Preprocessing the eigenvalues after numeralization

Keywords: Python

Objectives:

Understanding the characteristics of numerical and categorical data

Using MinMax Scaler to Realize Normalization of Characteristic Data

Standardization of Characteristic Data Using StandarScaler
 

Feature preprocessing:

The process of transforming feature data into feature data of more suitable algorithmic model by some transformation functions

Dimensionalization of numerical data (dimensionless, mathematical terms, data conversion from different specifications to uniform specifications)

Normalization: scaling based on maximum and minimum values, default range 0-1, easy to be affected by outliers, poor stability, only suitable for small scale data scenarios.

Standardization: raw data changes to 0-1 directly

Feature preprocessing API:

sklearn.preprocession

Why normalization / standardization?

The units or sizes of features vary greatly, or the variance of one feature is several orders of magnitude larger than that of other features, which easily affects (dominates) the target results, making some algorithms unable to learn other features.
 

1. Normalization

Definition: Mapping data to (default: [0,1]) by transforming raw data

X' = (x - min)/(max - min) x'' = x' * (mx - mi) + mi

(max is the maximum value of a column and min is the minimum value of a column. mx and mi are default mx of 1 and mi of 0 respectively for specified interval values.

 

sklearn.preprocessing.MinMaxScaler(feature_range = (0,1))

MinMaxScaler.fit_transform(X)

Data in X:numpy array format [n_samples, n_features]

Return: Converted array with the same shape
 

Normalized summary: Note that the maximum and minimum values are variable. In addition, the maximum and minimum values are very vulnerable to outliers, so this method has poor robustness, knowledge and traditional precise small data scenarios.

 

from sklearn.datasets import load_iris
from sklearn.preprocessing import MinMaxScaler
import pandas as pd

#normalization
def minmax_demo():
    #Use sklearn Incoming data sets
    iris = load_iris()
    data = pd.DataFrame(iris.data, columns = iris.feature_names)
    data_new = data.iloc[:, :4].values
    print("data_new:\n", data_new)
    
    transfer = MinMaxScaler(feature_range = [1, 2]) #default feature_range yes[0, 1]
    
    data_minmax_value = transfer.fit_transform(data_new)
    print("data_minmax_value:\n", data_minmax_value)
    
    return None

if __name__ == '__main__':
    minmax_demo()



