PERMAP
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 (Fitzgerald & Hubert, 1987).
Permap is an interactive computer
program. It offers both metric (ratio
and interval) and nonmetric (ordinal, ratio + bounds, interval + bounds) MDS
techniques. It solves problems in up to
eight dimensional space and allows boundary conditions to be imposed on the
solution. In the technical jargon,
Permap treats "weighted, incomplete, one-mode, two-way" or
"weighted, incomplete, two-mode,
two-way" data sets. Other jargon
would say it handles weighted, symmetric,
incomplete, triangular or rectangular data sets. The word “weighted” means each data point can
have its own multiplier that reflects in some way the importance or reliability
of the point. The word “symmetric” means
that Permap assumes that the (i, j) proximity value equals the (j, i) proximity
value, and “incomplete” means that it can handle missing data. The one-mode, two-way and square references
indicate that Permap can analyze a matrix of proximity information between
several objects, and the two-mode, two-way and rectangular references means it
can analyze objects each of which are specified by an array of attributes.
Permap can treat up to 1000 objects at a time (but see cautions in Section 11)
and each object can have up to 100 attributes.
It is easy to use, Windows 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.
The following provides an example
of a working data file. To be readable
by Permap this file must be stored in an unformatted text format. Therefore, if you want to actually run this
data, copy and paste it into a word processor and then save the file in ASCII
or ANSI format. Be sure that you do not
introduce any "strange" characters into the text file (sometimes
WordPerfect will add an invisible termination character at the end of a file,
and this can cause trouble). All lines
that do not start with a keyword or a number are comment lines. Comments are disregarded by Permap. This
example uses data from Kaufman and Rousseeuw's book "Finding Groups in
Data" that gives the subjective dissimilarities between eleven sciences as
seen by fourteen postgraduate economics students from several different
countries.
MESSAGE=Differences Between the
Sciences
NOBJECTS=11
DISSIMILARITYLIST
Astr, 0
Biol, 7.87,
0
Chem, 6.50, 2.93, 0
CSci, 5.00,
6.86, 6.50, 0
Econ, 8.00,
8.14, 8.21, 4.79,
0
Geog, 4.29,
7.00, 7.64, 7.71,
5.93, 0
Hist, 8.07,
8.14, 8.71, 8.57,
5.86, 3.86, 0
Math, 3.64,
7.14, 4.43, 1.43,
3.57, 7.07, 9.07,
0
Medi, 8.21,
2.50, 2.93, 6.36,
8.43, 7.86, 8.43,
6.29, 0
Phys, 2.71,
5.21, 4.57, 4.21,
8.36, 7.29, 8.64,
2.21, 5.07, 0
Psyc, 9.36,
5.57, 7.29, 7.21,
6.86, 8.29, 7.64,
8.71, 3.79, 8.64,
0
The data can be separated with
space(s), a comma, or both.
If there are missing data, they
should be entered as "NA" or "na."
The leading names shown above are
optional, but if used they must start with a letter, must not start with NA or
na, and must not contain non-alphanumeric characters.
Author
Kuldeep Chordia
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