Normalization#
Normalizing data is crucial when using machine learning algorithms because of how sensitive most of them are to un-normalized data. For example, the neighbors-based and k-means algorithms use the p-distance in their learning phase. Normalization is the first step before using a linear regression due to Gauss-Markov assumptions.
Unnormalized data can also create complications for the convergence of some ML algorithms. Normalization is also a way to encode the data and to retain the global distribution. When we know the estimators to use to normalize the data, we can easily un-normalize the data and come back to the original distribution.
There are three main normalization techniques:
Z-Score : We reduce and center the feature values using the average and standard deviation. This normalization is sensitive to outliers.
Robust Z-Score : We reduce and center the feature values using the median and the median absolute deviation. This normalization is robust to outliers.
Min-Max : We reduce the feature values by using a bijection to [0,1]. The max will reach 1 and the min will reach 0. This normalization is robust to outliers.
To demonstrate data normalization in VerticaPy, we will use the well-known ‘Titanic’ dataset.
[1]:
from verticapy.datasets import load_titanic
vdf = load_titanic()
display(vdf)
123 pclassInt | 123 survivedInt | Abc Varchar(164) | Abc sexVarchar(20) | 123 ageNumeric(6,3) | 123 sibspInt | 123 parchInt | Abc ticketVarchar(36) | 123 fareNumeric(10,5) | Abc cabinVarchar(30) | Abc embarkedVarchar(20) | Abc boatVarchar(100) | 123 bodyInt | Abc home.destVarchar(100) | |
1 | 1 | 0 | female | 2.0 | 1 | 2 | 113781 | 151.55 | C22 C26 | S | [null] | [null] | Montreal, PQ / Chesterville, ON | |
2 | 1 | 0 | male | 30.0 | 1 | 2 | 113781 | 151.55 | C22 C26 | S | [null] | 135 | Montreal, PQ / Chesterville, ON | |
3 | 1 | 0 | female | 25.0 | 1 | 2 | 113781 | 151.55 | C22 C26 | S | [null] | [null] | Montreal, PQ / Chesterville, ON | |
4 | 1 | 0 | male | 39.0 | 0 | 0 | 112050 | 0.0 | A36 | S | [null] | [null] | Belfast, NI | |
5 | 1 | 0 | male | 71.0 | 0 | 0 | PC 17609 | 49.5042 | [null] | C | [null] | 22 | Montevideo, Uruguay | |
6 | 1 | 0 | male | 47.0 | 1 | 0 | PC 17757 | 227.525 | C62 C64 | C | [null] | 124 | New York, NY | |
7 | 1 | 0 | male | [null] | 0 | 0 | PC 17318 | 25.925 | [null] | S | [null] | [null] | New York, NY | |
8 | 1 | 0 | male | 24.0 | 0 | 1 | PC 17558 | 247.5208 | B58 B60 | C | [null] | [null] | Montreal, PQ | |
9 | 1 | 0 | male | 36.0 | 0 | 0 | 13050 | 75.2417 | C6 | C | A | [null] | Winnipeg, MN | |
10 | 1 | 0 | male | 25.0 | 0 | 0 | 13905 | 26.0 | [null] | C | [null] | 148 | San Francisco, CA | |
11 | 1 | 0 | male | 45.0 | 0 | 0 | 113784 | 35.5 | T | S | [null] | [null] | Trenton, NJ | |
12 | 1 | 0 | male | 42.0 | 0 | 0 | 110489 | 26.55 | D22 | S | [null] | [null] | London / Winnipeg, MB | |
13 | 1 | 0 | male | 41.0 | 0 | 0 | 113054 | 30.5 | A21 | S | [null] | [null] | Pomeroy, WA | |
