Triadic Concept Analysis Research Articles

Triadic concept analysis for insights extraction from longitudinal studies in health

In the health field, longitudinal studies involve the recording of clinical observations of the same sample of patients over successive periods, referred to as waves. This type of database serves as a valuable source of information and insights, particularly when examining the temporal aspect, allowing the extraction of relevant and non-obvious knowledge. The triadic concept analysis theory has been proposed to describe the ternary relationships between objects, attributes, and conditions. In this study, we present a methodology for exploring longitudinal health databases using both the triadic theory and triadic rules, which are similar to association rules but incorporate temporal relations. Through four case studies, we demonstrate the potential of applying triadic analysis to longitudinal databases to identify risk patterns, enhance decision-making processes, and deepen our understanding of temporal dynamics. These findings suggest a promising approach for describing longitudinal databases and obtaining insights to improve clinical decision-support systems for disease treatment.

Exploring the 3-dimensional variability of websites' user-stories using triadic concept analysis

Configurable software systems and families of similar software systems are increasingly being considered by industry to provide software tailored to each customer's needs. Their development requires managing software variability, i.e. commonalities, differences and constraints. A primary step is properly analyzing the variability of software, which can be done at various levels, from specification to deployment. In this paper, we focus on the software variability expressed through user-stories, viz. short formatted sentences indicating which user role can perform which action at the specification level. At this level, variability is usually analyzed in a two dimension view, i.e. software described by features, and considering the roles apart. The novelty of this work is to model the three dimensions of the variability (i.e. software, roles, features) and explore it using Triadic Concept Analysis (TCA), an extension of Formal Concept Analysis. The variability exploration is based on the extraction of 3-dimensional implication rules. The adopted methodology is applied to a case study made of 65 commercial web sites in four domains, i.e. manga, martial arts sports equipment, board games including trading cards, and video-games. This work highlights the diversity of information provided by such methodology to draw directions for the development of a new product or for building software variability models.

A Novel Method for Network Intrusion Detection

Intrusion detection is one of the key research directions of network information security. In order to make up for the deficiencies of traditional security technologies such as firewall, encryption, and authentication, by analyzing the characteristics of network attacks and existing intrusion detection models, the advantages of triadic concept analysis and the application of fuzzy set theory in network intrusion detection are analyzed. The intrusion detection model FCTA based on triadic concept analysis is proposed, which promotes the further development of network intrusion detection. First, we analyze the characteristics of the data and use TF-IDF and Z-Score to normalize and standardize the data to construct a fuzzy triadic background containing quadratic characteristics. It is used to describe the triadic relationship between network connections, network connection characteristics, and intrusion types of network packets. Then, the (i)-induced operator is used to construct the fuzzy triadic concept set based on the fuzzy triadic background and transformed into a fuzzy attribute triadic concept set. Then, the new samples are classified by calculating the similarity between the new samples and the elements in the fuzzy attribute triadic concept set by using the Euclidean distance formula. In order to reduce the model space complexity, compression storage technology is adopted in the model building process.. Finally, by using the IDS-2018 dataset, the rationality and effectiveness of the FCTA model are demonstrated. The average accuracy and average intrusion detection rate of FCTA classification are much higher than BP neural network, SVM algorithm, and KNN algorithm, and the FCTA misjudgment rate is much lower than the BP neural network algorithm, the KNN algorithm, and the SVM algorithm; with the increase of data volume, the accuracy rate and intrusion detection rate increase significantly.

