This document provides a step-by-step introduction to performing a first step support vector machine (SVM) classification. It outlines 5 key steps: 1) plotting the initial data points, 2) defining the border between classes as a perpendicular line between two points, 3) determining the distance between each data point and candidate border lines, 4) selecting the border line with the lowest average distance to points, 5) plotting the final border line. Code for implementing this first step SVM approach can be found at a provided GitHub URL.

1. First Step SVM
Yoshinobu Tanno
http://ytanno.herokuapp.com/

2. Introduction ( How to )
0. Plot of data
1. The definition of the border
2. Determine the distance of the border line and the point ( each all points)
3. Select boarder that is lowest value of average 2. distance
4. Plot of 3. Line
5. Where is Sample Code ?

3. 0. Plot Data
• Very Easy !

4. 1 The definition of the border
• Determine the perpendicular line of each of the two points
Point Data P1(p1x,p1y) P2(p2x,p2y)
Midpoint M( (p1x + p2x) / 2.0, (p1y + p2y) / 2.0) = M(mx, my)
Perpendicular define y = ax + b
a = - 1.0 / ( (p1y – p2y ) / (p1x – p2x) )
b = my – mx * a

5. These Line are candidate border

6. Determine the distance of the
border line and the point
P(px,py)
y=ax+b
S(0,b)
θ
distance
A(1,a+b)
cosθ = P ・ A / |P||A| =
(px * 1 + a * (py –b)) /
( (√1 + a^2) * (√px^2 + (py-b)^2))
Θ = acos(cosθ)
Distance = |P|sinθ = (√px^2 + (py-b)^2)) *sinθ
P(px,py-b)
y=axS(0,0)
θ
distance
A(1,a)

7. Select boarder that is lowest value of average
distance
• For example
y=-0.438x + 54.719 avg dist 16.016 Best Border Line !
y=-9.400x + 522.000 avg dist 19.719
y=0.923x + 21.038 avg dist 35.785
y=1.500x + -62.500 avg dist 27.957
y=3.636x + -157.682 avg dist 24.643
y=0.654x + 27.691 avg dist 34.961
y=-3.200x + 146.900 avg dist 16.268
y=0.446x + 49.892 avg dist 42.602
y=0.186x + 56.821 avg dist 39.556

8. Plot of 3. Line
• Complete !

9. Where is sample code ?
• https://github.com/ytanno/svm