implementing zero mean and unit variance in numpy

I have a 2D Numpy array, in which I want to normalise each column to zero mean and unit variance. Since I'm primarily used to C++, the method in which I'm doing is to use loops to iterate over elements in a column and do the necessary operations, followed by repeating this for all columns. I wanted to know about a pythonic way to do so., Suppose, we have an array = and to normalize it in range means that it will convert array to as 1, 2 and 3 are equidistant. , 3 days ago Jul 29, 2022  · In order to normalize a vector in NumPy, we can use the np.linalg.norm () function, which returns the vector’s norm value. We can then use the norm value to divide each value in the array to get the normalized array. We can generate a reproducible NumPy array using the np.random.rand () function, which is used to generate random values. ,isn't equal to 0, implying that I have done something wrong in my normalisation. By isn't equal to 0, I don't mean very small numbers which can be attributed to floating point inaccuracies.

column_mean = numpy.sum(class_input_data, axis = 0) / class_input_data.shape[0]

import numpy as np eg_array = 5 + (np.random.randn(10, 10) * 2) normed = (eg_array - eg_array.mean(axis = 0)) / eg_array.std(axis = 0) normed.mean(axis = 0) Out[14]: array([1.16573418e-16, -7.77156117e-17, -1.77635684e-16, 9.43689571e-17, -2.22044605e-17, -6.09234885e-16, -2.22044605e-16, -4.44089210e-17, -7.10542736e-16, 4.21884749e-16]) normed.std(axis = 0) Out[15]: array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1.])

Returns the variance of the array elements, a measure of the spread of a distribution. The variance is computed for the flattened array by default, otherwise over the specified axis.,Axis or axes along which the variance is computed. The default is to compute the variance of the flattened array.,Compute the variance along the specified axis.,The mean is typically calculated as x.sum() / N, where N = len(x). If, however, ddof is specified, the divisor N - ddof is used instead. In standard statistical practice, ddof=1 provides an unbiased estimator of the variance of a hypothetical infinite population. ddof=0 provides a maximum likelihood estimate of the variance for normally distributed variables.

>>> a = np.array([
      [1, 2],
      [3, 4]
   ]) >>>
   np.var(a)
1.25
   >>>
   np.var(a, axis = 0)
array([1., 1.]) >>>
   np.var(a, axis = 1)
array([0.25, 0.25])

>>> a = np.zeros((2, 512 * 512), dtype = np.float32) >>>
   a[0,: ] = 1.0 >>>
   a[1,: ] = 0.1 >>>
   np.var(a)
0.20250003

>>> np.var(a, dtype = np.float64)
0.20249999932944759 # may vary
   >>>
   ((1 - 0.55) ** 2 + (0.1 - 0.55) ** 2) / 2
0.2025

>>> a = np.array([
      [14, 8, 11, 10],
      [7, 9, 10, 11],
      [10, 15, 5, 10]
   ]) >>>
   np.var(a)
6.833333333333333 # may vary
   >>>
   np.var(a, where = [
      [True],
      [True],
      [False]
   ])
4.0

This is where standardization or Z-score normalization comes into the picture. Rather than using the minimum and maximum values, we use the mean and standard deviation from the data. By consequence, all our features will now have zero mean and unit variance, meaning that we can now compare the variances between the features.,Standardization, or Z-score normalization: we scale the data so that the mean is zero and variance is 1.,In the previous example, we normalized our dataset based on the minimum and maximum values. Mean and standard deviation are however not standard, meaning that the mean is zero and that the standard deviation is one.,Many people have the question when to use normalization, and when to use standardization? This is a valid question - and I had it as well.

dataset = np.array([1.0, 12.4, 3.9, 10.4])

normalized_dataset = (dataset - min(dataset)) / (max(dataset) - min(dataset))

import numpy as np
dataset = np.array([1.0, 12.4, 3.9, 10.4])
normalized_dataset = (dataset - np.min(dataset)) / (np.max(dataset) - np.min(dataset))
print(normalized_dataset)

[0. 1. 0.25438596 0.8245614]

normalized_dataset = a + ((dataset - min(dataset)) * (b - a) / (max(dataset) - min(dataset)))

import numpy as np
a = 0
b = 1.5
dataset = np.array([1.0, 12.4, 3.9, 10.4])
normalized_dataset = a + ((dataset - np.min(dataset)) * (b - a) / (np.max(dataset) - np.min(dataset)))
print(normalized_dataset)

Last Updated : 25 Jul, 2022

[
   [0.25 0.5]
   [0.75 1.]
   [0.125 0.375]
   [0. 0.25]
]

[
   [0.33333333 0.33333333]
   [1. 1.]
   [0.16666667 0.16666667]
   [0. 0.]
]