A tool for creating and visualising formal concept trees

This paper presents a tool for creating and visualising formal concept trees. The concept tree provides an alternative visualisation to the more commonly known concept lattice. The tool described here is an extension of the In-Close formal concept mining program, where concepts are output in a format that can be visualised in a Web Browser using the Collapsible Tree Layout from the D3.js JavaScript library. Because the visualisation is expandable and collapsible, the tool is able to deal with large trees and the user is able to explore branches with single mouse clicks and by panning and zooming the tree. So-called ‘iceberg trees’ can also be produced, by specifying a minimum support for objects

Conceptual Views on Tree Ensemble Classifiers

Random Forests and related tree-based methods are popular for supervised learning from table based data. Apart from their ease of parallelization, their classification performance is also superior. However, this performance, especially parallelizability, is offset by the loss of explainability. Statistical methods are often used to compensate for this disadvantage. Yet, their ability for local explanations, and in particular for global explanations, is limited. In the present work we propose an algebraic method, rooted in lattice theory, for the (global) explanation of tree ensembles. In detail, we introduce two novel conceptual views on tree ensemble classifiers and demonstrate their explanatory capabilities on Random Forests that were trained with standard parameters

The Foundation of Pattern Structures and their Applications

This thesis is divided into a theoretical part, aimed at developing statements around the newly introduced concept of pattern morphisms, and a practical part, where we present use cases of pattern structures. A first insight of our work clarifies the facts on projections of pattern structures. We discovered that a projection of a pattern structure does not always lead again to a pattern structure. A solution to this problem, and one of the most important points of this thesis, is the introduction of pattern morphisms in Chapter4. Pattern morphisms make it possible to describe relationships between pattern structures, and thus enable a deeper understanding of pattern structures in general. They also provide the means to describe projections of pattern structures that lead to pattern structures again. In Chapter5 and Chapter6, we looked at the impact of morphisms between pattern structures on concept lattices and on their representations and thus clarified the theoretical background of existing research in this field. The application part reveals that random forests can be described through pattern structures, which constitutes another central achievement of our work. In order to demonstrate the practical relevance of our findings, we included a use case where this finding is used to build an algorithm that solves a real world classification problem of red wines. The prediction accuracy of the random forest is better, but the high interpretability makes our algorithm valuable. Another approach to the red wine classification problem is presented in Chapter 8, where, starting from an elementary pattern structure, we built a classification model that yielded good results

Changing a semantics: opportunism or courage?

The generalized models for higher-order logics introduced by Leon Henkin, and their multiple offspring over the years, have become a standard tool in many areas of logic. Even so, discussion has persisted about their technical status, and perhaps even their conceptual legitimacy. This paper gives a systematic view of generalized model techniques, discusses what they mean in mathematical and philosophical terms, and presents a few technical themes and results about their role in algebraic representation, calibrating provability, lowering complexity, understanding fixed-point logics, and achieving set-theoretic absoluteness. We also show how thinking about Henkin's approach to semantics of logical systems in this generality can yield new results, dispelling the impression of adhocness. This paper is dedicated to Leon Henkin, a deep logician who has changed the way we all work, while also being an always open, modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and Alonso, E., 201

Improving Predictions of Multiple Binary Models in ILP

Despite the success of ILP systems in learning first-order rules from small number of examples and complexly structured data in various domains, they struggle in dealing with multiclass problems. In most cases they boil down a multiclass problem into multiple black-box binary problems following the one-versus-one or one-versus-rest binarisation techniques and learn a theory for each one. When evaluating the learned theories of multiple class problems in one-versus-rest paradigm particularly, there is a bias caused by the default rule toward the negative classes leading to an unrealistic high performance beside the lack of prediction integrity between the theories. Here we discuss the problem of using one-versus-rest binarisation technique when it comes to evaluating multiclass data and propose several methods to remedy this problem. We also illustrate the methods and highlight their link to binary tree and Formal Concept Analysis (FCA). Our methods allow learning of a simple, consistent, and reliable multiclass theory by combining the rules of the multiple one-versus-rest theories into one rule list or rule set theory. Empirical evaluation over a number of data sets shows that our proposed methods produce coherent and accurate rule models from the rules learned by the ILP system of Aleph