14 | 1 | 0 | male | 48.0 | 0 | 0 | PC 17591 | 50.4958 | B10 | C | [null] | 208 | Omaha, NE | |
15 | 1 | 0 | male | [null] | 0 | 0 | 112379 | 39.6 | [null] | C | [null] | [null] | Philadelphia, PA | |
16 | 1 | 0 | male | 45.0 | 0 | 0 | 113050 | 26.55 | B38 | S | [null] | [null] | Washington, DC | |
17 | 1 | 0 | male | [null] | 0 | 0 | 113798 | 31.0 | [null] | S | [null] | [null] | [null] | |
18 | 1 | 0 | male | 33.0 | 0 | 0 | 695 | 5.0 | B51 B53 B55 | S | [null] | [null] | New York, NY | |
19 | 1 | 0 | male | 28.0 | 0 | 0 | 113059 | 47.1 | [null] | S | [null] | [null] | Montevideo, Uruguay | |
20 | 1 | 0 | male | 17.0 | 0 | 0 | 113059 | 47.1 | [null] | S | [null] | [null] | Montevideo, Uruguay | |
21 | 1 | 0 | male | 49.0 | 0 | 0 | 19924 | 26.0 | [null] | S | [null] | [null] | Ascot, Berkshire / Rochester, NY | |
22 | 1 | 0 | male | 36.0 | 1 | 0 | 19877 | 78.85 | C46 | S | [null] | 172 | Little Onn Hall, Staffs | |
23 | 1 | 0 | male | 46.0 | 1 | 0 | W.E.P. 5734 | 61.175 | E31 | S | [null] | [null] | Amenia, ND | |
24 | 1 | 0 | male | [null] | 0 | 0 | 112051 | 0.0 | [null] | S | [null] | [null] | Liverpool, England / Belfast | |
25 | 1 | 0 | male | 27.0 | 1 | 0 | 13508 | 136.7792 | C89 | C | [null] | [null] | Los Angeles, CA | |
26 | 1 | 0 | male | [null] | 0 | 0 | 110465 | 52.0 | A14 | S | [null] | [null] | Stoughton, MA | |
27 | 1 | 0 | male | 47.0 | 0 | 0 | 5727 | 25.5875 | E58 | S | [null] | [null] | Victoria, BC | |
28 | 1 | 0 | male | 37.0 | 1 | 1 | PC 17756 | 83.1583 | E52 | C | [null] | [null] | Lakewood, NJ | |
29 | 1 | 0 | male | [null] | 0 | 0 | 113791 | 26.55 | [null] | S | [null] | [null] | Roachdale, IN | |
30 | 1 | 0 | male | 70.0 | 1 | 1 | WE/P 5735 | 71.0 | B22 | S | [null] | 269 | Milwaukee, WI | |
31 | 1 | 0 | male | 39.0 | 1 | 0 | PC 17599 | 71.2833 | C85 | C | [null] | [null] | New York, NY | |
32 | 1 | 0 | male | 31.0 | 1 | 0 | F.C. 12750 | 52.0 | B71 | S | [null] | [null] | Montreal, PQ | |
33 | 1 | 0 | male | 50.0 | 1 | 0 | PC 17761 | 106.425 | C86 | C | [null] | 62 | Deephaven, MN / Cedar Rapids, IA | |
34 | 1 | 0 | male | 39.0 | 0 | 0 | PC 17580 | 29.7 | A18 | C | [null] | 133 | Philadelphia, PA | |
35 | 1 | 0 | female | 36.0 | 0 | 0 | PC 17531 | 31.6792 | A29 | C | [null] | [null] | New York, NY | |
36 | 1 | 0 | male | [null] | 0 | 0 | PC 17483 | 221.7792 | C95 | S | [null] | [null] | [null] | |
37 | 1 | 0 | male | 30.0 | 0 | 0 | 113051 | 27.75 | C111 | C | [null] | [null] | New York, NY | |
38 | 1 | 0 | male | 19.0 | 3 | 2 | 19950 | 263.0 | C23 C25 C27 | S | [null] | [null] | Winnipeg, MB | |
39 | 1 | 0 | male | 64.0 | 1 | 4 | 19950 | 263.0 | C23 C25 C27 | S | [null] | [null] | Winnipeg, MB | |
40 | 1 | 0 | male | [null] | 0 | 0 | 113778 | 26.55 | D34 | S | [null] | [null] | Westcliff-on-Sea, Essex | |
41 | 1 | 0 | male | [null] | 0 | 0 | 112058 | 0.0 | B102 | S | [null] | [null] | [null] | |
