In many datasets we find some of the features which are highly correlated that means which are some what linearly dependent with other features. These features contribute very less in predicting the output but increses the computational cost.
This data science python source code does the following:
1. Calculates correlation between different features.
2. Drops highly correlated features to escape curse of dimensionality.
3. Linear and non-linear correlation.
So we have to find out the correlation between the features and remove the features which have correlation coefficient greater than a certain limit.
So this recipe is a short example of how to find the correlation between the features and remove the highly correlated features.
import pandas as pd import numpy as np from sklearn import datasets
We have imported numpy, pandas and datasets. We will use datasets to get the inbuilt iris dataset.
Here we have used datasets to load the inbuilt iris dataset and we have created objects X and y to store the data and the target value respectively. With the data in X we have created a dataframe and printing the first five rows.
iris = datasets.load_iris()
X = iris.data
y = iris.target
df = pd.DataFrame(X)
So now we are creating a square matrix with dimensions equal to the number of features. In which we will have the elements as the absolute value of correlation between the features.
cor_matrix = df.corr().abs()
Note that Correlation matrix will be mirror image about the diagonal and all the diagonal elements will be 1.
So, It does not matter that we select the upper triangular or lower triangular part of the correlation matrix but we should not include the diagonal elements. So we are selecting the upper traingular.
upper_tri = cor_matrix.where(np.triu(np.ones(cor_matrix.shape),k=1).astype(np.bool))
So we are selecting the columns which are having absolute correlation greater than 0.95 and making a list of those columns named 'to_drop'.
to_drop = [column for column in upper_tri.columns if any(upper_tri[column] > 0.95)]
Now we are droping the columns which are in the list 'to_drop' from the dataframe
df1 = df.drop(df.columns[to_drop], axis=1)
In the output, initially there will be the dataframe with 4 columns. Then there will be the correlation matrix in which we can observe all diagonal elements as 1 and the upper triangular and lower triangular are the mirror image. After that there will be upper triangular matrix and the final dataframe with the highly correlated columns removed.
0 1 2 3 0 5.1 3.5 1.4 0.2 1 4.9 3.0 1.4 0.2 2 4.7 3.2 1.3 0.2 3 4.6 3.1 1.5 0.2 4 5.0 3.6 1.4 0.2 0 1 2 3 0 1.000000 0.117570 0.871754 0.817941 1 0.117570 1.000000 0.428440 0.366126 2 0.871754 0.428440 1.000000 0.962865 3 0.817941 0.366126 0.962865 1.000000 0 1 2 3 0 NaN 0.11757 0.871754 0.817941 1 NaN NaN 0.428440 0.366126 2 NaN NaN NaN 0.962865 3 NaN NaN NaN NaN  0 1 2 0 5.1 3.5 1.4 1 4.9 3.0 1.4 2 4.7 3.2 1.3 3 4.6 3.1 1.5 4 5.0 3.6 1.4