Scaling Techniques

Normalizing data is crucial when using machine learning algorithms because of how sensitive most of them are to un-scaled data. For example, the neighbors-based and KMeans algorithms use the p-distance in their learning phase.

Normalization is the first step before using a linear regression due to Gauss-Markov assumptions.

Unscaled 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 scale the data, we can easily un-scaled the data and come back to the original distribution.

There are three main scaling techniques:

• Z-Score: We reduce and center the feature values using the average and standard deviation. This scaling technique is sensitive to outliers.

• Robust Z-Score: We reduce and center the feature values using the median and the median absolute deviation. This scaling technique 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 scaling technique is robust to outliers.

To demonstrate data scaling in vastorbit, we will use the well-known titanic dataset.

from vastorbit.datasets import load_titanic

titanic = load_titanic()
titanic.head(100)

	123 pclass Integer 100%	123 survived Integer 100%	Abc name Varchar(164) 100%	Abc sex Varchar(20) 100%	123 age Double 79%	123 sibsp Integer 100%	123 parch Integer 100%	Abc ticket Varchar(36) 100%	123 fare Double 99%	Abc cabin Varchar(30) 22%	Abc embarked Varchar(20) 99%	Abc boat Varchar(100) 37%	123 body Integer 9%	Abc home.dest Varchar(100) 56%
1	3	1	McCormack, Mr. Thomas Joseph	male	[null]	0	0	367228	7.75	[null]	Q	[null]	[null]	[null]
2	3	1	McCoy, Miss. Agnes	female	[null]	2	0	367226	23.25	[null]	Q	16	[null]	[null]
3	3	1	McCoy, Miss. Alicia	female	[null]	2	0	367226	23.25	[null]	Q	16	[null]	[null]
4	3	1	McCoy, Mr. Bernard	male	[null]	2	0	367226	23.25	[null]	Q	16	[null]	[null]
5	3	1	McDermott, Miss. Brigdet Delia	female	[null]	0	0	330932	7.7875	[null]	Q	13	[null]	[null]
6	3	0	McEvoy, Mr. Michael	male	[null]	0	0	36568	15.5	[null]	Q	[null]	[null]	[null]
7	3	1	McGovern, Miss. Mary	female	[null]	0	0	330931	7.8792	[null]	Q	13	[null]	[null]
8	3	1	McGowan, Miss. Anna "Annie"	female	15.0	0	0	330923	8.0292	[null]	Q	[null]	[null]	[null]
9	3	0	McGowan, Miss. Katherine	female	35.0	0	0	9232	7.75	[null]	Q	[null]	[null]	[null]
10	3	0	McMahon, Mr. Martin	male	[null]	0	0	370372	7.75	[null]	Q	[null]	[null]	[null]
11	3	0	McNamee, Mr. Neal	male	24.0	1	0	376566	16.1	[null]	S	[null]	[null]	[null]
12	3	0	McNamee, Mrs. Neal (Eileen O'Leary)	female	19.0	1	0	376566	16.1	[null]	S	[null]	53	[null]
13	3	0	McNeill, Miss. Bridget	female	[null]	0	0	370368	7.75	[null]	Q	[null]	[null]	[null]
14	3	0	Meanwell, Miss. (Marion Ogden)	female	[null]	0	0	SOTON/O.Q. 392087	8.05	[null]	S	[null]	[null]	[null]
15	3	0	Meek, Mrs. Thomas (Annie Louise Rowley)	female	[null]	0	0	343095	8.05	[null]	S	[null]	[null]	[null]
16	3	0	Meo, Mr. Alfonzo	male	55.5	0	0	A.5. 11206	8.05	[null]	S	[null]	201	[null]
17	3	0	Mernagh, Mr. Robert	male	[null]	0	0	368703	7.75	[null]	Q	[null]	[null]	[null]
18	3	1	Midtsjo, Mr. Karl Albert	male	21.0	0	0	345501	7.775	[null]	S	15	[null]	[null]
19	3	0	Miles, Mr. Frank	male	[null]	0	0	359306	8.05	[null]	S	[null]	[null]	[null]
20	3	0	Mineff, Mr. Ivan	male	24.0	0	0	349233	7.8958	[null]	S	[null]	[null]	[null]
21	3	0	Minkoff, Mr. Lazar	male	21.0	0	0	349211	7.8958	[null]	S	[null]	[null]	[null]
22	3	0	Mionoff, Mr. Stoytcho	male	28.0	0	0	349207	7.8958	[null]	S	[null]	[null]	[null]
23	3	0	Mitkoff, Mr. Mito	male	[null]	0	0	349221	7.8958	[null]	S	[null]	[null]	[null]
