MULTI DIMENSIONAL SCALING (MDS)-
Also
known as Permap, i.e. Perceptual Mapping, the fundamental purpose of
Permap is to uncover hidden structure that might be residing in a complex data
set. Compared to other data mining and
data analysis techniques MDS is growing increasingly popular because its
mathematical basis is easier to understand and its results are easier to
interpret.
There are 2 approaches of MDS-
1.
Overall Similarity- It is used when there is similarity
in pairs and when we
have thorough knowledge of objects.
Advantage- It finds what easily cannot be found
by seeing.
Disadvantage- Thorough knowledge of attributes
is required.
2. Attribute Based- It is done by doing rating on attributes. It is used when we are sure
of using all the attributes.
Advantage- It is very simple to rate the
attribute.
Disadvantage- Some attributes may be left out.
Example of Perceptual Mapping-
Rate the
pairs between 0-9. Give higher rating to the pair which you think is more
similar & find average of all the response-
|
Brand
Names
|
Nikhil
|
Avinash
|
Ankit
|
Sushil
|
Kevin
|
Manish
|
Average
|
|
|
Coke
|
Pepsi
|
7
|
8
|
8
|
9
|
9
|
8
|
0.817
|
|
Coke
|
Slice
|
3
|
0
|
2
|
5
|
1
|
3
|
0.233
|
|
Coke
|
Maaza
|
4
|
1
|
3
|
0
|
1
|
2
|
0.183
|
|
Coke
|
MtDew
|
5
|
5
|
4
|
5
|
4
|
3
|
0.433
|
|
Coke
|
Sprite
|
5
|
5
|
6
|
5
|
3
|
5
|
0.483
|
|
Pepsi
|
Slice
|
4
|
1
|
3
|
0
|
1
|
2
|
0.183
|
|
Pepsi
|
Maaza
|
4
|
0
|
2
|
0
|
1
|
3
|
0.167
|
|
Pepsi
|
MtDew
|
5
|
6
|
5
|
5
|
1
|
4
|
0.433
|
|
Pepsi
|
Sprite
|
5
|
4
|
5
|
5
|
1
|
4
|
0.400
|
|
Slice
|
Maaza
|
8
|
9
|
8
|
9
|
9
|
8
|
0.850
|
|
Slice
|
MtDew
|
4
|
3
|
1
|
5
|
1
|
2
|
0.267
|
|
Slice
|
Sprite
|
2
|
3
|
2
|
5
|
1
|
3
|
0.267
|
|
Maaza
|
MtDew
|
2
|
5
|
2
|
5
|
1
|
3
|
0.300
|
|
Maaza
|
Sprite
|
3
|
3
|
2
|
5
|
1
|
2
|
0.267
|
|
MtDew
|
Sprite
|
9
|
7
|
5
|
9
|
7
|
4
|
0.683
|
·
Higher the average, more the similarity and
vice-versa.
Now
put the average rates in Distance matrix as shown below-
|
Distance
Matrix
|
||||||
|
|
Coke
|
Pepsi
|
Slice
|
Maaza
|
MtDew
|
Sprite
|
|
Coke
|
1
|
|
|
|
|
|
|
Pepsi
|
0.817
|
1
|
|
|
|
|
|
Slice
|
0.233
|
0.183
|
1
|
|
|
|
|
Maaza
|
0.183
|
0.167
|
0.850
|
1
|
|
|
|
MtDew
|
0.433
|
0.433
|
0.267
|
0.300
|
1
|
|
|
Sprite
|
0.483
|
0.400
|
0.267
|
0.267
|
0.683
|
1
|
·
For Permap only the bottom half or full matrix is used and not the top
half as software doesn't accepts it.
·
If distance between the same pair is 1, it is similarity matrix.
·
If distance between the same pair is 0, it is dissimilarity matrix.
The matrix can be directly made in text file or can be
copied to the same.
On the top of the text file following should be
mentioned-
title=Perception of soft drinks (i.e. title of study)
nobjects=6 (i.e. number of objects)
similaritylist (i.e. similarity or dissimilarity list)
Then, copy the bottom half of the matrix as done below-
Coke 1
Pepsi 0.817 1
Slice 0.233 0.183 1
Maaza 0.183 0.167 0.850 1
MtDew 0.433 0.433 0.267 0.300 1
Sprite 0.483 0.400 0.267 0.267 0.683 1
Then save the file, and open Permap.
In Permap open the loaded
file and press ‘START’ to locate the pairs and click outside the circle to see
the names of the pairs. Perceptual mapping of pairs is done in the circle.
•
Objective
function value(in permap) is the error.
Now, from the mapping the position w.r.t. the applied dimensions
are obtained. There are various functions that can be used to arrange the
position of objects, i.e. Mirror Click, Rotate Drag, Move Drag & Zoom Drag.
If the position of one object is corrected the remaining objects themselves
will take the respective positions.
Author-
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