Extracting concepts from triadic contexts using Binary Decision Diagram

Due to the high complexity of real problems, a considerable amount of research that deals with high volumes of information has emerged. The literature has considered new applications of data analysis for high dimensional environments in order to manage the difficulty in extracting knowledge from a database, especially with the increase in social and professional networks. Tri- adic Concept Analysis (TCA) is a technique used in the applied mathematical area of data analysis. Its main purpose is to enable knowledge extraction from a context that contains objects, attributes, and conditions in a hierarchical and systematized representation. There are several algorithms that can extract concepts, but they are inefficient when applied to large datasets because the compu- tational costs are exponential. The objective of this paper is to add a new data structure, binary decision diagrams (BDD), in the TRIAS algorithm and retrieve triadic concepts for high dimen- sional contexts. BDD was used to characterize formal contexts, objects, attributes, and conditions. Moreover, to reduce the computational resources needed to manipulate a high-volume of data, the usage of BDD was implemented to simplify and represent data. The results show that this method has a considerably better speedup when compared to the original algorithm. Also, our approach discovered concepts that were previously unachievable when addressing high dimensional contexts.

Triadic concept approximation

Formal Concept Analysis is a mathematical theory for knowledge representation as well as data analysis and visualization. It provides a mechanism for understanding and mining data through concept lattice construction and exploration. This theory assists in data processing by providing a framework for applying different analysis techniques. One of its potentials lies in its mathematical foundation that enables the generation, ordering, and visualization of knowledge in the form of formal concepts described in a hierarchy known as a concept lattice. However, as the input dataset grows, the search and especially the visualization and exploration of concepts becomes prohibitive. With the extension of the classical FCA approach to Triadic Concept Analysis, this problem becomes even more evident due to the complexity of the inherent structures in triadic concepts and relationships. In this work, we propose an approach to find triadic concepts when a query in the form of a triple is given, allowing the visualization and exploration of a Hasse diagram of triadic concepts.

Applying Zero-suppressed Binary Decision Diagram to Triadic Concept Analysis

Applying Zero-suppressed Binary Decision Diagram to Triadic Concept Analysis

Cloud provider profit-aware and triadic concept analysis-based data replication strategy for tenant performance improvement

Effective data management is very challenging to cloud providers, whose business model relies on maintaining an economic profit while satisfying the tenants' performance requirements. To address these challenges, many data replication strategies have been proposed. In this paper, we propose a new dynamic data replication strategy for cloud systems called RCPP1. In order to satisfy performance requirements, the proposed strategy exploits the valuable knowledge extracted from the tenants' past access history. Therefore, it uses the mathematical triadic concept analysis approach to determine correlated data to be replicated. Furthermore, the cloud provider's profit is taken into account. Hence, an economic model is proposed to estimate the revenues and expenditures of the provider. Experimental studies show the efficiency and effectiveness of RCPP compared to state-of-the-art strategies. RCPP is indeed proven able to reduce the total expenditures of the cloud provider significantly while achieving better performances.

Cloud provider profit-aware and triadic concept analysis-based data replication strategy for tenant performance improvement

Effective data management is very challenging to cloud providers, whose business model relies on maintaining an economic profit while satisfying the tenants' performance requirements. To address these challenges, many data replication strategies have been proposed. In this paper, we propose a new dynamic data replication strategy for cloud systems called RCPP1. In order to satisfy performance requirements, the proposed strategy exploits the valuable knowledge extracted from the tenants' past access history. Therefore, it uses the mathematical triadic concept analysis approach to determine correlated data to be replicated. Furthermore, the cloud provider's profit is taken into account. Hence, an economic model is proposed to estimate the revenues and expenditures of the provider. Experimental studies show the efficiency and effectiveness of RCPP compared to state-of-the-art strategies. RCPP is indeed proven able to reduce the total expenditures of the cloud provider significantly while achieving better performances.

An Axiomatic System for Conditional Attribute Implications in Triadic Concept Analysis

An Axiomatic System for Conditional Attribute Implications in Triadic Concept Analysis

Role based access control design using triadic concept analysis

Role based access control is one of the widely used access control models. There are investigations in the literature that use knowledge representation mechanisms such as formal concept analysis (FCA), description logics, and Ontology for representing access control mechanism. However, while using FCA, investigations reported in the literature so far work on the logic that transforms the three dimensional access control matrix into dyadic formal contexts. This transformation is mainly to derive the formal concepts, lattice structure and implications to represent role hierarchy and constraints of RBAC. In this work, we propose a methodology that models RBAC using triadic FCA without transforming the triadic access control matrix into dyadic formal contexts. Our discussion is on two lines of inquiry. We present how triadic FCA can provide a suitable representation of RBAC policy and we demonstrate how this representation follows role hierarchy and constraints of RBAC on sample healthcare network available in the literature.

