1. Multidimensional Scaling(MDS) Breakfast Food Perceptual Map

2. The ranking of similarities between Breakfast foods  10 breakfast foods  Asked 17 subjects to rate the similarities between each pair of breakfast foods  with 1 = most similar  With 45 = least similar  Why 1~45 ??? 12345678910 Similarities Ham eggs and home fries Pancakes and sausage Instant breakfast Pastry and or toast Hot cereal Eggs Lox and bagels Bacon and eggs Cold cereal Fruit dish 1 Ham eggs and home fries0245301652113140 2Pancakes and sausage2043321862432842 3Instant breakfast45430172233354189 4Pastry and or toast3032170253814441015 5Hot cereal161822250729111327 6Eggs563338702041936 7Lox and bagels2124351429200262337 8Bacon and eggs1341441142603439 9Cold cereal312881013192334012 10Fruit dish404291527363739120

3. Reduce the similarities to a two- dimensional

4. Distance  Location (Decision Variables)  Distance between two points  (x1-x2)^2+(Y1-Y2)^2  =(INDEX(location,$E18,1)- INDEX(location,G$16,1))^2+(INDEX( location,$E18,2)- INDEX(location,G$16,2))^2 xy 6.719.77 6.859.71 5.410.09 1.463.33 7.145.84 6.738.46 1.008.38 7.379.51 4.263.34 4.000.44 12345678910 Distances Ham eggs and home fries Pancakes and sausage Instant breakfast Pastry and or toast Hot cereal Eggs Lox and bagels Bacon and eggs Cold cereal Fruit dish 1 Ham eggs and home fries00.02956915.61.697350.54794 2Pancakes and sausage0.0209569.815.11.565360.34794 3Instant breakfast95.294.5026.13671.778893122.1 4Pastry and or toast6969.826038.654.1326737.815 5Hot cereal15.615.13638.607.06444141539 6Eggs1.71.577254.17.060331.53272 7Lox and bagels34.636.18825.744.232.860423672 8Bacon and eggs0.510.319373.213.61.5194204894 9Cold cereal47.3 127.8514.532.37364808.5 10Fruit dish94.394.12.114.83971.8372948.50

5. Ranking  RANK(number,ref,[order])  Number 必要 。 這是要找出其排名的數字 。  Ref 必要 。 這是數列的陣列或參照 。 會忽略 ref 中的非數 值。  Order 選用 。 這是指定排列數 值 方式的數字 。  如果 order 為 0 ( 零 ) 或被省略 ， 則 Microsoft Excel 把 ref 當成以遞減順序排序的數列來為 number 排名 。  如果 order 不是 0 ， 則 Microsoft Excel 會將 ref 當成以遞增順序排序的數列來來為 number 排名 。

6. Ranking based on the distance  =IF(G$29=$E33,0,RANK(G20,$G$18:$P$27,1)) 12345678910 Ranks Ham eggs and home fries Pancakes and sausage Instant breakfast Pastry and or toast Hot cereal Eggs Lox and bagels Bacon and eggs Cold cereal Fruit dish 1 Ham eggs and home fries0119975412151156995 2Pancakes and sausage1109777391957136793 3Instant breakfast9997045537987893123 4Pastry and or toast7577450597343852737 5Hot cereal4139535902565333561 6Eggs2119797325049174781 7Lox and bagels5157874365490635583 8Bacon and eggs1513898533176307191 9Cold cereal6967312735475571029 10Fruit dish9593233761818391290 12345678910 Distances Ham eggs and home fries Pancakes and sausage Instant breakfast Pastry and or toast Hot cereal Eggs Lox and bagels Bacon and eggs Cold cereal Fruit dish 1 Ham eggs and home fries00.02956915.61.697350.54794 2Pancakes and sausage0.0209569.815.11.565360.34794 3Instant breakfast95.294.5026.13671.778893122.1 4Pastry and or toast6969.826038.654.1326737.815 5Hot cereal15.615.13638.607.06444141539 6Eggs1.71.577254.17.060331.53272 7Lox and bagels34.636.18825.744.232.860423672 8Bacon and eggs0.510.319373.213.61.5194204894 9Cold cereal47.3 127.8514.532.37364808.5 10Fruit dish94.394.12.114.83971.8372948.50

7.  Objective Function  MAX (B3)=MAX( CORREL(similarities, ranks)) correlation 0.988148 Asked 17 subjects to rate the similarities between each pair of breakfast foods based on one dimensional Ranking based on the distance between two points via two dimensional (X,Y) data