Study Of Knowledge Acquisition Models Based On Formal Concept Analysis Theory

Formal Concept Analysis (FCA) is an order-theoretic method for the mathematical analysis of scientific data, pioneered by R.Wille in mid80’s. Over the past twenty years, FCA has been widely studied and become a powerful tool for machine learning, software engineering and information retrieval.Tracking the international research status, the thesis mainly researches knowledge acquisition models based on formal concept analysis theory. Achieved results not only enrich and improve formal concept analysis theory, but also are expected enormous applied value due to the widespread applied background of these theories.In the thesis, we make a systematic and in-depth investigation on FCA. The main results and originalities are summarized as follows:1. By introducing formal concept analysis into rough set theory, we propose the rough set model based on formal concept analysis. In this model, a solution to an algebraic structure problem is first provided in an information system:a lattice structure is inferred from the information system and corresponding nodes are called rough concepts. How to deal with common problems in rough set theory based on rough concepts is then explored, such as upper and lower approximation operators, reducts and cores. Decision dependency has become a common form of knowledge representation owing to its properties of expressiveness and ease of understanding, so it has been widely used in practice. Finally, application of rough concepts to the extraction of decision dependencies from a decision table is studied; a complete and non-redundant set of decision dependencies can be obtained from a decision table. This model not only provides a better understanding of rough set theory from the perspective of formal concept analysis, but also demonstrates a new way of combining rough set theory and formal concept analysis.2. By introducing concept lattice and ensemble learning technique into multi-instance learning, we propose the multi-instance ensemble learning model based on concept lattice. In this model, bags rather than instances in bags will serve as objects of formal context in the process of concept lattice building, the corresponding time complexity and space complexity can be effectively descend to a certain extent; Since the unique target feature set obtained by traditional methods could only classify part rather than the whole training set correctly, multiple local target feature sets rather than the unique target feature set are introduced to classify the whole training set almost correctly. Because the nature of the concept lattice is the clustering (a concept is a class), it can cluster the training set into multiple classes; the multi-instance learning problem is divided into multiple local multi-instance learning problems, and the local target feature set is found in each local multi-instance learning problem. By introducing ensemble learning technique the ensemble of all local target feature sets predicts the label of bags out of the training set, and all positive bags can be further clustered into multiple classes. This model could be viewed as the initial exploration of applying concept lattice to machine learning, and provides a new way for solving multi-instance learning problem.3. By introducing concept lattice and granular computing into ontology research, we present the domain ontology model based on concept lattice in different granulations. This model provides a unified method for ontology building, ontology merging and ontology connection based on the domain ontology base. In order to alleviate the impact of mass concepts in the complex field granular computing is introduced to hide low-level concepts, that is, important concepts can be found within a smaller range and from the higher level. A new similarity measure between domain concepts is given in different granulations and the similarity measure of connection between ontologies in multi-granulations is proposed, which can help experts judge relations except for inheritance relation. Although for example ontology building etc cannot dispense with the intervention of domain experts yet, this model provides a new way for the further combination of concept lattice and ontology. How to get ontology automatically by knowledge mining method and artificial intelligence method is one focus of our future research.4. By introducing granular computing into formal concept analysis, we present the knowledge acquisition model of formal concept analysis for different granulations. This model provides a unified method for concept lattice building and rule extraction based on a fuzzy granularity base, and it can overcome the impact of complex lattice structure and mass rules by introducing granular computing. This model focuses on the concept lattice building in different granulations and decision rules extraction in multi-granulations. Since there are many redundant rules in decision rule sets, by introducing inference rules we can remove all redundant decision rules and obtain the complete and non-redundant rule sets. This model provides a useful method for building simple structure concept lattice and reducing mass concepts and rules.This thesis proposes four knowledge acquisition models based on formal concept analysis, that is, the rough set model based on formal concept analysis, the multi-instance ensemble learning model based on concept lattice, the domain ontology model based on formal concept analysis and the knowledge acquisition model of formal concept analysis for different granulations, which not only develop formal concept analysis in theory but also promote the application of formal concept analysis actively.