Perceptual Mapping

PERMAP is a program that uses multidimensional scaling (MDS) to reduce multiple pairwise relationships to 2-D pictures, commonly called perceptual maps.

The fundamental purpose of Permap is to uncover hidden structure that might be residing in a complex data set. A unique feature of PERMAP is that it embeds the mapping techniques in an interactive, graphical system that minimizes several difficulties associated with multidimensional scaling practices. It is particularly effective at exposing artifacts due to local minimal, incomplete convergence, and the effects of outliers.

PERMAP takes object-to-object proximity values (also called similarities, dissimilarities, correlations, distances, interactions, psychological distances, dependencies, preferences etc.) and uses multidimensional scaling (MDS) to make a map that shows the relationships between the objects. PERMAP makes classical metric and non-metric MDS analyses in one, two, and three … or eight dimensions, for one-mode two-way or two-mode two-way data, with up to 1000 objects and with missing values allowed.

Another important aspect of perceptual maps is that they are forgiving of missing or imprecise data points. Whereas some analytical techniques cannot tolerate missing elements in the input matrix, MDS results are often unaffected.

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 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 dissimilarity.

When the distance between two objects in a matrix is 1 then the matrix is called as the similarity matrix. Otherwise if the distance between two objects in a matrix is 0 then the matrix is called as the dissimilarity matrix.

An Attribute is some aspect of an object.  It may be called a factor, characteristic, trait, property, component, quantity, variable, dimension (not a good choice in MDS work, but occasionally seen), parameter, and so forth.  The attributes should be presented in a form where each is normalized  (standardized) to some kind of range or standard deviation, but Permap can do the normalizing internally if so desired. 

Permap's data files are based on free form data entry. All values must be non negative and diagonal values must be zero.  The data can be separated with space(s), a comma, or both.  DISSIMILARITYLIST is all one word. If the data are dissimilarities then these diagonal values must be zero by definition.

If your proximity information is in the form of similarities instead of dissimilarities, then replace the keyword DISSIMILARITYLIST with SIMILARITYLIST and be sure that the diagonal values are all equal and are not exceeded by any other similarity value.  There is no space before the "LIST" part of the keyword and capitalization is not important.

Example: Distance between different cities

Step 1: Distance matrix was created in Excel

Step 2: Copy the data to notepad as follows –

Step 3: Open the notepad file on Pemap.           Once the file is loaded, click on START

Field Movements (Mirror, Rotate, Move, Zoom)

Occasionally you will want to control the final orientation of a map in order to a simple comparison to previous results, or you might want to expand a map to inspect a small, congested, area.  These needs can be satisfied by mirroring, rotating, moving, or zooming in.  These operations are known as "field movements”. The field movement controls are activated by clicking the Field button or right clicking the mouse on an open area. 

•    If Mirror is chosen, then clicking near an axis will cause the map to be mirrored about that axis. 
•    If Rotate is chosen, then dragging the mouse about the center of the map will cause the object set to rotate about the center.
•    If Move is chosen, then dragging the mouse in any direction will cause the object set to move in that direction. 
•    If Zoom is chosen, then dragging the mouse away from the center of the map will cause the object set to expand, and vice versa. 

PERMAP's lets you drag-and-drop objects in and out of the active set while the map is evolving and being displayed.  Therefore, single objects can be taken out and placed in “Parked objects” to see how it affects the result.