Today we studied about MDS (Multi-Dimensional Scaling)
and Permap (Perceptual Mapping).
PERMAP takes
object-to-object proximity values (also called similarities, dissimilarities,
correlations, distances, interactions, psychological distances, dependencies,
confusabilities, preferences, joint or conditional probabilities, etc.), or up
to 30 object attribute values which can be used to calculate one of the
forgoing types of proximities, and uses MDS to make a map that shows the
relationships between the objects. Succinctly, PERMAP makes classical metric
and nonmetric MDS analyses in one, two, 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.
Its fundamental purpose is to
uncover any "hidden structure" that might be residing in a complex data
set.
Perceptual mapping is of two
types: Overall Similarity and Attribute Based
In Overall Similarity, we try to look at a broader vision. Its main
advantage is that the attributes which are hidden also can come out while
mapping. But its biggest disadvantage is that in order to interpret data, we
need to have overall information of the data.
In Attribute Based mapping, we try to look at the different attributes.
Its advantage is that more precision can be put in the analysis using
individual attributes. But its disadvantage is that we may forget to consider any
attribute that may be critically important for the analysis to happen. If that
happens, the analysis may be wrong.
It also allows complete on-line
control of the badness function, distance metric, attributes-to-proximities
formula, attribute set composition, mapping weights, and metric or nonmetric
MDS, again, while the solution is running and the developing map is being
displayed. The solution can be mirrored, rotated, translated, or zoomed.
On the left hand side of the map,
there is control box called On-Line Controls which has four Controls: MDS type,
Badness, Dimensions, and Attribute Fns.
First option is the MDS type option. PREMAP can make ratio,
interval, or ordinal analyses, as well as ratio and interval analyses using MDS
type.
The second option is a badness function. A Badness Function is
simply a definition of what it is that makes the positions of a pair of objects
bad. Fundamentally, the object pair
should be separated by a distance that is consistent with the pair's dissimilarity. Thus, the badness should involve a measure of
the mismatch between the two objects. There are several valid ways of defining this
mismatch. PREMAP offers the five most common types of badness measure, Stress,
Stress1, SStress, Multiscale, and Fractional. The choice of the badness measure
is not always important. But, each of the five badness types must be adjusted
for the type of MDS being used.
In short, Permap is easy to use, PC-based, visually oriented, and allows
real-time interaction with the analysis.
It has been designed to have an intuitive interface and it avoids many
of the arcane alternatives that are seen in the research literature but are
never used in practice.
Author: Vivek Agarwal (11020841119)
Team B, Operations
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