42 | 1 | 0 | male | 37.0 | 1 | 0 | 113803 | 53.1 | C123 | S | [null] | [null] | Scituate, MA | |
43 | 1 | 0 | male | 47.0 | 0 | 0 | 111320 | 38.5 | E63 | S | [null] | 275 | St Anne's-on-Sea, Lancashire | |
44 | 1 | 0 | male | 24.0 | 0 | 0 | PC 17593 | 79.2 | B86 | C | [null] | [null] | [null] | |
45 | 1 | 0 | male | 71.0 | 0 | 0 | PC 17754 | 34.6542 | A5 | C | [null] | [null] | New York, NY | |
46 | 1 | 0 | male | 38.0 | 0 | 1 | PC 17582 | 153.4625 | C91 | S | [null] | 147 | Winnipeg, MB | |
47 | 1 | 0 | male | 46.0 | 0 | 0 | PC 17593 | 79.2 | B82 B84 | C | [null] | [null] | New York, NY | |
48 | 1 | 0 | male | [null] | 0 | 0 | 113796 | 42.4 | [null] | S | [null] | [null] | [null] | |
49 | 1 | 0 | male | 45.0 | 1 | 0 | 36973 | 83.475 | C83 | S | [null] | [null] | New York, NY | |
50 | 1 | 0 | male | 40.0 | 0 | 0 | 112059 | 0.0 | B94 | S | [null] | 110 | [null] | |
51 | 1 | 0 | male | 55.0 | 1 | 1 | 12749 | 93.5 | B69 | S | [null] | 307 | Montreal, PQ | |
52 | 1 | 0 | male | 42.0 | 0 | 0 | 113038 | 42.5 | B11 | S | [null] | [null] | London / Middlesex | |
53 | 1 | 0 | male | [null] | 0 | 0 | 17463 | 51.8625 | E46 | S | [null] | [null] | Brighton, MA | |
54 | 1 | 0 | male | 55.0 | 0 | 0 | 680 | 50.0 | C39 | S | [null] | [null] | London / Birmingham | |
55 | 1 | 0 | male | 42.0 | 1 | 0 | 113789 | 52.0 | [null] | S | [null] | 38 | New York, NY | |
56 | 1 | 0 | male | [null] | 0 | 0 | PC 17600 | 30.6958 | [null] | C | 14 | [null] | New York, NY | |
57 | 1 | 0 | female | 50.0 | 0 | 0 | PC 17595 | 28.7125 | C49 | C | [null] | [null] | Paris, France New York, NY | |
58 | 1 | 0 | male | 46.0 | 0 | 0 | 694 | 26.0 | [null] | S | [null] | 80 | Bennington, VT | |
59 | 1 | 0 | male | 50.0 | 0 | 0 | 113044 | 26.0 | E60 | S | [null] | [null] | London | |
60 | 1 | 0 | male | 32.5 | 0 | 0 | 113503 | 211.5 | C132 | C | [null] | 45 | [null] | |
61 | 1 | 0 | male | 58.0 | 0 | 0 | 11771 | 29.7 | B37 | C | [null] | 258 | Buffalo, NY | |
62 | 1 | 0 | male | 41.0 | 1 | 0 | 17464 | 51.8625 | D21 | S | [null] | [null] | Southington / Noank, CT | |
63 | 1 | 0 | male | [null] | 0 | 0 | 113028 | 26.55 | C124 | S | [null] | [null] | Portland, OR | |
64 | 1 | 0 | male | [null] | 0 | 0 | PC 17612 | 27.7208 | [null] | C | [null] | [null] | Chicago, IL | |
65 | 1 | 0 | male | 29.0 | 0 | 0 | 113501 | 30.0 | D6 | S | [null] | 126 | Springfield, MA | |
66 | 1 | 0 | male | 30.0 | 0 | 0 | 113801 | 45.5 | [null] | S | [null] | [null] | London / New York, NY | |
67 | 1 | 0 | male | 30.0 | 0 | 0 | 110469 | 26.0 | C106 | S | [null] | [null] | Brockton, MA | |
68 | 1 | 0 | male | 19.0 | 1 | 0 | 113773 | 53.1 | D30 | S | [null] | [null] | New York, NY | |
69 | 1 | 0 | male | 46.0 | 0 | 0 | 13050 | 75.2417 | C6 | C | [null] | 292 | Vancouver, BC | |
70 | 1 | 0 | male | 54.0 | 0 | 0 | 17463 | 51.8625 | E46 | S | [null] | 175 | Dorchester, MA | |
71 | 1 | 0 | male | 28.0 | 1 | 0 | PC 17604 | 82.1708 | [null] | C | [null] | [null] | New York, NY | |
