Makoto Haraguchi

Data abstractions for decision tree induction

When descriptions of data values in a database are too concrete or too detailed, the computational complexity needed to discover useful knowledge from the database will be generally increased. Furthermore, discovered knowledge tends to become complicated. A notion of data abstraction seems useful to resolve this kind of problems, as we obtain a smaller and more general database after the abstraction, from which we can quickly extract more abstract knowledge that is expected to be easier to understand. In general, however, since there exist several possible abstractions, we have to carefully select one according to which the original database is generalized. An inadequate selection would make the accuracy of extracted knowledge worse.From this point of view, we propose in this paper a method of selecting an appropriate abstraction from possible ones, assuming that our task is to construct a decision tree from a relational database. Suppose that, for each attribute in a relational database, we have a class of possible abstractions for the attribute values. As an appropriate abstraction for each attribute, we prefer an abstraction such that, even after the abstraction, the distribution of target classes necessary to perform our classification task can be preserved within an acceptable error range given by user.By the selected abstractions, the original database can be transformed into a small generalized database written in abstract values. Therefore, it would be expected that, from the generalized database, we can construct a decision tree whose size is much smaller than one constructed from the original database. Furthermore, such a size reduction can be justified under some theoretical assumptions. The appropriateness of abstraction is precisely defined in terms of the standard information theory. Therefore, we call our abstraction framework Information Theoretical Abstraction.We show some experimental results obtained by a system ITA that is an implementation of our abstraction method. From those results, it is verified that our method is very effective in reducing the size of detected decision tree without making classification errors so worse.

A goal-dependent abstraction for legal reasoning by analogy

This paper presents a new algorithm to find an appropriate similarityunder which we apply legal rules analogically. Since there may exist a lotof similarities between the premises of rule and a case in inquiry, we haveto select an appropriate similarity that is relevant to both thelegal rule and a top goal of our legal reasoning. For this purpose, a newcriterion to distinguish the appropriate similarities from the others isproposed and tested. The criterion is based on Goal-DependentAbstraction(GDA) to select a similarity such that an abstraction basedon the similarity never loses the necessary information to prove the ground (purpose of legislation) of the legal rule. In order to cope withour huge space of similarities, our GDA algorithm uses some constraintsto prune useless similarities.

An Appropriate Boolean Query Reformulation Interface for Information Retrieval Based on Adaptive Generalization

When implementing an IR system that can support comprehensive searches from a wide variety of documents, it is crucial to have a mechanism for selecting appropriate query formulations. For this purpose, many IR systems can modify query terms by estimating the users information need. However, because modified query terms are usually represented in a complicated form, it is difficult to judge how appropriate they are. In this research, we assume all relevant documents should contain words that correspond to concepts that the user would like to retrieve. Therefore, a Boolean query formula is one good way to represent a users information need with high readability. To find the required concepts in a relevant document set, we have previously proposed a new IR system that calculates appropriate generalized concepts to represent the users need. In this study, we implement a user interface that supports reformulation of IR queries by using abstract concepts

An Appropriate Abstraction for an Attribute-Oriented Induction

An attribute-oriented induction is a useful data mining method that generalizes databases under an appropriate abstraction hierarchy to extract meaningful knowledge. The hierarchy is well designed so as to exclude meaningless rules from a particular point of view. However, there may exist several ways of generalizing databases according to users intention. It is therefore important to provide a multi-layered abstraction hierarchy under which several generalizations are possible and are well controlled. In fact, too-general or too-specific databases are inappropriate for mining algorithms to extract significant rules. From this viewpoint, this paper proposes a generalization method based on an information theoretical measure to select an appropriate abstraction hierarchy. Furthermore, we present a system, called ITA (Information Theoretical Abstraction), based on our method and an attribute-oriented induction. We perform some practical experiments in which ITA discovers meaningful rules from a census database US Census Bureau and discuss the validity of ITA based on the experimental results.

Constructing predicate mappings for goal-dependent abstraction

In theorem proving with abstraction, it is required for system designers to provide a useful abstraction. However, such a task is so difficult that it would be worth studying an automatic construction of abstraction. In this paper, we propose a new framework of Goal-Dependent Abstraction in which an appropriate abstraction is selected according to each goal to be proved. Towards Goal-Dependent Abstraction, we present an algorithm for constructing an appropriate abstraction for a given goal. The appropriateness is defined in terms of Upward-Property and Downward-Property. Since our abstraction is based on predicate mapping, the algorithm in fact computes predicate mappings based on which appropriate abstractions can be constructed. Given a goal, candidate predicate mappings are generated and then tested for their appropriateness for the goal. In order to find appropriate mappings efficiently, we present a property to prune useless candidate generations. The numbers of pruned candidates are evaluated in the best and worst cases. Furthermore some experimental results show that many useless candidates can be pruned with the property and the obtained appropriate predicate mappings (abstractions) fit our intuition. From the experimental results, we could expect our study in this paper to contribute to the fields of analogical reasoning and case-based reasoning as well as theorem-proving.

