395940 | -6.586471 | -9.651765 | 6.651012 | 0 |
200 rows × 8 columns
data4_x=data4.iloc[:,:data4.shape[1]-1].values
data4_y=data4.iloc[:,data4.shape[1]-1].values
2.3 定义假设函数、代价函数和梯度下降算法
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
2.4 学习这四个分类模型
import matplotlib.pyplot as plt
#初始化超参数
iter_num,alpha=600000,0.001
#训练第1个模型
w1,cost_lst1=grandient(data1_x,data1_y,iter_num,alpha)
plt.plot(range(iter_num),cost_lst1,"b-o")
[<matplotlib.lines.Line2D at 0x25624eb08e0>]
#训练第2个模型
w2,cost_lst2=grandient(data2_x,data2_y,iter_num,alpha)
plt.plot(range(iter_num),cost_lst2,"b-o")
[<matplotlib.lines.Line2D at 0x25631b87a60>]
#训练第3个模型
w3,cost_lst3=grandient(data3_x,data3_y,iter_num,alpha)
plt.plot(range(iter_num),cost_lst3,"b-o")
[<matplotlib.lines.Line2D at 0x2562bcdfac0>]
#训练第4个模型
w4,cost_lst4=grandient(data4_x,data4_y,iter_num,alpha)
plt.plot(range(iter_num),cost_lst4,"b-o")
[<matplotlib.lines.Line2D at 0x25631ff4ee0>]
2.5 利用模型进行预测
data_x
array([[ 2.11663151e+00, 7.97280013e+00, -9.32896918e+00,
-8.22460526e+00, -1.21784287e+01, 5.49844655e+00],
[ 1.88644899e+00, 4.62100554e+00, 2.84159548e+00,
4.31244563e-01, -2.47135027e+00, 2.50783257e+00],
[ 2.39132949e+00, 6.46460915e+00, -9.80590050e+00,
-7.28996786e+00, -9.65098460e+00, 6.38845956e+00],
...,
[ 2.03146167e+00, 7.80442707e+00, -8.53951210e+00,
-9.82440872e+00, -1.00469351e+01, 6.91808489e+00],
[ 4.08188906e+00, 6.12768483e+00, 1.10911262e+01,
4.81201082e+00, -5.91530191e-03, 5.34221079e+00],
[ 9.85744105e-01, 7.28573657e+00, -8.39593964e+00,
-6.58647097e+00, -9.65176507e+00, 6.65101187e+00]])
data_x=np.insert(data_x,0,1,axis=1)
data_x.shape
(200, 7)
w3.shape
(7, 1)
multi_pred=pd.DataFrame(zip(h(data_x,w1).ravel(),h(data_x,w2).ravel(),h(data_x,w3).ravel(),h(data_x,w4).ravel()))
multi_pred
| 0 | 1 | 2 | 3 | |
|---|---|---|---|---|
| 0 | 0.020436 | 4.556248e-15 | 9.999975e-01 | 2.601227e-27 |
| 1 | 0.820488 | 4.180906e-05 | 3.551499e-05 | 5.908691e-05 |
| 2 | 0.109309 | 7.316201e-14 | 9.999978e-01 | 7.091713e-24 |
| 3 | 0.036608 | 9.999562e-01 | 1.048562e-09 | 5.724854e-03 |
| 4 | 0.003075 | 9.999292e-01 | 2.516742e-09 | 6.423038e-05 |
| ... | ... | ... | ... | ... |
| 195 | 0.017278 | 3.221293e-06 | 3.753372e-14 | 9.999943e-01 |
| 196 | 0.003369 | 9.999966e-01 | 6.673394e-10 | 2.281428e-03 |
| 197 | 0.000606 | 1.118174e-13 | 9.999941e-01 | 1.780212e-28 |
| 198 | 0.013072 | 4.999118e-05 | 9.811154e-14 | 9.996689e-01 |
| 199 | 0.151548 | 1.329623e-13 | 9.999447e-01 | 2.571989e-24 |
200 rows × 4 columns
2.6 计算准确率
np.sum(np.argmax(multi_pred.values,axis=1)==data_y.ravel())/len(data)
1.0