//Output results:
data_new:
 [[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 0.1]
 [5.  3.2 1.2 0.2]
 [5.5 3.5 1.3 0.2]
 [4.9 3.1 1.5 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_minmax_value:
 [[1.22222222 1.625      1.06779661 1.04166667]
 [1.16666667 1.41666667 1.06779661 1.04166667]
 [1.11111111 1.5        1.05084746 1.04166667]
 [1.08333333 1.45833333 1.08474576 1.04166667]
 [1.19444444 1.66666667 1.06779661 1.04166667]
 [1.30555556 1.79166667 1.11864407 1.125     ]
 [1.08333333 1.58333333 1.06779661 1.08333333]
 [1.19444444 1.58333333 1.08474576 1.04166667]
 [1.02777778 1.375      1.06779661 1.04166667]
 [1.16666667 1.45833333 1.08474576 1.        ]
 [1.30555556 1.70833333 1.08474576 1.04166667]
 [1.13888889 1.58333333 1.10169492 1.04166667]
 [1.13888889 1.41666667 1.06779661 1.        ]
 [1.         1.41666667 1.01694915 1.        ]
 [1.41666667 1.83333333 1.03389831 1.04166667]
 [1.38888889 2.         1.08474576 1.125     ]
 [1.30555556 1.79166667 1.05084746 1.125     ]
 [1.22222222 1.625      1.06779661 1.08333333]
 [1.38888889 1.75       1.11864407 1.08333333]
 [1.22222222 1.75       1.08474576 1.08333333]
 [1.30555556 1.58333333 1.11864407 1.04166667]
 [1.22222222 1.70833333 1.08474576 1.125     ]
 [1.08333333 1.66666667 1.         1.04166667]
 [1.22222222 1.54166667 1.11864407 1.16666667]
 [1.13888889 1.58333333 1.15254237 1.04166667]
 [1.19444444 1.41666667 1.10169492 1.04166667]
 [1.19444444 1.58333333 1.10169492 1.125     ]
 [1.25       1.625      1.08474576 1.04166667]
 [1.25       1.58333333 1.06779661 1.04166667]
 [1.11111111 1.5        1.10169492 1.04166667]
 [1.13888889 1.45833333 1.10169492 1.04166667]
 [1.30555556 1.58333333 1.08474576 1.125     ]
 [1.25       1.875      1.08474576 1.        ]
 [1.33333333 1.91666667 1.06779661 1.04166667]
 [1.16666667 1.45833333 1.08474576 1.        ]
 [1.19444444 1.5        1.03389831 1.04166667]
 [1.33333333 1.625      1.05084746 1.04166667]
 [1.16666667 1.45833333 1.08474576 1.        ]
 [1.02777778 1.41666667 1.05084746 1.04166667]
 [1.22222222 1.58333333 1.08474576 1.04166667]
 [1.19444444 1.625      1.05084746 1.08333333]
 [1.05555556 1.125      1.05084746 1.08333333]
 [1.02777778 1.5        1.05084746 1.04166667]
 [1.19444444 1.625      1.10169492 1.20833333]
 [1.22222222 1.75       1.15254237 1.125     ]
 [1.13888889 1.41666667 1.06779661 1.08333333]
 [1.22222222 1.75       1.10169492 1.04166667]
 [1.08333333 1.5        1.06779661 1.04166667]
 [1.27777778 1.70833333 1.08474576 1.04166667]
 [1.19444444 1.54166667 1.06779661 1.04166667]
 [1.75       1.5        1.62711864 1.54166667]
 [1.58333333 1.5        1.59322034 1.58333333]
 [1.72222222 1.45833333 1.66101695 1.58333333]
 [1.33333333 1.125      1.50847458 1.5       ]
 [1.61111111 1.33333333 1.61016949 1.58333333]
 [1.38888889 1.33333333 1.59322034 1.5       ]
 [1.55555556 1.54166667 1.62711864 1.625     ]
 [1.16666667 1.16666667 1.38983051 1.375     ]
 [1.63888889 1.375      1.61016949 1.5       ]
 [1.25       1.29166667 1.49152542 1.54166667]
 [1.19444444 1.         1.42372881 1.375     ]
 [1.44444444 1.41666667 1.54237288 1.58333333]
 [1.47222222 1.08333333 1.50847458 1.375     ]
 [1.5        1.375      1.62711864 1.54166667]
 [1.36111111 1.375      1.44067797 1.5       ]
 [1.66666667 1.45833333 1.57627119 1.54166667]
 [1.36111111 1.41666667 1.59322034 1.58333333]
 [1.41666667 1.29166667 1.52542373 1.375     ]
 [1.52777778 1.08333333 1.59322034 1.58333333]
 [1.36111111 1.20833333 1.49152542 1.41666667]
 [1.44444444 1.5        1.6440678  1.70833333]
 [1.5        1.33333333 1.50847458 1.5       ]
 [1.55555556 1.20833333 1.66101695 1.58333333]
 [1.5        1.33333333 1.62711864 1.45833333]
 [1.58333333 1.375      1.55932203 1.5       ]
 [1.63888889 1.41666667 1.57627119 1.54166667]
 [1.69444444 1.33333333 1.6440678  1.54166667]
 [1.66666667 1.41666667 1.6779661  1.66666667]
 [1.47222222 1.375      1.59322034 1.58333333]
 [1.38888889 1.25       1.42372881 1.375     ]
 [1.33333333 1.16666667 1.47457627 1.41666667]
 [1.33333333 1.16666667 1.45762712 1.375     ]
 [1.41666667 1.29166667 1.49152542 1.45833333]
 [1.47222222 1.29166667 1.69491525 1.625     ]
 [1.30555556 1.41666667 1.59322034 1.58333333]
 [1.47222222 1.58333333 1.59322034 1.625     ]
 [1.66666667 1.45833333 1.62711864 1.58333333]
 [1.55555556 1.125      1.57627119 1.5       ]
 [1.36111111 1.41666667 1.52542373 1.5       ]
 [1.33333333 1.20833333 1.50847458 1.5       ]
 [1.33333333 1.25       1.57627119 1.45833333]
 [1.5        1.41666667 1.61016949 1.54166667]
 [1.41666667 1.25       1.50847458 1.45833333]
 [1.19444444 1.125      1.38983051 1.375     ]
 [1.36111111 1.29166667 1.54237288 1.5       ]
 [1.38888889 1.41666667 1.54237288 1.45833333]
 [1.38888889 1.375      1.54237288 1.5       ]
 [1.52777778 1.375      1.55932203 1.5       ]
 [1.22222222 1.20833333 1.33898305 1.41666667]
 [1.38888889 1.33333333 1.52542373 1.5       ]
 [1.55555556 1.54166667 1.84745763 2.        ]
 [1.41666667 1.29166667 1.69491525 1.75      ]
 [1.77777778 1.41666667 1.83050847 1.83333333]
 [1.55555556 1.375      1.77966102 1.70833333]
 [1.61111111 1.41666667 1.81355932 1.875     ]
 [1.91666667 1.41666667 1.94915254 1.83333333]
 [1.16666667 1.20833333 1.59322034 1.66666667]
 [1.83333333 1.375      1.89830508 1.70833333]
 [1.66666667 1.20833333 1.81355932 1.70833333]
 [1.80555556 1.66666667 1.86440678 2.        ]
 [1.61111111 1.5        1.69491525 1.79166667]
 [1.58333333 1.29166667 1.72881356 1.75      ]
 [1.69444444 1.41666667 1.76271186 1.83333333]
 [1.38888889 1.20833333 1.6779661  1.79166667]
 [1.41666667 1.33333333 1.69491525 1.95833333]
 [1.58333333 1.5        1.72881356 1.91666667]
 [1.61111111 1.41666667 1.76271186 1.70833333]
 [1.94444444 1.75       1.96610169 1.875     ]
 [1.94444444 1.25       2.         1.91666667]
 [1.47222222 1.08333333 1.6779661  1.58333333]
 [1.72222222 1.5        1.79661017 1.91666667]
 [1.36111111 1.33333333 1.66101695 1.79166667]
 [1.94444444 1.33333333 1.96610169 1.79166667]
 [1.55555556 1.29166667 1.66101695 1.70833333]
 [1.66666667 1.54166667 1.79661017 1.83333333]
 [1.80555556 1.5        1.84745763 1.70833333]
 [1.52777778 1.33333333 1.6440678  1.70833333]
 [1.5        1.41666667 1.66101695 1.70833333]
 [1.58333333 1.33333333 1.77966102 1.83333333]
 [1.80555556 1.41666667 1.81355932 1.625     ]
 [1.86111111 1.33333333 1.86440678 1.75      ]
 [2.         1.75       1.91525424 1.79166667]
 [1.58333333 1.33333333 1.77966102 1.875     ]
 [1.55555556 1.33333333 1.69491525 1.58333333]
 [1.5        1.25       1.77966102 1.54166667]
 [1.94444444 1.41666667 1.86440678 1.91666667]
 [1.55555556 1.58333333 1.77966102 1.95833333]
 [1.58333333 1.45833333 1.76271186 1.70833333]
 [1.47222222 1.41666667 1.6440678  1.70833333]
 [1.72222222 1.45833333 1.74576271 1.83333333]
 [1.66666667 1.45833333 1.77966102 1.95833333]
 [1.72222222 1.45833333 1.69491525 1.91666667]
 [1.41666667 1.29166667 1.69491525 1.75      ]
 [1.69444444 1.5        1.83050847 1.91666667]
 [1.66666667 1.54166667 1.79661017 2.        ]
 [1.66666667 1.41666667 1.71186441 1.91666667]
 [1.55555556 1.20833333 1.6779661  1.75      ]
 [1.61111111 1.41666667 1.71186441 1.79166667]
 [1.52777778 1.58333333 1.74576271 1.91666667]
 [1.44444444 1.41666667 1.69491525 1.70833333]]

