Lecture notes and Mathematica packages for Data Mining (by Luis Javier HERNÁNDEZ PARICIO)

EDH is a mathematica package for the following uses:

1) Aproaching a data file by a pure cubical complex,

2) Dividing a pure cubical complex into its pseudocomponents,

3) Computing the dual of a pure cubic complex and

4) Computing the homology of a finite cubical complex.

For the elaboration of this package we have used the functions of the package ElementaryDecomposition (by Frank Zizza, University of Arizona) which is also included in this distribution. You can download the version your prefer of the following compressed files

EDH sit zip tgz

In the following paper, it is proposed to approach a data file by density map which domain is a cubical complex. The study of the orography of this map by homological tecniques is a new tool to study and classify data files.

Orografía homológica cúbica para la minería de datos (Spanish)

In the following preprint, partial derivations for density maps are defined. On the one hand, we use this derivations to compute the homology of a cubical complex and, on the other hand, we compute interpolation polynomials.

Derivaciones discretas y homología (Spanish)