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2D Space, 3D Space, Higher-Dimensional Spaces In Machine Learning

This article describes the 2D space, 3D spaces, and higher-dimensional spaces in Machine Learning.

2D Space

A 2D space means you have two features (or variables) per data point. Consider a dataset with the height and weight of people.

Each person is a point on a 2D graph, where the x-axis = height, and the y-axis = weight.

A 3D space means you have three features (or variables) per data point. Consider a dataset with the height, weight, and age of people.

Person	Height (cm)	Weight (kg)	Age (years)
P1	170	65	21
P2	182	78	24
P3	160	55	18
P4	175	72	28
P5	168	61	22
P6	181	80	30
P7	169	67	26
P8	158	54	19
P9	177	74	27
P10	164	59	20

An n-dimensional space means your data has n features. Consider the following 5D space. Consider the following example: -

Point	Feature_1	Feature_2	Feature_3	Feature_4	Feature_5
P1	5.3	2.1	7.8	4.5	6.2
P2	3.7	8.4	1.5	9.2	2.8
P3	6.1	4.2	3.9	7.1	5.4
P4	2.9	6.7	5.6	3.8	7.9
P5	7.4	1.9	2.3	6.4	4.1
P6	4.8	3.3	8.1	2.5	6.7
P7	5.9	7.2	4.6	1.9	3.5
P8	3.4	5.1	6.9	8.3	2.2
P9	6.7	2.8	3.1	5.7	4.9
P10	4.2	8	7.4	3.6	5.8

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Person	Height (cm)	Weight (kg)	Age (years)
P1	170	65	21
P2	182	78	24
P3	160	55	18
P4	175	72	28
P5	168	61	22
P6	181	80	30
P7	169	67	26
P8	158	54	19
P9	177	74	27
P10	164	59	20

Point	Feature_1	Feature_2	Feature_3	Feature_4	Feature_5
P1	5.3	2.1	7.8	4.5	6.2
P2	3.7	8.4	1.5	9.2	2.8
P3	6.1	4.2	3.9	7.1	5.4
P4	2.9	6.7	5.6	3.8	7.9
P5	7.4	1.9	2.3	6.4	4.1
P6	4.8	3.3	8.1	2.5	6.7
P7	5.9	7.2	4.6	1.9	3.5
P8	3.4	5.1	6.9	8.3	2.2
P9	6.7	2.8	3.1	5.7	4.9
P10	4.2	8	7.4	3.6	5.8

Person	Height (cm)	Weight (kg)	Age (years)
P1	170	65	21
P2	182	78	24
P3	160	55	18
P4	175	72	28
P5	168	61	22
P6	181	80	30
P7	169	67	26
P8	158	54	19
P9	177	74	27
P10	164	59	20

Point	Feature_1	Feature_2	Feature_3	Feature_4	Feature_5
P1	5.3	2.1	7.8	4.5	6.2
P2	3.7	8.4	1.5	9.2	2.8
P3	6.1	4.2	3.9	7.1	5.4
P4	2.9	6.7	5.6	3.8	7.9
P5	7.4	1.9	2.3	6.4	4.1
P6	4.8	3.3	8.1	2.5	6.7
P7	5.9	7.2	4.6	1.9	3.5
P8	3.4	5.1	6.9	8.3	2.2
P9	6.7	2.8	3.1	5.7	4.9
P10	4.2	8	7.4	3.6	5.8

Person	Height (cm)	Weight (kg)	Age (years)
P1	170	65	21
P2	182	78	24
P3	160	55	18
P4	175	72	28
P5	168	61	22
P6	181	80	30
P7	169	67	26
P8	158	54	19
P9	177	74	27
P10	164	59	20

Point	Feature_1	Feature_2	Feature_3	Feature_4	Feature_5
P1	5.3	2.1	7.8	4.5	6.2
P2	3.7	8.4	1.5	9.2	2.8
P3	6.1	4.2	3.9	7.1	5.4
P4	2.9	6.7	5.6	3.8	7.9
P5	7.4	1.9	2.3	6.4	4.1
P6	4.8	3.3	8.1	2.5	6.7
P7	5.9	7.2	4.6	1.9	3.5
P8	3.4	5.1	6.9	8.3	2.2
P9	6.7	2.8	3.1	5.7	4.9
P10	4.2	8	7.4	3.6	5.8