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II. 2. Support vector machine (SVM): Given two sets of points C = {x1,..., xc} and D = {y1,..., Ya} where xi, Yi E R", we find a hyperplane with vector a e R" and bias b e R to minimize the following objective function. min ||a||2, a E R" s.t. a"x; <-1, i= 1,.., c a" yi 2 1, i = 1,..., d (1) State the conditions with which the above formulation can have valid solutions. (2) Rewrite equations 2 & 3 as two simultaneous linear inequalities in matrix format. (3) Use enumeration oriented format to express the two convex hulls of sets C and D. (4) Create a numerical example with c=5, d= 4, n=2. (2 pts)

II. 2. Support vector machine (SVM): Given two sets of points C = {x1,..., xc} and D = {y1,..., Ya} where xi, Yi E R", we find a hyperplane with vector a e R" and bias b e R to minimize the following objective function. min ||a||2, a E R" s.t. a"x; <-1, i= 1,.., c a" yi 2 1, i = 1,..., d (1) State the conditions with which the above formulation can have valid solutions. (2) Rewrite equations 2 & 3 as two simultaneous linear inequalities in matrix format. (3) Use enumeration oriented format to express the two convex hulls of sets C and D. (4) Create a numerical example with c=5, d= 4, n=2. (2 pts)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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II. 2. Support vector machine (SVM): Given two sets of points C = {x1,..., xc} and D = {y1,..., Ya}, where xi, Y; E R", we find a hyperplane with vector a e R" and bias b e R to minimize the following objective function. min ||a||2, a e R" s.t. a' x; < -1, i= 1,..., c a" y; 2 1, i = 1, ..., d (1) State the conditions with which the above formulation can have valid solutions. (2) Rewrite equations 2 & 3 as two simultaneous linear inequalities in matrix format. (3) Use enumeration oriented format to express the two convex hulls of sets C and D. (4) Create a numerical example with c = 5, d = 4, n = 2. (2 pts)
Transcribed Image Text:II. 2. Support vector machine (SVM): Given two sets of points C = {x1,..., xc} and D = {y1,..., Ya}, where xi, Y; E R", we find a hyperplane with vector a e R" and bias b e R to minimize the following objective function. min ||a||2, a e R" s.t. a' x; < -1, i= 1,..., c a" y; 2 1, i = 1, ..., d (1) State the conditions with which the above formulation can have valid solutions. (2) Rewrite equations 2 & 3 as two simultaneous linear inequalities in matrix format. (3) Use enumeration oriented format to express the two convex hulls of sets C and D. (4) Create a numerical example with c = 5, d = 4, n = 2. (2 pts)
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