 

 

2. Standardization

Definition: Transform the original data to a mean of 0 and a standard deviation of 1.

Formula: X'= (x - mean)/

mean is the average and is the standard deviation.

For normalization, if there are outliers that affect the maximum and minimum values, the results will obviously change.

For standardization, if there are abnormal points, due to a certain amount of data, the effect of the discussed abnormal points on the average value is not large, so the variance change is small.

Summary: It is more stable when there are enough samples, and it is suitable for modern noisy data scenarios.

 

from sklearn.datasets import load_iris
from sklearn.preprocessing import StandardScaler
import pandas as pd

def standard_demo():
    iris = load_iris()
    data = pd.DataFrame(iris.data, columns = iris.feature_names)
    data_new = data.iloc[:, :4].values
    
    print("data_new:\n", data_new)
    
    transfer = StandardScaler()
    
    data_standard_value = transfer.fit_transform(data_new)
    print("data_standard_value:\n", data_standard_value)
    
    return None

if __name__ == '__main__':
    standard_demo()



//Output results:
data_new:
 [[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 0.1]
 [5.  3.2 1.2 0.2]
 [5.5 3.5 1.3 0.2]
 [4.9 3.1 1.5 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]
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data_standard_value:
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Reference link: https://www.cnblogs.com/ftl1012/p/10498480.html

Posted by Teen0724 on Wed, 02 Oct 2019 20:21:07 -0700

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