24	3	1	Mockler, Miss. Helen Mary "Ellie"	female	[null]	0	0	330980	7.8792	[null]	Q	16	[null]	[null]
25	3	0	Moen, Mr. Sigurd Hansen	male	25.0	0	0	348123	7.65	F G73	S	[null]	309	[null]
26	3	1	Moor, Master. Meier	male	6.0	0	1	392096	12.475	E121	S	14	[null]	[null]
27	3	1	Moor, Mrs. (Beila)	female	27.0	0	1	392096	12.475	E121	S	14	[null]	[null]
28	3	0	Moore, Mr. Leonard Charles	male	[null]	0	0	A4. 54510	8.05	[null]	S	[null]	[null]	[null]
29	3	1	Moran, Miss. Bertha	female	[null]	1	0	371110	24.15	[null]	Q	16	[null]	[null]
30	3	0	Moran, Mr. Daniel J	male	[null]	1	0	371110	24.15	[null]	Q	[null]	[null]	[null]
31	3	0	Moran, Mr. James	male	[null]	0	0	330877	8.4583	[null]	Q	[null]	[null]	[null]
32	3	0	Morley, Mr. William	male	34.0	0	0	364506	8.05	[null]	S	[null]	[null]	[null]
33	3	0	Morrow, Mr. Thomas Rowan	male	[null]	0	0	372622	7.75	[null]	Q	[null]	[null]	[null]
34	3	1	Moss, Mr. Albert Johan	male	[null]	0	0	312991	7.775	[null]	S	B	[null]	[null]
35	3	1	Moubarek, Master. Gerios	male	[null]	1	1	2661	15.2458	[null]	C	C	[null]	[null]
36	3	1	Moubarek, Master. Halim Gonios ("William George")	male	[null]	1	1	2661	15.2458	[null]	C	C	[null]	[null]
37	3	1	Moubarek, Mrs. George (Omine "Amenia" Alexander)	female	[null]	0	2	2661	15.2458	[null]	C	C	[null]	[null]
38	3	1	Moussa, Mrs. (Mantoura Boulos)	female	[null]	0	0	2626	7.2292	[null]	C	[null]	[null]	[null]
39	3	0	Moutal, Mr. Rahamin Haim	male	[null]	0	0	374746	8.05	[null]	S	[null]	[null]	[null]
40	3	1	Mullens, Miss. Katherine "Katie"	female	[null]	0	0	35852	7.7333	[null]	Q	16	[null]	[null]
41	3	1	Mulvihill, Miss. Bertha E	female	24.0	0	0	382653	7.75	[null]	Q	15	[null]	[null]
42	3	0	Murdlin, Mr. Joseph	male	[null]	0	0	A./5. 3235	8.05	[null]	S	[null]	[null]	[null]
43	3	1	Murphy, Miss. Katherine "Kate"	female	[null]	1	0	367230	15.5	[null]	Q	16	[null]	[null]
44	3	1	Murphy, Miss. Margaret Jane	female	[null]	1	0	367230	15.5	[null]	Q	16	[null]	[null]
45	3	1	Murphy, Miss. Nora	female	[null]	0	0	36568	15.5	[null]	Q	16	[null]	[null]
46	3	0	Myhrman, Mr. Pehr Fabian Oliver Malkolm	male	18.0	0	0	347078	7.75	[null]	S	[null]	[null]	[null]
47	3	0	Naidenoff, Mr. Penko	male	22.0	0	0	349206	7.8958	[null]	S	[null]	[null]	[null]
48	3	1	Najib, Miss. Adele Kiamie "Jane"	female	15.0	0	0	2667	7.225	[null]	C	C	[null]	[null]
49	3	1	Nakid, Miss. Maria ("Mary")	female	1.0	0	2	2653	15.7417	[null]	C	C	[null]	[null]
50	3	1	Nakid, Mr. Sahid	male	20.0	1	1	2653	15.7417	[null]	C	C	[null]	[null]
51	3	1	Nakid, Mrs. Said (Waika "Mary" Mowad)	female	19.0	1	1	2653	15.7417	[null]	C	C	[null]	[null]
52	3	0	Nancarrow, Mr. William Henry	male	33.0	0	0	A./5. 3338	8.05	[null]	S	[null]	[null]	[null]
53	3	0	Nankoff, Mr. Minko	male	[null]	0	0	349218	7.8958	[null]	S	[null]	[null]	[null]
54	3	0	Nasr, Mr. Mustafa	male	[null]	0	0	2652	7.2292	[null]	C	[null]	[null]	[null]
55	3	0	Naughton, Miss. Hannah	female	[null]	0	0	365237	7.75	[null]	Q	[null]	[null]	[null]
56	3	0	Nenkoff, Mr. Christo	male	[null]	0	0	349234	7.8958	[null]	S	[null]	[null]	[null]
57	3	1	Nicola-Yarred, Master. Elias	male	12.0	1	0	2651	11.2417	[null]	C	C	[null]	[null]
58	3	1	Nicola-Yarred, Miss. Jamila	female	14.0	1	0	2651	11.2417	[null]	C	C	[null]	[null]
59	3	0	Nieminen, Miss. Manta Josefina	female	29.0	0	0	3101297	7.925	[null]	S	[null]	[null]	[null]
60	3	0	Niklasson, Mr. Samuel	male	28.0	0	0	363611	8.05	[null]	S	[null]	[null]	[null]
61	3	1	Nilsson, Miss. Berta Olivia	female	18.0	0	0	347066	7.775	[null]	S	D	[null]	[null]
62	3	1	Nilsson, Miss. Helmina Josefina	female	26.0	0	0	347470	7.8542	[null]	S	13	[null]	[null]
