Concept lattice

In Formal Concept Analysis (FCA), a concept lattice graphically portrays the underlying relationships between the objects and attributes of an information system. One of the key complexity problems of concept lattices lies in extracting the useful information. The unorganized nature of attributes in huge contexts often does not yield an informative lattice in FCA. Moreover, understanding the collective relationships between attributes and objects in a larger many valued context is more complicated. In this paper, we introduce a novel approach for deducing a smaller and meaningful concept lattice from which excerpts of concepts can be inferred. In existing attribute-based concept lattice reduction methods for FCA, mostly either the attribute size or the context size is reduced. Our approach involves in organizing the attributes into clusters using their structural similarities and dissimilarities, which is commonly known as attribute clustering, to produce a derived context. We have observed that the deduced concept lattice inherits the structural relationship of the original one. Furthermore, we have mathematically proved that a unique surjective inclusion mapping from the original lattice to the deduced one exists.

Fuzzy Formal Concept Analysis (FCA) is a mathematical tool for the effective representation of imprecise and vague knowledge. However, with a large number of formal concepts from a fuzzy context, the task of knowledge representation becomes complex. Hence, knowledge reduction is an important issue in FCA with a fuzzy setting. The purpose of this current study is to address this issue by proposing a method that computes the corresponding crisp order for the fuzzy relation in a given fuzzy formal context. The obtained formal context using the proposed method provides a fewer number of concepts when compared to original fuzzy context. The resultant lattice structure is a reduced form of its corresponding fuzzy concept lattice and preserves the specialized and generalized concepts, as well as stability. This study also shows a step-by-step demonstration of the proposed method and its application.

This study explored the use of formal concept analysis (FCA), a data mining technique, to analyze coral reef transect data (in terms of life forms) and comparing its results to the standard assessment analysis. Utilizing the quadrat-life form as the object- attribute pair, the results derived from the context was analyzed to assess the coral reefs in the study site which consisted of three stations. Data from Station 1 and Station 2 showed the dominance of Acropora digitate and Acropora branching life forms, respectively. Some life forms were absent from both Stations 1 and 2 but all life forms were present in Station 3 with eight life forms having the highest occurrence. Station 3 had the highest diversity of life forms while Station 2 had the highest live coral cover. This study showed how FCA can be used to generate new knowledge from transect data that can be veri ed by traditional coral reef assessment results, a possible complement to standard coral reef assessment analytical tools. FCA approach shines when it deals with large data sets from many different sources, which may pave the way for data-driven ecological assessment analysis studies such as those already being done for agriculture.

Recent literature reports the growing interests in data analysis using FormalConceptAnalysis (FCA), in which data is represented in the form of object and attribute relations. FCA analyzes and then subsequently visualizes the data based on duality called Galois connection. Attribute exploration is a knowledge acquisition process in FCA, which interactively determines the implications holding between the attributes. The objective of this paper is to demonstrate the attribute exploration to understand the dependencies among the attributes in the data. While performing this process, we add domain experts’ knowledge as background knowledge. We demonstrate the method through experiments on two real world healthcare datasets. The results show that the knowledge acquired through exploration process coupled with domain expert knowledge has better classification accuracy.

While small concept lattices are often represented by line diagrams to better understand their full structure, large diagrams may be too complex to do this. However, such a diagram may still be used to receive new ideas about the inherent structure of a concept lattice. This will be demonstrated for a certain family of formal contexts arising from mathematical musicology.

Querying image databases with similarity searches and relevance feedback has been largely investigated in the literature. In contrast, browsing has not been as much studied. We propose a browsing technique based on clustering and Galois' (concept) lattices. The for- mer technique help to avoid the high cost incurred by Galois' lattices alone. The result is a kind of hypertext of images that combines classification and visualization issues in a high- dimensionality space. RÉSUMÉ. L'interrogation des bases de données d'images grâce aux méthodes de recherche par similarité et par rétroaction a été largement explorée dans la littérature. Par contraste, la navi- gation est un domaine qui a été moins étudié. Nous proposons dans cet article une technique de navigation basée sur un processus de résumé de données et les treillis de Galois. La première technique contribut à réduire le coût élevé qu'induit la construction d'un treillis de Galois lors- qu'il e...

Numerous data mining methods have been designed to help extract relevant and significant information from large datasets. Computing concept lattices allows clustering data according to their common features and making all relationships between them explicit. However, the size of such lattices increases exponentially with the volume of data and its number of dimensions. This paper proposes to use spatial (pixel-oriented) and tree-based visualizations of these conceptual structures in order to optimally exploit their expressivity.

