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we find the intersects of yab and yed with the x and y axes: Pe (0, Yable-=o) = (0, 5) 3 (0, yedlkmo) = (0,2). G0). 2 (2,0). Pa* (9.1) Pd Thus, yep contains the points: (0, ysepla=o) = (0,-(Yablamo +yalx=o)) = (0, ?) Yed Ysep -1 Yab GG+2),0) = (,0). From the equation of a line that passes through two points, we find: -2 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 Ysep -x. (9.2) Figure 9.1: Plot of the * and classes. 3. No, because the separation of the two sets of points depends only on the two support vectors, i.e. the two points in yab and the two points in yed, but not on the other two points. 4. Yes, because now the * set has only one point (-1,-1) and thus the line separating the two sets of points is different. 2. Line yab passes through the points: (*p, » Y») = (-1,;) 1 (*p Ypn) = (1, –;). From the equation of a line that passes through two points: 3 Yab 2 (x+1) +» Yab= Line yed passes through the points: 3 1. 3 7. From the equation of a line that passes through two points: Yed- * Yed =2-x The line ysep that separates the two sets of points and has the maximal distance to the two sets is thus parallel to both yab andyed and equally distant from both lines. To describe ysep

we find the intersects of yab and yed with the x and y axes: Pe (0, Yable-=o) = (0, 5) 3 (0, yedlkmo) = (0,2). G0). 2 (2,0). Pa* (9.1) Pd Thus, yep contains the points: (0, ysepla=o) = (0,-(Yablamo +yalx=o)) = (0, ?) Yed Ysep -1 Yab GG+2),0) = (,0). From the equation of a line that passes through two points, we find: -2 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 Ysep -x. (9.2) Figure 9.1: Plot of the * and classes. 3. No, because the separation of the two sets of points depends only on the two support vectors, i.e. the two points in yab and the two points in yed, but not on the other two points. 4. Yes, because now the * set has only one point (-1,-1) and thus the line separating the two sets of points is different. 2. Line yab passes through the points: (*p, » Y») = (-1,;) 1 (*p Ypn) = (1, –;). From the equation of a line that passes through two points: 3 Yab 2 (x+1) +» Yab= Line yed passes through the points: 3 1. 3 7. From the equation of a line that passes through two points: Yed- * Yed =2-x The line ysep that separates the two sets of points and has the maximal distance to the two sets is thus parallel to both yab andyed and equally distant from both lines. To describe ysep

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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i understand part 1,3 and 4 can someone explain part 2 to me 

84 Chapter 9. Data Science: Classification 85 we find the intersects of yab and ycd with the x and y axes: 4 (0, yablx=0) = (0,;) (0, yca |x=0) = (0,2). Pc 3 2 Pa*. (2,0). (9.1) 1 Ра Thus, ysep contains the points: Pb 1 (0, ysepla=o) = (0,Vablx=o+Yed lz-0)) = (0,;) Ycd Yab Ysep GG+2).0) = G,0). -1 From the equation of a line that passes through two points, we find: -2 -2 -1.5 -1 -0.5 0.5 1.5 2.5 3 3.5 Ysep = 4 5 - x. (9.2) Figure 9.1: Plot of the * and • classes. 3. No, because the separation of the two sets of points depends only on the two support vectors, i.e. the two points in yab and the two points in ycd, but not on the other two points. 4. Yes, because now the * set has only one point (-1, –1) and thus the line separating the two 2. Line yab passes through the points: sets of points is different. (*p.Ypa) = (-1,;) 1 (¥ps,Ypu) = (1, –;). From the equation of a line that passes through two points: 3 1 Yab - 2 (x+1) + yab = - x 2 2 Line yed passes through the points: 3 1 (*p. Yp.) = 55) (Xp4»Ypa) = (-3). 2'2 From the equation of a line that passes through two points: 1 Ycd - (x)- A ycd = 2–x that separates the two sets of points and has the maximal distance to the two sets is thus parallel to both yab andyed and equally distant from both lines. To describe ysep The line Ysep
Transcribed Image Text:84 Chapter 9. Data Science: Classification 85 we find the intersects of yab and ycd with the x and y axes: 4 (0, yablx=0) = (0,;) (0, yca |x=0) = (0,2). Pc 3 2 Pa*. (2,0). (9.1) 1 Ра Thus, ysep contains the points: Pb 1 (0, ysepla=o) = (0,Vablx=o+Yed lz-0)) = (0,;) Ycd Yab Ysep GG+2).0) = G,0). -1 From the equation of a line that passes through two points, we find: -2 -2 -1.5 -1 -0.5 0.5 1.5 2.5 3 3.5 Ysep = 4 5 - x. (9.2) Figure 9.1: Plot of the * and • classes. 3. No, because the separation of the two sets of points depends only on the two support vectors, i.e. the two points in yab and the two points in ycd, but not on the other two points. 4. Yes, because now the * set has only one point (-1, –1) and thus the line separating the two 2. Line yab passes through the points: sets of points is different. (*p.Ypa) = (-1,;) 1 (¥ps,Ypu) = (1, –;). From the equation of a line that passes through two points: 3 1 Yab - 2 (x+1) + yab = - x 2 2 Line yed passes through the points: 3 1 (*p. Yp.) = 55) (Xp4»Ypa) = (-3). 2'2 From the equation of a line that passes through two points: 1 Ycd - (x)- A ycd = 2–x that separates the two sets of points and has the maximal distance to the two sets is thus parallel to both yab andyed and equally distant from both lines. To describe ysep The line Ysep
Exercise 9.1 –(1) Support Vector Machines. Consider the following set of points: Class y 1 1 3 -1 -1 -1 3 - 2 3 3 1. Plot these six points. Are the classes {*,•} linearly separable? Justify. 2. Write the equation of the line that separates the two sets of points and has the maximal distance to the two sets. You may want to use in your calculations the equation of a line that passes through points (x1,y1) and (x2, y2): y2 - yi y - yı = " (x – x1), X2 - x1 3. Does the line described in 2. change if we remove point (3,3)? Justify. Hint: you do not need to have answered 2. 4. Does the line described in 2. change if we remove points (1, –) and (–1,)? Justify. Hint: you do not need to have answered 2.
Transcribed Image Text:Exercise 9.1 –(1) Support Vector Machines. Consider the following set of points: Class y 1 1 3 -1 -1 -1 3 - 2 3 3 1. Plot these six points. Are the classes {*,•} linearly separable? Justify. 2. Write the equation of the line that separates the two sets of points and has the maximal distance to the two sets. You may want to use in your calculations the equation of a line that passes through points (x1,y1) and (x2, y2): y2 - yi y - yı = " (x – x1), X2 - x1 3. Does the line described in 2. change if we remove point (3,3)? Justify. Hint: you do not need to have answered 2. 4. Does the line described in 2. change if we remove points (1, –) and (–1,)? Justify. Hint: you do not need to have answered 2.
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