Session 9 & 10 | Group F

By Piyush Upmanyu
SIBM Bangalore (HR)
Group F

Multi-Dimensional Scaling & Premap

MDS & Permap

Permap is a tool used to find clusters (not visible) that might be residing in a complex data set. Permap is more popular tool amongst its competitors due to simpler interface and accurate results.

• It is an interactive computer program. 
• It offers both metric and nonmetric MDS techniques. 
• It solves problems in up to eight dimensional space and allows boundary conditions to be imposed on the solution. 
• Permap can treat up to 1000 objects at a time and each object can have up to 100 attributes. 
• It is easy to use, visually oriented, and allows real-time interaction with the analysis.

MDS Maps

Perceptual maps are also referred to as product maps, sociograms, sociometric maps, psychometric maps, stimulus-response diagrams, relationship maps, concept maps, etc. If one is interested in how certain objects relate to each other, and if one would like to present these relationships in the form of a map, then MDS is used.

The MDS algorithm uses object-to-object proximity information to construct the map. A proximity is some measure of likeness or nearness, or difference or distance, between objects. It can be either a similarity (called a resemblance in some disciplines) or a dissimilarity. If the proximity value gets larger when objects become more alike or closer in some sense, then the proximity is a similarity. If the opposite is the case, the proximity is a dissimilarity.
Proximity values can be calculated, measured, or just assigned based on someone's best judgment. If calculated, they typically are based on some mathematical measure of association (correlation, distance, interaction, relatedness, dependence, joint or conditional probability) operating on a set of attributes.

Data Input
Data are entered from a text file (i.e., a file stored in ASCII or ANSI format). The Windows Notepad can be used to input the data.

Here is a very simple data set:
Title=Perception
nObjects=4

SimilarityList
Coke    0           
Pepsi    8    0       
Sprite   5    4    0   
Dew     4    6    7    0

Dis/similarity data can be in either a lower-left half-matrix, as shown above, or in a whole matrix format. If a whole square matrix is entered, the upper-right triangle is ignored. Entering a square matrix is allowed simply to facilitate data interchange with other programs such as Excel.

Key Points

• No Space should be between the word similarity and list.
• Use dissimilarity instead of similarity if that is required.

Permap gives a graphical interpretation related to the proximity of variables in a very easy to understand way in which one can easily find out the related distances between each pair of variables.