MIN-MAX scaling in statistics.
In data processing scaling is a method used to normalize the range of independent variables or features of data, it is also known as data normalization and is generally performed during the data preprocessing step.
MIN-MAX scaling or MIN-MAX normalization is the simplest method and consists in rescaling the range of features to scale the range in [0, 1] or sometimes [−1, 1] which is called unity-normed data scale. Selecting the target range depends on the nature of the data.
Creating data and MIN-MAX scaling:
import matplotlib.pyplot as plt
import numpy as np
N = 42
data = np.log(np.random.rand(N))*234 + 934
# get min and max
dataMin = min(data)
dataMax = max(data)
# now min-max scale
dataS = (data-dataMin) / (dataMax-dataMin)
# now plot
fig,ax = plt.subplots(1,2,figsize=(8,4))
ax[0].plot(1+np.random.randn(N)/20,data,'ks')
ax[0].set_xlim([0,2])
ax[0].set_xticks([])
ax[0].set_ylabel('Original data scale')
ax[0].set_title('Original data')
ax[1].plot(1+np.random.randn(N)/20,dataS,'ks')
ax[1].set_xlim([0,2])
ax[1].set_xticks([])
ax[1].set_ylabel('Unity-normed data scale')
ax[1].set_title('Scaled data')
plt.show()
Scaling to arbitrary data range:
## any arbitrary data range
# step 1 is to [0,1] normalize as above
# step 2:
newMin = 4
newMax = 8.7
dataSS = dataS*(newMax-newMin) + newMin
# test it!
print([min(dataSS), max(dataSS)])