72 | 1 | 0 | male | 65.0 | 0 | 0 | 13509 | 26.55 | E38 | S | [null] | 249 | East Bridgewater, MA | |
73 | 1 | 0 | male | 44.0 | 2 | 0 | 19928 | 90.0 | C78 | Q | [null] | 230 | Fond du Lac, WI | |
74 | 1 | 0 | male | 55.0 | 0 | 0 | 113787 | 30.5 | C30 | S | [null] | [null] | Montreal, PQ | |
75 | 1 | 0 | male | 47.0 | 0 | 0 | 113796 | 42.4 | [null] | S | [null] | [null] | Washington, DC | |
76 | 1 | 0 | male | 37.0 | 0 | 1 | PC 17596 | 29.7 | C118 | C | [null] | [null] | Brooklyn, NY | |
77 | 1 | 0 | male | 58.0 | 0 | 2 | 35273 | 113.275 | D48 | C | [null] | 122 | Lexington, MA | |
78 | 1 | 0 | male | 64.0 | 0 | 0 | 693 | 26.0 | [null] | S | [null] | 263 | Isle of Wight, England | |
79 | 1 | 0 | male | 65.0 | 0 | 1 | 113509 | 61.9792 | B30 | C | [null] | 234 | Providence, RI | |
80 | 1 | 0 | male | 28.5 | 0 | 0 | PC 17562 | 27.7208 | D43 | C | [null] | 189 | ?Havana, Cuba | |
81 | 1 | 0 | male | [null] | 0 | 0 | 112052 | 0.0 | [null] | S | [null] | [null] | Belfast | |
82 | 1 | 0 | male | 45.5 | 0 | 0 | 113043 | 28.5 | C124 | S | [null] | 166 | Surbiton Hill, Surrey | |
83 | 1 | 0 | male | 23.0 | 0 | 0 | 12749 | 93.5 | B24 | S | [null] | [null] | Montreal, PQ | |
84 | 1 | 0 | male | 29.0 | 1 | 0 | 113776 | 66.6 | C2 | S | [null] | [null] | Isleworth, England | |
85 | 1 | 0 | male | 18.0 | 1 | 0 | PC 17758 | 108.9 | C65 | C | [null] | [null] | Madrid, Spain | |
86 | 1 | 0 | male | 47.0 | 0 | 0 | 110465 | 52.0 | C110 | S | [null] | 207 | Worcester, MA | |
87 | 1 | 0 | male | 38.0 | 0 | 0 | 19972 | 0.0 | [null] | S | [null] | [null] | Rotterdam, Netherlands | |
88 | 1 | 0 | male | 22.0 | 0 | 0 | PC 17760 | 135.6333 | [null] | C | [null] | 232 | [null] | |
89 | 1 | 0 | male | [null] | 0 | 0 | PC 17757 | 227.525 | [null] | C | [null] | [null] | [null] | |
90 | 1 | 0 | male | 31.0 | 0 | 0 | PC 17590 | 50.4958 | A24 | S | [null] | [null] | Trenton, NJ | |
91 | 1 | 0 | male | [null] | 0 | 0 | 113767 | 50.0 | A32 | S | [null] | [null] | Seattle, WA | |
92 | 1 | 0 | male | 36.0 | 0 | 0 | 13049 | 40.125 | A10 | C | [null] | [null] | Winnipeg, MB | |
93 | 1 | 0 | male | 55.0 | 1 | 0 | PC 17603 | 59.4 | [null] | C | [null] | [null] | New York, NY | |
94 | 1 | 0 | male | 33.0 | 0 | 0 | 113790 | 26.55 | [null] | S | [null] | 109 | London | |
95 | 1 | 0 | male | 61.0 | 1 | 3 | PC 17608 | 262.375 | B57 B59 B63 B66 | C | [null] | [null] | Haverford, PA / Cooperstown, NY | |
96 | 1 | 0 | male | 50.0 | 1 | 0 | 13507 | 55.9 | E44 | S | [null] | [null] | Duluth, MN | |
97 | 1 | 0 | male | 56.0 | 0 | 0 | 113792 | 26.55 | [null] | S | [null] | [null] | New York, NY | |
98 | 1 | 0 | male | 56.0 | 0 | 0 | 17764 | 30.6958 | A7 | C | [null] | [null] | St James, Long Island, NY | |
99 | 1 | 0 | male | 24.0 | 1 | 0 | 13695 | 60.0 | C31 | S | [null] | [null] | Huntington, WV | |
100 | 1 | 0 | male | [null] | 0 | 0 | 113056 | 26.0 | A19 | S | [null] | [null] | Streatham, Surrey |
Let’s look at the ‘fare’ and ‘age’ of the passengers.
