Question

du, dz) = (d, dz)/|d2||d2|| tributes Attributes no sody ID: Name: Q3. Given two objects represented by the tuples (22, 1, 42, 10) and (20, 0, 36, 8), compute the: Euclidean distance r=2 Cosine similarity x(x, y) = ({ lxx-Yul") KE -os (4,, dz) = (2, .dz ) Ildilo

Answer 1

We have two objects . suppose, Ist object is & Indy 7= (x, , H2, H3, 2) = (22, 1,42, 10) 7=(4, Yz, Y3 Yy) = (20,0,36,8) To compute Euclidean distance, d(x,y) = E(X; -71)2 = 162.99 +673-433 +60187 43=6274432 = J (22-2037 (1-0) ²+ (42-36) ²+ (10-872 = √62)² + (15²+ (6) 2+ (2,2 = 145 d (x,y) = 6.7082 is Cosine similarity, coscdi, da) = (d, x dz) Il dlllldal ie cos (X,Y)= (3x ) = ( x ) = (22720 + 1X0 +42X36 + 1078) = 440 tot 1512 + 80 ( RP) = 2032 -

Where, 11x11 & llyll is a magnitude of object X & Y respectively. | 11x11 = ar tartaz txez = √(2257 (15+ (4257 (1632 - 2349 11%) = 48.4665 - 3 AYIL = √(20) ²7108+ (36)²+(882 - 11760 lyll = 41.9524 - 4 From ean ② , ③ & 4 , ean becomes. COS CX,Y) = 2032 (4814665) x (41.9524) cos (X,Y) = 0.9994