Towards a legal analogical reasoning system: knowledge representation and reasoning methods

Analogy has many important functions in the domain of law. Since the number of legal rules is restricted and their content is often incomplete, it is necessary at times for a lawyer to opt for an analogical application of a legal rule to a given case in order to decide the case properly. He may apply the rule, though it may not have originally been deemed related to such an event, on the basis of some similarity between the event of the case and the requirement of the relevant legal rule. This type of reasoning is called legal analogy. This paper analyzes an actual case of legal analogy in the field of Japanese civil law in order to clarify the reasoning methods used in analogy, as well as knowledge to justify the analogy. Finally it will be shown how the knowledge is utilized in a symbolic reasoning system both in terms of inverse and standard resolution.

Detecting a Compact Decision Tree Based on an Appropriate Abstraction

It is generally convinced that pre-processing for data mining is needed to exclude irrelevant and meaningless aspects of data before applying data mining algorithms. From this viewpoint, we have already proposcd a notion of Information Theoretical Abstraction, and implemented a system ITA. Given a relational database and a family of possible abstractions for its attribute values, called an anstraction hierarchy, ITA selects the best abstraction among the possible ones so that class disatribution needed to perform our classification task arc preserved as possibly as we can. According to our previous experiment, just one application of abstraction for the whole database has shown its effectiveness in reducing the size of detected rules, without making the classification error worse. However, as C4.5 performs serial attribute-selection repeatedly, ITA does not generally guarantee the preservingness of class distributions, given a sequence of attribute-selections. For this reason, in this paper, we propose a new version of ITA, called iterntizie ITA, so that it tries to keep the class distributions in each attribute selection step as possibly as we call.

Creating Abstract Concepts for Classification by Finding Top-N Maximal Weighted Cliques

This paper presents a method for creating abstract concepts for classification rule mining. We try to find abstract concepts that are useful for the classification in the sense that assuming such a concept can well discriminate a target class and supports data as much as possible. Our task of finding useful concepts is formalized as an optimization problem in which its constraint and objective function are given by entropy and probability of class distributions, respectively. Concepts to be found can be stated in terms of maximal weighted cliques in a graph constructed from the possible distributions. From the graph, as useful abstract concepts, top-N maximal weighted cliques are efficiently extracted with two pruning techniques: branch-and-bound and entropy-based pruning. It is shown that our entropy-based pruning can safely prune only useless cliques by adding distributions in increasing order of their entropy in the process of clique expansion. Preliminary experimental results show that useful concepts can be created in our framework.

Constructing Approximate Informative Basis of Association Rules

In the study of discovering association rules, it is regarded as an important task to reduce the number of generated rules without loss of any information about the significant rules. From this point of view, Bastide, et al. have proposed to generate only non-redundant rules [2]. Although the number of generated rules can be reduced drastically by taking the redundancy into account, many rules are often still generated. In this paper, we try to propose a method for reducing the number of the generated rules by extending the original framework. For this purpose, we introduce a notion of approximate generator and consider an approximate redundancy. According to our new notion of redundancy, many non-redundant rules in the original sense are judged redundant and invisible to users. This achieves the reduction of generated rules. Furthermore, it is shown that any redundant rule can be easily reconstructed from our non-redundant rule with its approximate support and confidence. The maximum errors of these values can be evaluated by a user-defined parameter. We present an algorithm for constructing a set of non-redundant rules, called an approximate informative basis. The completeness and weak-soundness of the basis are theoretically shown. Any significant rule can be reconstructed from the basis and any rule reconstructed from the basis is (approximately) significant. Some experimental results show an effectiveness of our method as well.

Discovery of Maximal Analogies between Stories

Given two documents in the form of texts, we present a notion of maximal analogy representing a generalized event sequence of documents with a maximal set of events. They are intended to be used as extended indices of documents to automatically organize a document database from various viewpoints. The maximal analogy is defined so as to satisfy a certain consistency condition and a cost condition. Under the consistency condition, a term in an event sequence is generalized to more abstract term independently of its occurrence positions. The cost condition is introduced so that meaningless similarities between documents are never concluded. As the cost function is monotone, we can present an optimized bottom-up search procedure to discover a maximal analogy under an upper bound of cost. We also show some experimental results based on which we discuss a future plan.