[2]:
vdf.select(["age", "fare"])
[2]:
123 ageNumeric(6,3) | 123 fareNumeric(10,5) | |
1 | 2.0 | 151.55 |
2 | 30.0 | 151.55 |
3 | 25.0 | 151.55 |
4 | 39.0 | 0.0 |
5 | 71.0 | 49.5042 |
6 | 47.0 | 227.525 |
7 | [null] | 25.925 |
8 | 24.0 | 247.5208 |
9 | 36.0 | 75.2417 |
10 | 25.0 | 26.0 |
11 | 45.0 | 35.5 |
12 | 42.0 | 26.55 |
13 | 41.0 | 30.5 |
14 | 48.0 | 50.4958 |
15 | [null] | 39.6 |
16 | 45.0 | 26.55 |
17 | [null] | 31.0 |
18 | 33.0 | 5.0 |
19 | 28.0 | 47.1 |
20 | 17.0 | 47.1 |
21 | 49.0 | 26.0 |
22 | 36.0 | 78.85 |
23 | 46.0 | 61.175 |
24 | [null] | 0.0 |
25 | 27.0 | 136.7792 |
26 | [null] | 52.0 |
27 | 47.0 | 25.5875 |
28 | 37.0 | 83.1583 |
29 | [null] | 26.55 |
30 | 70.0 | 71.0 |
31 | 39.0 | 71.2833 |
32 | 31.0 | 52.0 |
33 | 50.0 | 106.425 |
34 | 39.0 | 29.7 |
35 | 36.0 | 31.6792 |
36 | [null] | 221.7792 |
37 | 30.0 | 27.75 |
38 | 19.0 | 263.0 |
39 | 64.0 | 263.0 |
40 | [null] | 26.55 |
41 | [null] | 0.0 |
42 | 37.0 | 53.1 |
43 | 47.0 | 38.5 |
44 | 24.0 | 79.2 |
45 | 71.0 | 34.6542 |
46 | 38.0 | 153.4625 |
47 | 46.0 | 79.2 |
48 | [null] | 42.4 |
49 | 45.0 | 83.475 |
50 | 40.0 | 0.0 |
51 | 55.0 | 93.5 |
52 | 42.0 | 42.5 |
53 | [null] | 51.8625 |
54 | 55.0 | 50.0 |
55 | 42.0 | 52.0 |
56 | [null] | 30.6958 |
57 | 50.0 | 28.7125 |
58 | 46.0 | 26.0 |
59 | 50.0 | 26.0 |
60 | 32.5 | 211.5 |
61 | 58.0 | 29.7 |
62 | 41.0 | 51.8625 |
63 | [null] | 26.55 |
64 | [null] | 27.7208 |
65 | 29.0 | 30.0 |
66 | 30.0 | 45.5 |
67 | 30.0 | 26.0 |
68 | 19.0 | 53.1 |
69 | 46.0 | 75.2417 |
70 | 54.0 | 51.8625 |
71 | 28.0 | 82.1708 |
72 | 65.0 | 26.55 |
73 | 44.0 | 90.0 |
74 | 55.0 | 30.5 |
75 | 47.0 | 42.4 |
76 | 37.0 | 29.7 |
77 | 58.0 | 113.275 |
78 | 64.0 | 26.0 |
79 | 65.0 | 61.9792 |
80 | 28.5 | 27.7208 |
81 | [null] | 0.0 |
82 | 45.5 | 28.5 |
83 | 23.0 | 93.5 |
84 | 29.0 | 66.6 |
85 | 18.0 | 108.9 |
86 | 47.0 | 52.0 |
87 | 38.0 | 0.0 |
88 | 22.0 | 135.6333 |
89 | [null] | 227.525 |
90 | 31.0 | 50.4958 |
91 | [null] | 50.0 |
92 | 36.0 | 40.125 |
93 | 55.0 | 59.4 |
94 | 33.0 | 26.55 |
95 | 61.0 | 262.375 |
96 | 50.0 | 55.9 |
97 | 56.0 | 26.55 |
98 | 56.0 | 30.6958 |
99 | 24.0 | 60.0 |
100 | [null] | 26.0 |
These lie in different numerical intervals so it’s probably a good idea to normalize them. To normalize data in VerticaPy, we can use the ‘normalize’ method.
