Multidimensional ScalingMDS Breakfast Food Perceptual Map The ranking

Multidimensional Scaling(MDS) Breakfast Food Perceptual Map

The ranking of similarities between Breakfast foods Similarities Ham eggs and home 1 fries 2 Pancakes and sausage 3 Instant breakfast 4 Pastry and or toast 5 Hot cereal 6 Eggs 7 Lox and bagels 8 Bacon and eggs 9 Cold cereal 10 Fruit dish Why 1~45 ? ? ? Cold cereal Bacon and eggs With 45 = least similar Lox and bagels Eggs with 1 = most similar Hot cereal 10 Pastry and or toast Asked 17 subjects to rate the similarities between each pair of breakfast 1 2 3 4 5 6 7 8 9 foods Instant breakfast Pancakes and sausage 10 breakfast foods Ham eggs and home fries 0 2 45 30 16 5 21 1 31 40 2 0 43 32 18 6 24 3 28 42 45 43 0 17 22 33 35 41 8 9 30 32 17 0 25 38 14 44 10 15 16 18 22 25 0 7 29 11 13 27 5 6 33 38 7 0 20 4 19 36 21 24 35 14 29 20 0 26 23 37 1 3 41 44 11 4 26 0 34 39 31 28 8 10 13 19 23 34 0 12 40 42 9 15 27 36 37 39 12 0

Reduce the similarities to a twodimensional Breakfast food MDS 12. 00 12 10. 00 8 6 7 8. 00 5 Preparation time 6. 00 y 9 4 4. 00 2. 00 10 3 0. 00 1. 00 2. 00 3. 00 4. 00 5. 00 6. 00 Nutritional value or Hot vs. Cold 7. 00 8. 00

=(INDEX(location, $E 18, 1)INDEX(location, G$16, 1))^2+(INDEX( location, $E 18, 2)INDEX(location, G$16, 2))^2 15. 6 15. 1 36 38. 6 0 7. 06 44. 2 13. 6 14. 5 39 1. 697 1. 565 71. 77 54. 13 7. 064 0 32. 86 1. 519 32. 37 71. 83 35 36 88 26 44 33 0 42 36 72 9 10 Fruit dish 69 69. 8 26. 1 0 38. 6 54. 1 25. 7 73. 2 7. 85 14. 8 7 Cold cereal (x 1 -x 2)^2+(Y 1 -Y 2)^2 0. 02 95 0 95 94. 5 0 69. 8 26 15. 1 36 1. 57 72 36. 1 88 0. 31 93 47. 3 12 94. 1 2. 1 5 Bacon and eggs 0 0. 02 95. 2 69 15. 6 1. 7 34. 6 0. 51 47. 3 94. 3 6 Lox and bagels Distance between two points Distances Ham eggs and home 1 fries 2 Pancakes and sausage 3 Instant breakfast 4 Pastry and or toast 5 Hot cereal 6 Eggs 7 Lox and bagels 8 Bacon and eggs 9 Cold cereal 10 Fruit dish 4 Eggs 9. 77 9. 71 0. 09 3. 33 5. 84 8. 46 8. 38 9. 51 3. 34 0. 44 3 Hot cereal y 6. 71 6. 85 5. 41 1. 46 7. 14 6. 73 1. 00 7. 37 4. 26 4. 00 2 Pastry and or toast x 1 Instant breakfast Location (Decision Variables) Ham eggs and home fries Pancakes and sausage Distance 8 0. 5 0. 3 93 73 14 1. 5 42 0 48 94 47 94 12 2. 1 7. 8 15 15 39 32 72 36 72 48 94 0 8. 5 0

Ranking based on the distance Hot cereal Eggs Lox and bagels Bacon and eggs Cold cereal Fruit dish 0. 02 95 0 95 94. 5 0 69. 8 26 15. 1 36 1. 57 72 36. 1 88 0. 31 93 47. 3 12 94. 1 2. 1 69 69. 8 26. 1 0 38. 6 54. 1 25. 7 73. 2 7. 85 14. 8 15. 6 15. 1 36 38. 6 0 7. 06 44. 2 13. 6 14. 5 39 1. 697 1. 565 71. 77 54. 13 7. 064 0 32. 86 1. 519 32. 37 71. 83 35 36 88 26 44 33 0 42 36 72 0. 5 0. 3 93 73 14 1. 5 42 0 48 94 47 94 12 2. 1 7. 8 15 15 39 32 72 36 72 48 94 0 8. 5 0 2 3 4 5 6 7 8 9 10 Fruit dish Pastry and or toast 0 0. 02 95. 2 69 15. 6 1. 7 34. 6 0. 51 47. 3 94. 3 Ranks Ham eggs and home 1 fries 2 Pancakes and sausage 3 Instant breakfast 4 Pastry and or toast 5 Hot cereal 6 Eggs 7 Lox and bagels 8 Bacon and eggs 9 Cold cereal 10 Fruit dish 1 Cold cereal 10 Bacon and eggs 9 Lox and bagels 8 Eggs 7 Hot cereal 6 Pastry and or toast 5 Instant breakfast 4 Pancakes and sausage 3 Ham eggs and home fries 2 Instant breakfast Distances Ham eggs and home 1 fries 2 Pancakes and sausage 3 Instant breakfast 4 Pastry and or toast 5 Hot cereal 6 Eggs 7 Lox and bagels 8 Bacon and eggs 9 Cold cereal 10 Fruit dish 1 Pancakes and sausage =IF(G$29=$E 33, 0, RANK(G 20, $G$18: $P$27, 1)) Ham eggs and home fries 0 11 99 75 41 21 51 15 69 95 11 0 97 77 39 19 57 13 67 93 99 97 0 45 53 79 87 89 31 23 75 77 45 0 59 73 43 85 27 37 41 39 53 59 0 25 65 33 35 61 21 19 79 73 25 0 49 17 47 81 51 57 87 43 65 49 0 63 55 83 15 13 89 85 33 17 63 0 71 91 69 67 31 27 35 47 55 71 0 29 95 93 23 37 61 81 83 91 29 0

Ranking based on the distance between two points via two dimensional (X, Y) data Objective Function MAX (B 3)=MAX( CORREL(similarities , ranks)) correlation 0. 988148 Asked 17 subjects to rate the similarities between each pair of breakfast foods based on one dimensional