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Math
- Bayesian Classification (AutoClass): Theory and Results
(package: autoclass)
- We describe AutoClass, an approach to unsupervised
classification based upon the classical mixture model, supplemented
by a Bayesian method for determining the optimal classes. We include
a moderately detailed exposition of the mathematics behind the
AutoClass system. We emphasize that no current unsupervised
classification system can produce maximally useful results when
operated alone. It is the interaction between domain experts and
the machine searching over the model space, that generates new
knowledge. Both bring unique information and abilities to the
database analysis task, and each enhances the others' effectiveness.
We illustrate this point with several applications of AutoClass to
complex real world databases, and describe the resulting successes
and failures.
- Bayesian Classification Theory
(package: autoclass)
- The task of inferring a set of classes and class
descriptions most likely to explain a given data set can be placed on
a firm theoretical foundation using Bayesian statistics. Within this
framework, and using various mathematical and algorithmic
approximations, the AutoClass system searches for the most probable
classifications, automatically choosing the number of classes and
complexity of class descriptions. A simpler version of AutoClass
has been applied to many large real data sets, have discovered new
independently-verified phenomena, and have been released as a robust
software package. Recent extensions allow attributes to the
selectively correlated within particular classes, and allow classes
to inherit, or share, model parameters through a class hierarchy. In
this paper we summarize the mathematical foundations of Autoclass.
- Hypre High-Performance Preconditioners
(package: hypre-doc)
- HYPRE is a software library for solving large, sparse linear systems
of equations on massively parallel computers. The library was created with
the primary goal of providing users with advanced parallel preconditioners.
Issues of robustness, ease of use, flexibility, and interoperability also play
an important role.
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