[3]:
help(vdf["age"].normalize)
Help on method normalize in module verticapy.vcolumn:
normalize(method:str='zscore', by:list=[], return_trans:bool=False) method of verticapy.vcolumn.vColumn instance
---------------------------------------------------------------------------
Normalizes the input vColumns using the input method.
Parameters
----------
method: str, optional
Method to use to normalize.
zscore : Normalization using the Z-Score (avg and std).
(x - avg) / std
robust_zscore : Normalization using the Robust Z-Score (median and mad).
(x - median) / (1.4826 * mad)
minmax : Normalization using the MinMax (min and max).
(x - min) / (max - min)
by: list, optional
vColumns used in the partition.
return_trans: bool, optimal
If set to True, the method will return the transformation used instead of
the parent vDataFrame. This parameter is used for testing purpose.
Returns
-------
vDataFrame
self.parent
See Also
--------
vDataFrame.outliers : Computes the vDataFrame Global Outliers.
The three main normalization techniques are available. Let’s normalize the ‘fare’ and the ‘age’ using the ‘MinMax’ method.
[4]:
vdf["age"].normalize(method = "minmax")
vdf["fare"].normalize(method = "minmax")
vdf.select(["age", "fare"])
[4]:
123 ageNumeric(20,15) | 123 fareNumeric(24,15) | |
1 | 0.020961466047446 | 0.295805899800363 |
2 | 0.37241119618426 | 0.295805899800363 |
3 | 0.309652315802686 | 0.295805899800363 |
4 | 0.485377180871093 | 0.0 |
5 | 0.887034015313167 | 0.096625763278767 |
6 | 0.585791389481612 | 0.44409922370226 |
7 | [null] | 0.050602229972447 |
8 | 0.297100539726371 | 0.483128426019833 |
9 | 0.447721852642149 | 0.146862017624605 |
10 | 0.309652315802686 | 0.050748620223091 |
11 | 0.560687837328982 | 0.069291385304605 |
12 | 0.523032509100038 | 0.05182214872781 |
13 | 0.510480733023723 | 0.059532035261703 |
14 | 0.598343165557926 | 0.098561237579275 |
15 | [null] | 0.077294052339785 |
16 | 0.560687837328982 | 0.05182214872781 |
17 | [null] | 0.060507970265993 |
18 | 0.410066524413204 | 0.009759350042902 |
19 | 0.34730764403163 | 0.091933077404138 |
20 | 0.209238107192168 | 0.091933077404138 |
21 | 0.610894941634241 | 0.050748620223091 |
22 | 0.447721852642149 | 0.153904950176566 |
23 | 0.573239613405297 | 0.119405647774907 |
24 | [null] | 0.0 |
25 | 0.334755867955316 | 0.266975218277623 |
26 | [null] | 0.101497240446182 |
27 | 0.585791389481612 | 0.049943473844552 |
28 | 0.460273628718464 | 0.162314191734533 |
29 | [null] | 0.05182214872781 |
30 | 0.874482239236852 | 0.13858277060921 |
31 | 0.485377180871093 | 0.139135735382641 |
32 | 0.384962972260575 | 0.101497240446182 |
33 | 0.623446717710556 | 0.207727765663171 |
34 | 0.485377180871093 | 0.057970539254838 |
35 | 0.447721852642149 | 0.061833680375821 |
36 | [null] | 0.432884169006959 |
