Abstract
Formal concept analysis (FCA) is largely applied in different areas. However, in some FCA applications the volume of information that needs to be processed can become unfeasible. Thus, the demand for new approaches and algorithms that enable processing large amounts of information is increasing substantially. This article presents a new algorithm for extracting proper implications from high-dimensional contexts. The proposed algorithm, called ImplicPBDD, was based on the PropIm algorithm, and uses a data structure called binary decision diagram (BDD) to simplify the representation of the formal context and enhance the extraction of proper implications. In order to analyze the performance of the ImplicPBDD algorithm, we performed tests using synthetic contexts varying the number of objects, attributes and context density. The experiments show that ImplicPBDD has a better performance—up to 80% faster—than its original algorithm, regardless of the number of attributes, objects and densities.
Highlights
With the advance of technology, the volume of data collected and stored to attend society’s new requirements and services has increased significantly
We introduce a new algorithm named ImplicPBDD, which is capable of manipulating high-dimensional formal contexts
The results showed that ImplicPBDD has a better performance—up to 80% faster—than
Summary
With the advance of technology, the volume of data collected and stored to attend society’s new requirements and services has increased significantly. The FCA is a field of mathematics applied for data analysis where associations and dependencies between instances and attributes are identified from a dataset [2,3]. It has been applied in different areas such as text mining [4], Information Retrieval [5], linguistics [6], security analysis [7], web services [8], Information 2018, 9, 266; doi:10.3390/info9110266 www.mdpi.com/journal/information. Formal concept analysis (FCA) is a field of mathematics that allows the identification of a dataset’s concepts and dependencies (implications), which are represented in a formal context [1]. The incidences (“X”) are the relationships between objects and attributes
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