Multi-layer neural networks have been successfully applied in a wide range of supervised and unsupervised learning applications. As they often produce incomprehensible models they are not widely used in data mining applications. To avoid such limitations, comprehensive models have been previously introduced making use of an apriori knowl- edge to build the network architecture. They permit to neural network methods

Multilayer feedforward neural networks have been successfully applied in different domains. Defining an interpretable architecture of a multilayer perceptron (MLP) for a given problem is still challenging. We propose a novel approach based on concept lattices to automatically design a neural network architecture. The designed architecture can then be trained with the backpropagation algorithm. We report experimental results obtained on

We introduce the notion of iceberg concept lattices and show their use in Knowledge Discovery in Databases (KDD). Iceberg lattices are a conceptual clustering method, which is well suited for analyzing very large databases. They also serve as a condensed representation of frequent itemsets, as starting point for computing bases of association rules, and as a visualization method for asso

In order to enrich the existing rule acquisition theory in formal decision contexts, this study puts forward three new types of rules: decision association rules, non-redundant decision association rules and simplest decision association rules. Then, we analyze the relationship among these three types of rules, and develop methods to acquire them from single-scale formal decision contexts. Some numerical experiments are also conducted to compare the performance of the method of acquiring the simplest decision association rules with that of the existing one of acquiring the non-redundant decision rules. Moreover, the new three types of rules are employed to introduce three types of consistencies in multi-scale formal decision contexts. In addition, the notion of an optimal scale is defined by each type of consistency, and how to select an optimal scale is investigated as well. Finally, two applications in smart city for the proposed rule acquisition and optimal scale selection methods are applied to smart city.

This paper proposes a novel application of Formal Concept Analysis (FCA) to neural decoding: the semantic relationships between the neural representations of large sets of stimuli are explored using concept lattices. In particular, the effects of neural code sparsity are modelled using the lattices. An exact Bayesian approach is employed to construct the formal context needed by FCA. This method is explained using an example of neurophysiological data from the high-level visual cortical area STSa. Prominent features of the resulting concept lattices are discussed, including indications for hierarchical face representation and a product-of-experts code in real neurons. The robustness of these features is illustrated by studying the effects of scaling the attributes.

Traditional software in Formal Concept Analysis makes little use of visualization techniques, producing poorly readable concept lattice representations when the number of concepts exceeds a few dozens. This is problematic as the number of concepts in such lattices grows significantly with the size of the data and the number of its dimensions. In this work we propose several methods to enhance the readability of concept lattices firstly though colouring and distortion techniques, and secondly by extracting and visualizing trees derived from concept lattice structures. These contributions represent an important step in the visual analysis of conceptual structures, as domain experts may visually explore larger datasets that traditional visualizations of concept lattice cannot represent effectively.

The construction of the concept lattice of a context is a time consuming process. However, in many practical cases where FCA has proven to provide theoretical strength, e.g., in data mining, the volume of data to analyze is huge. This fact emphasizes the need for efficient lattice manipulations. The processing of large datasets has often been approached with parallel algorithms and some preliminary studies on parallel lattice construction exist in the literature. We propose here a novel divide-and-conquer (D&C) approach that operates by data slicing. In this paper, we present a new parallel algorithm, called DAC-ParaLaX, which borrows its main operating primitives from an existing sequential procedure and integrates them into a multi-process architecture. The algorithm has been implemented using a parallel dialect of the C ++ language and its practical performances have been compared to those of a homologue sequential algorithm.

Recently, by combining rough set theory with granular computing, pessimistic and optimistic multigranulation rough sets have been proposed to derive “AND” and “OR” decision rules from decision systems. At the same time, by integrating granular computing and formal concept analysis, Wille’s concept lattice and object-oriented concept lattice were used to obtain granular rules and disjunctive rules from formal decision contexts. So, the problem of rule acquisition can bring rough set theory, granular computing and formal concept analysis together. In this study, to shed some light on the comparison and combination of rough set theory, granular computing and formal concept analysis, we investigate the relationship between multigranulation rough sets and concept lattices via rule acquisition. Some interesting results are obtained in this paper: 1) “AND” decision rules in pessimistic multigranulation rough sets are proved to be granular rules in concept lattices, but the inverse may not be true; 2) the combination of the truth parts of an “OR” decision rule in optimistic multigranulation rough sets is an item of the decomposition of a disjunctive rule in concept lattices; 3) a non-redundant disjunctive rule in concept lattices is shown to be the multi-combination of the truth parts of “OR” decision rules in optimistic multigranulation rough sets; 4) the same rule is defined with a same certainty factor but a different support factor in multigranulation rough sets and concept lattices. Moreover, algorithm complexity analysis is made for the acquisition of “AND” decision rules, “OR” decision rules, granular rules and disjunctive rules.