A classifier uses four linear discriminant functions in the plane: 91 = 1, 92 = 2,...

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A classifier uses four linear discriminant functions in the plane: 91 = 1, 92 = 2, 93=2+1-3, and 94 = 22 -1 + 1. i) Sketch the line boundaries in pattern space and label each region with a 4-bit binary codeword. ii) Make a logical table, identifying for each codeword whether or not there is an associated region. iii) Sketch the four-dimensional hypercube in state space. (Don't panic! Use two 3- dimensional projections, one yielding a 3D cube for the case T = 0 and the other giving a 3D cube for T = 1.). Label each vertex with its corresponding binary codeword. Draw a curved line joining each vertex in the first cube with the corresponding vertex in the second cube. 4 ii) Consider the discriminant function y = sgn(T; -2.5). Sketch the decision region induced by this rule in the (2D) feature space. A classifier uses four linear discriminant functions in the plane: 91 = 1, 92 = 2, 93=2+1-3, and 94 = 22 -1 + 1. i) Sketch the line boundaries in pattern space and label each region with a 4-bit binary codeword. ii) Make a logical table, identifying for each codeword whether or not there is an associated region. iii) Sketch the four-dimensional hypercube in state space. (Don't panic! Use two 3- dimensional projections, one yielding a 3D cube for the case T = 0 and the other giving a 3D cube for T = 1.). Label each vertex with its corresponding binary codeword. Draw a curved line joining each vertex in the first cube with the corresponding vertex in the second cube. 4 ii) Consider the discriminant function y = sgn(T; -2.5). Sketch the decision region induced by this rule in the (2D) feature space.

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Solution to Question 1 i Sketch the line boundaries in pattern space and label each region with a 4bit binary codeword The four linear discriminant fu... View the full answer