Ontological Data Mining

Our Relational Data Mining approach has the following main points:

1. Any Data Mining method assumes explicitly or implicitly defined:

data types;

language to manipulate and interpret data;

hypothesis to be tested on data;

2. Different DM methods are considered from the point of view of their Data Types, Languages and Hypotheses.

3. Scientific Discovery Theory and the Data Mining Tool Discovery are the ways for further development of various DM methods and include:

Extension of the Data Types (English) (Russian) notion, using first-order logic with unlimited descriptive possibilities.

Measurement Theory for describing various Data Types in the first-order logic; Krantz DH, Luce RD, Suppes P, and Tversky A: Foundations of Measurement V.1-3, Acad. Press, NY, London. 1971, 1989, 1990.

Predicate Invention of new features, properties and relations defined for Data Types in first-order logic, using Measurement Theory

Using any Background Knowledge for Learning and Forecasting.

Rule Type (English) (Russian) notions describing hypotheses classes; Such classes are not defined apriori as in most DM methods; Examples of rules discovered in Time Series and in Breast Cancer Diagnosis

Law-like rules notions satisfying all the properties of scientific laws: simplicity, maximum refutability and logical generality; The notions of Rule Type and law-like rules significantly reduce the search space and make the problem tractable;

DM Tool Discovery for discovering the sets of law-like rules by specification of Data Types, Invented predicates, and Rule Types; Theory of DM Tool Discovery;

Comparison of DM Tool Discovery with other well known DM methods: Neural Networks, Decision trees, ARIMA, Rule extraction from Neural Networks and FOIL. System Discovery outperforms these methods on S&P500 index forecasting.

We denote the possibility of overcoming limitations of some Data Mining methods concerning particular data types, language to manipulate (interpret) data and hypothesis class to be tested.

The Discovery DM Tool may be considered as a Tool, generating a set of forecasting law-like rules by the specification of Data Types, Invented predicates and Rule Types.

The study of Machine Methods for Discovering Regularities (MMDR) was initiated in the seventies at the Institute of Mathematics, Russian Academy of Sciences.

History of MMDR