37 | 0.37241119618426 | 0.054164392738107 |
38 | 0.234341659344797 | 0.513341812256651 |
39 | 0.799171582778963 | 0.513341812256651 |
40 | [null] | 0.05182214872781 |
41 | [null] | 0.0 |
42 | 0.460273628718464 | 0.10364429745562 |
43 | 0.585791389481612 | 0.075146995330346 |
44 | 0.297100539726371 | 0.154588104679569 |
45 | 0.887034015313167 | 0.067640493651348 |
46 | 0.472825404794778 | 0.299538851191773 |
47 | 0.573239613405297 | 0.154588104679569 |
48 | [null] | 0.08275928836381 |
49 | 0.560687837328982 | 0.162932348966251 |
50 | 0.497928956947408 | 0.0 |
51 | 0.68620559809213 | 0.182499845802269 |
52 | 0.523032509100038 | 0.082954475364668 |
53 | [null] | 0.101228858320002 |
54 | 0.68620559809213 | 0.097593500429021 |
55 | 0.523032509100038 | 0.101497240446182 |
56 | [null] | 0.059914211409383 |
57 | 0.623446717710556 | 0.056043067621365 |
58 | 0.573239613405297 | 0.050748620223091 |
59 | 0.623446717710556 | 0.050748620223091 |
60 | 0.403790636375047 | 0.412820506814759 |
61 | 0.723860926321074 | 0.057970539254838 |
62 | 0.510480733023723 | 0.101228858320002 |
63 | [null] | 0.05182214872781 |
64 | [null] | 0.054107398133856 |
65 | 0.359859420107945 | 0.058556100257413 |
66 | 0.37241119618426 | 0.088810085390409 |
67 | 0.37241119618426 | 0.050748620223091 |
68 | 0.234341659344797 | 0.10364429745562 |
69 | 0.573239613405297 | 0.146862017624605 |
70 | 0.673653822015815 | 0.101228858320002 |
71 | 0.34730764403163 | 0.16038672010106 |
72 | 0.811723358855278 | 0.05182214872781 |
73 | 0.548136061252667 | 0.175668300772238 |
74 | 0.68620559809213 | 0.059532035261703 |
75 | 0.585791389481612 | 0.08275928836381 |
76 | 0.460273628718464 | 0.057970539254838 |
77 | 0.723860926321074 | 0.221098075221947 |
78 | 0.799171582778963 | 0.050748620223091 |
79 | 0.811723358855278 | 0.120975341635808 |
80 | 0.353583532069788 | 0.054107398133856 |
81 | [null] | 0.0 |
82 | 0.566963725367139 | 0.055628295244542 |
83 | 0.284548763650056 | 0.182499845802269 |
84 | 0.359859420107945 | 0.129994542571456 |
85 | 0.221789883268482 | 0.212558643934408 |
86 | 0.585791389481612 | 0.101497240446182 |
87 | 0.472825404794778 | 0.0 |
88 | 0.271996987573742 | 0.264738570434791 |
89 | [null] | 0.44409922370226 |
90 | 0.384962972260575 | 0.098561237579275 |
91 | [null] | 0.097593500429021 |
92 | 0.447721852642149 | 0.078318784094289 |
93 | 0.68620559809213 | 0.115941078509677 |
94 | 0.410066524413204 | 0.05182214872781 |
95 | 0.761516254550019 | 0.512121893501288 |
96 | 0.623446717710556 | 0.109109533479646 |
97 | 0.698757374168445 | 0.05182214872781 |
98 | 0.698757374168445 | 0.059914211409383 |
99 | 0.297100539726371 | 0.117112200514825 |
100 | [null] | 0.050748620223091 |
Both of the features now scale in [0,1]. It is also possible to normalize by a specific partition with the ‘by’ parameter.