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MDSJ is a free Java library for Multidimensional Scaling
(MDS).
It is a free, non-graphical, self-contained, lightweight
implementation of basic MDS
algorithms and intended to be used both as a standalone application
and as a building block in Java based data analysis and visualization
software.
It is developed at
the University of
Konstanz, Department of
Computer & Information
Science, Algorithmics
Group. It is free for academic and research purposes; no
registration is required. See the License
Conditions below for the conditions of use.
Multidimensional Scaling is a family of methods for the geometric
representation of data. It turns the information about the similarity
of data objects into geometric positions in such a way that,
hopefully, similar objects are close together and dissimilar objects
are far apart.
Finding these geometric positions is useful for visualizing data
that are intrinsically non-geometric, but among which (dis)similarity
information is present or can be constructed. MDS has applications in
manifold areas, such as psychology, computer graphics, statistics,
data analysis etc.
More formally, there are n data objects 1,...,n. For
each possible pair of i,j of these objects a nonnegative
d(i,j) expresses how dissimilar the two objects i and
j are. The resulting positions x1,...,xn should have
Euclidean distance ||xi – xj|| that approximates the
original dissimilarity d(i,j) as closely as possible.
The current version is v0.2 [2009-11-18]. It does not depend
on a specific operating system or platform, but merely requires a
runtime environment of Java 1.5 or higher to be installed on your system.
The file mdsj.jar is required to be included on your classpath.
Usage as a class library: You can use all classes in the
mdsj.* package in your own Java software.
Javadoc API Documentation
| A sample Java class using MDSJ (MDSJExample.java). |
import mdsj.MDSJ;
public class MDSJExample {
public static void main(String[] args) {
double[][] input={ // input dissimilarity matrix
{0.00,2.04,1.92,2.35,2.06,2.12,2.27,2.34,2.57,2.43,1.90,2.41},
{2.04,0.00,2.10,2.00,2.23,2.04,2.38,2.36,2.23,2.36,2.57,2.34},
{1.92,2.10,0.00,1.95,2.21,2.23,2.32,2.46,1.87,1.88,2.41,1.97},
{2.35,2.00,1.95,0.00,2.05,1.78,2.08,2.27,2.14,2.14,2.38,2.17},
{2.06,2.23,2.21,2.05,0.00,2.35,2.23,2.18,2.30,1.98,1.74,2.06},
{2.12,2.04,2.23,1.78,2.35,0.00,2.21,2.12,2.21,2.12,2.17,2.23},
{2.27,2.38,2.32,2.08,2.23,2.21,0.00,2.04,2.44,2.19,1.74,2.13},
{2.34,2.36,2.46,2.27,2.18,2.12,2.04,0.00,2.19,2.09,1.71,2.17},
{2.57,2.23,1.87,2.14,2.30,2.21,2.44,2.19,0.00,1.81,2.53,1.98},
{2.43,2.36,1.88,2.14,1.98,2.12,2.19,2.09,1.81,0.00,2.00,1.52},
{1.90,2.57,2.41,2.38,1.74,2.17,1.74,1.71,2.53,2.00,0.00,2.33},
{2.41,2.34,1.97,2.17,2.06,2.23,2.13,2.17,1.98,1.52,2.33,0.00}
};
int n=input[0].length; // number of data objects
double[][] output=MDSJ.classicalScaling(input); // apply MDS
for(int i=0; i<n; i++) { // output all coordinates
System.out.println(output[0][i]+" "+output[1][i]);
}
}
}
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In the source code example MDSJExample.java a 12 x 12 matrix of
dissimilarities is set up; see below for an explanation of this sample
data set. Classical scaling is used to generate a two-dimensional
configuration of the 12 objects.
