Andrei Majidian

Finding Fuzzy Concepts for Creative Knowledge Discovery

Creative knowledge discovery—finding useful, previously unknown links between concepts—is a vital tool in unlocking the economic and social value of the vast range of networked data and services that is now available. We define “standard” knowledge discovery as the search for explanatory and predictive patterns in a specific domain, usually with a large volume of data. In contrast, creative knowledge discovery is concerned with the creation of new (and effective) patterns—either by generalization of existing patterns or by analogy to patterns in other domains. An important precondition for creative knowledge discovery is that we understand the relations within the data. Fuzzy formal concept analysis is a powerful approach that enables us to find embedded structure in data and to extract novel concepts that can be used in subsequent processing such as creative knowledge discovery.

A general approach to the measurement of change in fuzzy concept lattices

The quantity of unstructured and semi-structured data available is growing rapidly. Adding structure to such data by grouping similar items into fuzzy categories (or granules) can be a productive approach, and can lead to additional knowledge (e.g. by monitoring association and other relations between classes). Formal concept analysis (and fuzzy formal concept analysis) enables us to identify hierarchical structure arising from similarities in attribute values. However, in an environment where source data is updated, this data-driven approach may lead to concept lattices whose structure varies over time (that is, the number of concepts and their relation to each other may change significantly as updates are processed). In this paper, we describe a novel way of measuring the distance between concept lattices. The method can be applied to comparison of lattices derived from the same set of objects using different attributes or to different sets of objects categorised by the same attributes. We prove that the proposed method is a distance metric and illustrate its use by means of examples.

Measuring change in fuzzy concept lattices

The quantity of unstructured and semi-structured data available is growing rapidly. Adding structure to such data (by means of ontologies and tag-based taxonomic classifications) is potentially a very productive approach, which can lead to additional knowledge (e.g. by monitoring association and other relations between classes) as well as enabling more effective use and re-use of online knowledge. Formal concept analysis (and fuzzy formal concept analysis) enables us to identify hierarchical structure arising from similarities in attribute values, giving a starting point for an ontology. However, it is often difficult to determine the “best” attributes to use. Furthermore, in an environment where source data is updated, this data-driven approach may lead to concept lattices which vary in structure. In this paper, we describe a novel way of measuring the distance between concept lattices. The method can be applied to comparison of lattices derived from the same set of objects using different attributes or to different sets of objects categorised by the same attributes. Simple examples are used to illustrate the idea.

Soft Concept Hierarchies to Summarise Data Streams and Highlight Anomalous Changes

A hierarchical approach is natural when managing large volumes of information, from both static (database) and dynamic (datastream) sources. Hierarchies allow progressively finer division into more specific categories, but frequently the categories are fuzzy rather than crisp. In this paper, we use fuzzy formal concept analysis to extract soft hierarchies from data. The hierarchies are used to classify data and to monitor changes over time by means of a fuzzy confidence measure for association analysis. A (simulated) stream of terrorism incident data is used as proof of concept.

Extracting Taxonomies from Data - A Case Study Using Fuzzy Formal Concept Analysis

Taxonomies and, more generally, ontologies, are at the core of the semantic web. In practice, it is rare to find data with meta-data markup in accordance with a full ontology, due to the intensive manual effort involved in the production and maintenance of both the ontology and the data. In many cases, however, data is stored in XML documents or relational tables with implicit taxonomic information such as product type, location, business category, etc. In this work we aim to use methods from formal concept analysis (FCA) to extract such embedded taxonomies, as a starting point for creation of a formal ontology or for further processing of the data. Due to noise, data incompleteness, etc, a soft computing approach is necessary for all but the simplest cases.