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• FracDim
  This is a Perl package for computing the fractal dimension of vector data. If you're doing research in the area, the code may be of interest to you.

  It requires Perl 5 and Berkeley DBM or other implementation of DB_File; if you want the setup/testing script generate and show a plot, you'll need Gnuplot and Ghostview as well.

  This has been tested most heavily on Linux and Solaris. The basics have been tested on Windows NT with a combination of Cygwin 1.1, and the Cygutils ports of Perl 5.6.0 and db-2.7.7, with editing of the scripts to specify the location of Perl rather than querying the shell.

  Five most recent releases:

  • October 15, 2003: patch from 2003-06-04. Trivial change: TriGen.pl was using much more memory than it should be. There's no sense queueing items which won't be read.
  • June 4, 2003: patch from 2002-02-20. Minor changes. Cross-counting removed (it's now part of the FDC patch, because it uses FDC-only code), correlations computed are actually returned (the ones computed on all points, not just the half used for 'robust' fitting).
  • February 20, 2002: patch from 2002-01-14. A few minor changes, such as DFD now returning undef instead of dying if *no* points were returned (this happens mostly with almost-constant single-column sets). The Wrapper module now supports returning columns, although it's slow since everything is organized by rows.
  • January 14, 2002: patch from 2002-01-09. Fixes typos in RUNME.pl. Otherwise, no major changes.
  • January 9, 2002: patch from 2002-01-03. Bug-fix release. Fixes inane bugs dealing with hithertoo little-used functions like get_loglog() and get_loglog_trimmed().
• FDC
  This is a port of the Pair_Count.pm's box-counting algorithm to C++. It's an early stage; while the algorithm has been implemented, it has not yet been rigourously tested. No test script or installation script is provided yet.

  There is an included Perl module and a Perl script for compatibility with the Pair_Count code; the module falls back to the Pair_Count.pm module when necessary (the C++ port does not support the quadratic pair-wise method, for instance; nor does it support hypercube normalization) and hence is a supplement rather than a complete replacement. It can also translate the old option interface to the new option names, which have changed to become more compliant with common practice. The script serves much as the old Pair_Count.pl does.

  Just as with the Perl code, this requires the Berkeley database -- specifically, one built with the C++ API enabled. It also requires getopt_long() support, which may limit it to Unices.

  There are now multiple integration patches.

  • July 2, 2005: Brings FracDim in sync with the Feb. 12, 2004 distribution of FDC.
  • August 13, 2002: The only difference between this and the last one is that this one does not add a comment in the middle of a qw()...
  • June 4, 2002: This patch is meant to go with the 20020604 release of the FracDim code. The big difference is that cross-counting (FDC only) now goes here entirely instead of having useless code in FracDim. This should also apply cleanly.
  • January 15, 2002: This patch is meant to go with the FracDim and FDC releases of the previous day, due to a typo fix RUNME.pl.
  • January 9, 2002: This patch is meant to go with the FracDim and FDC releases of the same day. Use it so that fixes to the DFD module do not get overwritten with an older patch.

  Releases:

  • February 12, 2004: patch from 2004-02-10. Found and fixed related fatal bug in external hash table iteration.
  • February 10, 2004: patch from 2003-10-15. Found and fixed fatal bug in external hash table iteration.
  • October 15, 2003: patch from 2002-01-15. No code changes. The README now has a section at the end summarizing how to use it with FracDim.
  • January 15, 2002: patch from 2002-01-14. The quad-count parameters were tweaked, the tabs were untabified, and 'string.h' was #included in QuadCount.cc. Also fixes argument parsing silliness in FDC.pl.
  • January 14, 2002: patch from 2002-01-09. Typo fixer, but more importantly, adds a quadratic-order implementation that may work when there are too few points (or pairs of corresponding points, in cross-counting) to get a reliable tally.
• Tug of War
  The "Tug of War" package provides an alternative algorithm for computing the fractal dimension. Instead of box-counting, this implements the algorithm described in our (Wong, Wu, Gibbons) FractalKDD 2003 paper. To summarize, it uses a probably approximately correct method to approximate second moments in order to compute correlation fractal dimensions with very little storage cost and in an iterative fashion. The algorithm could, for instance, be readily used on streams. See the README, run the RUNME.pl. The code base itself is in C++; Perl is necessary if you wish to use the sample test script and the accompanying data set generators.
  • September 1, 2003. First public release.
• stats
  This blandly-named set of files is a collection of Perl modules and scripts used mainly for (a) fractal-based feature selection (using the FracDim and FDC packages) and (b) transforming numerical attributes, such as by applying the cumulative distribution functions of univariate random distributions. As such, this odd group of packages provides a variety of functions such as estimators for several distributions, expectation-maximization, numerical integration via Simpson's rule, and numerical inversion of continuous functions. For support purposes, the Numerical module includes a fair number of numerical approaches for Gaussian elimination, singular value decomposition, and other matrix methods.
  • May 5, 2005: patch from December 30, 2004. Fixed typo in pdf computation for truncated normals.
  • December 30, 2004: patch from August 20, 2004. Fixed typos, reversed inequality signs, other bogosities in K-S code.
  • August 20, 2004: patch from August 19, 2004. Fixed errors in computation of Kolmogorov-Smirnov critical values for non-trivial $n.
  • August 19, 2004: patch from July 9, 2004. Support for Kolmogorov-Smirnov goodness of fit, including a reasonably precise pregenerated table of critical values.
  • July 9, 2004: patch from February 26, 2004. Fixes to SEM, Numerical regarding possible non-termination issues.