Normalization VS. numpy way to normalize?

Question

I'm supposed to normalize an array. I've read about normalization and come across a formula:

I wrote the following function for it:

def normalize_list(list):
    max_value = max(list)
    min_value = min(list)
    for i in range(0, len(list)):
        list[i] = (list[i] - min_value) / (max_value - min_value)

That is supposed to normalize an array of elements.

Then I have come across this: https://stackoverflow.com/a/21031303/6209399 Which says you can normalize an array by simply doing this:

def normalize_list_numpy(list):
    normalized_list = list / np.linalg.norm(list)
    return normalized_list

---

If I normalize this test array test_array = [1, 2, 3, 4, 5, 6, 7, 8, 9] with my own function and with the numpy method, I get these answers:

My own function: [0.0, 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875, 1.0]
The numpy way: [0.059234887775909233, 0.11846977555181847, 0.17770466332772769, 0.23693955110363693, 0.29617443887954614, 0.35540932665545538, 0.41464421443136462, 0.47387910220727386, 0.5331139899831830

---

Why do the functions give different answers? Is there others way to normalize an array of data? What does numpy.linalg.norm(list) do? What do I get wrong?

Answer 1

The question/answer that you reference doesn't explicitly relate your own formula to the np.linalg.norm(list) version that you use here.

One NumPy solution would be this:

import numpy as np
def normalize(x):
    x = np.asarray(x)
    return (x - x.min()) / (np.ptp(x))

print(normalize(test_array))    
# [ 0.     0.125  0.25   0.375  0.5    0.625  0.75   0.875  1.   ]

Here np.ptp is peak-to-peak ie

Range of values (maximum - minimum) along an axis.

This approach scales the values to the interval [0, 1] as pointed out by @phg.

The more traditional definition of normalization would be to scale to a 0 mean and unit variance:

x = np.asarray(test_array)
res = (x - x.mean()) / x.std()
print(res.mean(), res.std())
# 0.0 1.0

Or use sklearn.preprocessing.normalize as a pre-canned function.

Using test_array / np.linalg.norm(test_array) creates a result that is of unit length; you'll see that np.linalg.norm(test_array / np.linalg.norm(test_array)) equals 1. So you're talking about two different fields here, one being statistics and the other being linear algebra.