Usage from the command line: MDSJ can be used as a
standalone application from the command line
- starting the JAR file:
java -jar mdsj.jar or
- through addressing its main
class:
java -classpath mdsj.jar mdsj.MDSJ
The following is the standard help output by MDSJ when called without
parameters. In the syntax below, the command MDSJ is to
be replaced by the command correspondig to your settings, e.g., java -jar mdsj.jar.
| Calling MDSJ from the command line |
software/mdsj> java -jar mdsj.jar
MDSJ - Multidimensional Scaling for Java v0.2 (c) 2009 University of Konstanz
usage: MDSJ [options] infile [outfile] see manual for more details
options
-dD output dimensions (default: D=2)
-eE use exponential weight=dissimilarity^E (default: E=0)
-fF data format: -fm matrix (default), -fl list, -fo optimized list
-q quiet mode, do not print analysis results
-rR stress minimization for at most R rounds
-sS stress minimization until relative change is below 10^(-S)
-tT stress minimization for up to T milliseconds
example: MDSJ -t2000 -s4 -d3 -q in.txt out.txt
-rR -sS -tT may be used jointly (termination once any condition holds)
output is written to stdout when no outfile specified
software/mdsj> _
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It reads an input text file infile containing the
input dissimilarities and writes an output text file
outfile containing the coordinates computed by MDS. Each
line in the input file represents one row in the input matrix. The
entries must be parseable as doubles and separated by at
least one blank. See nations.txt for a
sample file. When an output file for the final coordinates is
specified, it is in the same format, i.e., each line contains the
coordinates for one object in each dimension. If no outfile is
specified, the coordinates are written to the standard output.
A sample data file: Wish (1971) asked 18 students about
their perception of similarity (1=very dissimilar, 9=very similar)
between 12 nations: Brazil, Congo, Cuba, Egypt, France, India, Israel,
Japan, China, UdSSR, USA, Yugoslavia. Every similarity score is
converted to a dissimilarity by dissimilarity =
sqrt(9-similarity) and can be used as MDS input.
Classical Scaling turns these dissimilarities (nations.txt) into coordinates (nations-cmds.txt), which can be processed
further, e.g., plotted with gnuplot.
The data is due to: Wish, Individual differences in perceptions and
preferences among nations, in: King and Tigert (eds.), Attitude
research reaches new heights. Am. Marketing Assoc., 1971. Original
data set of similarity scores.
- v0.2 [2009-11-18]: Added features. Made linear algebra
computations a bit more robust. Extended command line interface.
- Detailed spectral analysis of input dissimilarity matrix
- Stress Minimization with arbitrary weight matrix
- Verbose/quiet mode
- IO via standard input/output
- Sparse Stress Minimization
- Customizable termination criterion
- v0.1 [2008-06-11]: First pre-alpha release.
Some features are candiates for inclusion in
future versions:
- Nonmetric Scaling
- Order Constraints
- Procrustes Analysis
- Unfolding
License Conditions: MDSJ is available under the terms and conditions of the Creative
Commons License "by-nc-sa" 3.0. This means that you can
- freely copy, share, and distribute the library at no cost and
- re-use the library as a component in your software,
as long as you
- include the citation below (by),
- do not use MDSJ for any commercial purposes (nc), and
- apply
these conditions to all your pieces of software that make use of MDSJ (sa).
Please feel free to contact us for any questions regarding these conditions.
Citation:
"Algorithmics Group. MDSJ: Java Library for Multidimensional Scaling (Version 0.2).
Available at http://www.inf.uni-konstanz.de/algo/software/mdsj/. University of Konstanz, 2009."
Disclaimer: The MDSJ Java library
("software") is developed and maintained in the Algorithmics Group,
Department of Computer & Information Science, University of Konstanz, Germany
("author"). Some rights reserved. The software is provided "AS
IS", with no warranty, express or implied, including but not
limited to the implied warranties of merchantability and fitness for a
particular use. In no event shall the author be liable for any
damages, direct or indirect, even if advised of the possibility of
such damages. If you do not accept these restrictions, you do not
have permission to download or use MDSJ.
Please
let us know what you use MDSJ for. Comments, suggestions,
ideas, and bug reports are welcome and will help us in improving the
quality of the software.
Corresponding author: Christian Pich.
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