63	3	0	Nilsson, Mr. August Ferdinand	male	21.0	0	0	350410	7.8542	[null]	S	[null]	[null]	[null]
64	3	0	Nirva, Mr. Iisakki Antino Aijo	male	41.0	0	0	SOTON/O2 3101272	7.125	[null]	S	[null]	[null]	Finland Sudbury, ON
65	3	1	Niskanen, Mr. Juha	male	39.0	0	0	STON/O 2. 3101289	7.925	[null]	S	9	[null]	[null]
66	3	0	Nosworthy, Mr. Richard Cater	male	21.0	0	0	A/4. 39886	7.8	[null]	S	[null]	[null]	[null]
67	3	0	Novel, Mr. Mansouer	male	28.5	0	0	2697	7.2292	[null]	C	[null]	181	[null]
68	3	1	Nysten, Miss. Anna Sofia	female	22.0	0	0	347081	7.75	[null]	S	13	[null]	[null]
69	3	0	Nysveen, Mr. Johan Hansen	male	61.0	0	0	345364	6.2375	[null]	S	[null]	[null]	[null]
70	3	0	O'Brien, Mr. Thomas	male	[null]	1	0	370365	15.5	[null]	Q	[null]	[null]	[null]
71	3	0	O'Brien, Mr. Timothy	male	[null]	0	0	330979	7.8292	[null]	Q	[null]	[null]	[null]
72	3	1	O'Brien, Mrs. Thomas (Johanna "Hannah" Godfrey)	female	[null]	1	0	370365	15.5	[null]	Q	[null]	[null]	[null]
73	3	0	O'Connell, Mr. Patrick D	male	[null]	0	0	334912	7.7333	[null]	Q	[null]	[null]	[null]
74	3	0	O'Connor, Mr. Maurice	male	[null]	0	0	371060	7.75	[null]	Q	[null]	[null]	[null]
75	3	0	O'Connor, Mr. Patrick	male	[null]	0	0	366713	7.75	[null]	Q	[null]	[null]	[null]
76	3	0	Odahl, Mr. Nils Martin	male	23.0	0	0	7267	9.225	[null]	S	[null]	[null]	[null]
77	3	0	O'Donoghue, Ms. Bridget	female	[null]	0	0	364856	7.75	[null]	Q	[null]	[null]	[null]
78	3	1	O'Driscoll, Miss. Bridget	female	[null]	0	0	14311	7.75	[null]	Q	D	[null]	[null]
79	3	1	O'Dwyer, Miss. Ellen "Nellie"	female	[null]	0	0	330959	7.8792	[null]	Q	[null]	[null]	[null]
80	3	1	Ohman, Miss. Velin	female	22.0	0	0	347085	7.775	[null]	S	C	[null]	[null]
81	3	1	O'Keefe, Mr. Patrick	male	[null]	0	0	368402	7.75	[null]	Q	B	[null]	[null]
82	3	1	O'Leary, Miss. Hanora "Norah"	female	[null]	0	0	330919	7.8292	[null]	Q	13	[null]	[null]
83	3	1	Olsen, Master. Artur Karl	male	9.0	0	1	C 17368	3.1708	[null]	S	13	[null]	[null]
84	3	0	Olsen, Mr. Henry Margido	male	28.0	0	0	C 4001	22.525	[null]	S	[null]	173	[null]
85	3	0	Olsen, Mr. Karl Siegwart Andreas	male	42.0	0	1	4579	8.4042	[null]	S	[null]	[null]	[null]
86	3	0	Olsen, Mr. Ole Martin	male	[null]	0	0	Fa 265302	7.3125	[null]	S	[null]	[null]	[null]
87	3	0	Olsson, Miss. Elina	female	31.0	0	0	350407	7.8542	[null]	S	[null]	[null]	[null]
88	3	0	Olsson, Mr. Nils Johan Goransson	male	28.0	0	0	347464	7.8542	[null]	S	[null]	[null]	[null]
89	3	1	Olsson, Mr. Oscar Wilhelm	male	32.0	0	0	347079	7.775	[null]	S	A	[null]	[null]
90	3	0	Olsvigen, Mr. Thor Anderson	male	20.0	0	0	6563	9.225	[null]	S	[null]	89	Oslo, Norway Cameron, WI
91	3	0	Oreskovic, Miss. Jelka	female	23.0	0	0	315085	8.6625	[null]	S	[null]	[null]	[null]
92	3	0	Oreskovic, Miss. Marija	female	20.0	0	0	315096	8.6625	[null]	S	[null]	[null]	[null]
93	3	0	Oreskovic, Mr. Luka	male	20.0	0	0	315094	8.6625	[null]	S	[null]	[null]	[null]
94	3	0	Osen, Mr. Olaf Elon	male	16.0	0	0	7534	9.2167	[null]	S	[null]	[null]	[null]
95	3	1	Osman, Mrs. Mara	female	31.0	0	0	349244	8.6833	[null]	S	[null]	[null]	[null]
96	3	0	O'Sullivan, Miss. Bridget Mary	female	[null]	0	0	330909	7.6292	[null]	Q	[null]	[null]	[null]
97	3	0	Palsson, Master. Gosta Leonard	male	2.0	3	1	349909	21.075	[null]	S	[null]	4	[null]
98	3	0	Palsson, Master. Paul Folke	male	6.0	3	1	349909	21.075	[null]	S	[null]	[null]	[null]
99	3	0	Palsson, Miss. Stina Viola	female	3.0	3	1	349909	21.075	[null]	S	[null]	[null]	[null]
100	3	0	Palsson, Miss. Torborg Danira	female	8.0	3	1	349909	21.075	[null]	S	[null]	[null]	[null]

