Multidimensional Scaling(MDS) Breakfast Food Perceptual Map

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 ??? 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 fries Pancakes and sausage Instant breakfast Pastry and or toast Hot cereal Eggs Lox and bagels Bacon and eggs Cold cereal Fruit dish

Reduce the similarities to a two- dimensional

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 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 fries Pancakes and sausage Instant breakfast Pastry and or toast Hot cereal Eggs Lox and bagels Bacon and eggs Cold cereal Fruit dish

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 。

Ranking based on the distance  =IF(G$29=$E33,0,RANK(G20,$G$18:$P$27,1)) 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 fries Pancakes and sausage Instant breakfast Pastry and or toast Hot cereal Eggs Lox and bagels Bacon and eggs Cold cereal Fruit dish 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 fries Pancakes and sausage Instant breakfast Pastry and or toast Hot cereal Eggs Lox and bagels Bacon and eggs Cold cereal Fruit dish

 Objective Function  MAX (B3)=MAX( CORREL(similarities, ranks)) correlation 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