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What is interpolation and how can we implement it in the SciPy Python library?
Interpolation is a method of generating a value between two given points on a line or a curve. In machine learning, interpolation is used to substitute the missing values in a dataset. This method of filling the missing values is called imputation. Another important use of interpolation is to smooth the discrete points in a dataset.
SciPy provides us a module named scipy.interpolate having many functions with the help of which we can implement interpolation.
Example
In the below example we will implement Interpolation by using the scipy.interpolate() package −
First let’s generate some data to implement interpolation on that −
import numpy as np from scipy.interpolate import interp1d import matplotlib.pyplot as plt A = np.linspace(0, 10, num=11, endpoint=True) B = np.cos(-A**2/9.0) print (A, B)
Output
The above script will generate the following points between 0 and 4 −
[ 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.] [ 1. 0.99383351 0.90284967 0.54030231 -0.20550672 -0.93454613 -0.65364362 0.6683999 0.67640492 -0.91113026 0.11527995]
Now, let’s plot these points as follows
plt.plot(A, B, '.') plt.show()
Now we need to create a interpolate function based on fixed data points. Let’s create it −
function_interpolate = interp1d(A, B, kind = 'linear')
To see the clear difference of interpolation, we will create a new input of more length by using the same function as used for old input −
Anew = np.linspace(0, 10, num=30, endpoint=True) plt.plot(A, B, '.', Anew, function_interpolate(Anew), '-') plt.legend(['data', 'linear'], loc = 'best') plt.show()
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