Let’s look at the fare and age of the passengers.

titanic.select(["age", "fare"])

	123 age Double 79%	123 fare Double 99%
1	[null]	7.75
2	[null]	23.25
3	[null]	23.25
4	[null]	23.25
5	[null]	7.7875
6	[null]	15.5
7	[null]	7.8792
8	15.0	8.0292
9	35.0	7.75
10	[null]	7.75
11	24.0	16.1
12	19.0	16.1
13	[null]	7.75
14	[null]	8.05
15	[null]	8.05
16	55.5	8.05
17	[null]	7.75
18	21.0	7.775
19	[null]	8.05
20	24.0	7.8958

These lie in different numerical intervals so it’s probably a good idea to scale them. To scale data in vastorbit, we can use the scale() method.

help(titanic["age"].scale)

The three main scaling techniques are available. Let’s scale the fare and the age using the MinMax method.

titanic["age"].scale(method = "minmax")
titanic["fare"].scale(method = "minmax")
titanic.select(["age", "fare"])

	123 age Double 79%	123 fare Double 99%
1	[null]	0.015126992566498259
2	[null]	0.04538097769949478
3	[null]	0.04538097769949478
4	[null]	0.04538097769949478
5	[null]	0.015200187691820024
6	[null]	0.030253985132996517
7	[null]	0.01537917417160685
8	0.18576976074157586	0.015671954672893913
9	0.4363021420518602	0.015126992566498259
10	[null]	0.015126992566498259
11	0.2985093323312038	0.031425107138144774
12	0.2358762370036327	0.031425107138144774
13	[null]	0.015126992566498259
14	[null]	0.015712553569072387
15	[null]	0.015712553569072387
16	0.6930978328949017	0.015712553569072387
17	[null]	0.015126992566498259
18	0.26092947513466114	0.015175789316712771
19	[null]	0.015712553569072387
20	0.2985093323312038	0.015411575213749284

Both of the features now scale in [0,1]. It is also possible to scale by a specific partition with the by parameter.