A research summary about triadic concept analysis

Triadic concept analysis (TCA) is an extension of formal concept analysis (FCA), which can be applied to machine learning, data mining, information retrieval, and so on. This paper summarizes the current situation and the development tendency of TCA. We introduce TCA in this paper from four aspects: basic notions of triadic concept analysis, triadic implications and triadic association rules, triadic factor analysis and triadic fuzzy concept analysis.

Triadic concept lattices in the framework of aggregation structures

Triadic concept analysis is a method of analysis of three-way tabular data describing objects by binary attributes they have under various conditions. It aims to extract a set of three-dimensional clusters, so-called triadic concepts, from the data. While the method was recently extended to handle the case of graded data, this extension is only one of a variety of possible generalizations, namely the one where the so-called antitone concept-forming operators are considered. The generalizations not covered by the mentioned approach include isotone concept-forming operators, one sided concepts, the use of truth stressing hedges and many others. Since all of the generalizations have their applications, for example in factor analysis of relational data, it is desirable to have a uniform mathematical foundations covering all of the cases. In this paper we provide such foundations. By using triadic aggregation structures as a scale of truth degrees we develop triadic concept analysis in a very general setting that covers a wide variety of its possible extensions in a uniform way.

Biclustering meets triadic concept analysis

Biclustering numerical data became a popular data-mining task at the beginning of 2000’s, especially for gene expression data analysis and recommender systems. A bicluster reflects a strong association between a subset of objects and a subset of attributes in a numerical object/attribute data-table. So-called biclusters of similar values can be thought as maximal sub-tables with close values. Only few methods address a complete, correct and non-redundant enumeration of such patterns, a well-known intractable problem, while no formal framework exists. We introduce important links between biclustering and Formal Concept Analysis (FCA). Indeed, FCA is known to be, among others, a methodology for biclustering binary data. Handling numerical data is not direct, and we argue that Triadic Concept Analysis (TCA), the extension of FCA to ternary relations, provides a powerful mathematical and algorithmic framework for biclustering numerical data. We discuss hence both theoretical and computational aspects on biclustering numerical data with triadic concept analysis. These results also scale to n-dimensional numerical datasets.

Can triconcepts become triclusters?

Two novel approaches to triclustering of three-way binary data are proposed. Tricluster is defined as a dense subset of a ternary relation Y defined on sets of objects, attributes, and conditions, or, equivalently, as a dense submatrix of the adjacency matrix of the ternary relation Y. This definition is a scalable relaxation of the notion of triconcept in Triadic Concept Analysis, whereas each triconcept of the initial data-set is contained in a certain tricluster. This approach generalizes the one previously introduced for concept-based biclustering. We also propose a hierarchical spectral triclustering algorithm for mining dense submatrices of the adjacency matrix of the initial ternary relation Y. Finally, we describe some applications of the proposed techniques, compare proposed approaches and study their performance in a series of experiments with real data-sets.

Triadic concept lattices of data with graded attributes

We present foundations for triadic concept analysis of data with graded attributes. Triadic concept analysis departs from the dyadic case by taking into account modi, such as time instances or conditions, under which objects have attributes. That is, instead of a two-dimensional table filled with 0's and 1's (equivalently, binary relation or two-dimensional binary matrix), the input data in triadic concept analysis consist of a three-dimensional table (equivalently, ternary relation or three-dimensional binary matrix). In the ordinary triadic concept analysis, one assumes that the ternary relationship between objects, attributes, and modi, which specifies whether a given object has a given attribute under a given modus, is a yes-or-no relationship. In the present paper, we show how triadic concept analysis is developed in a setting in which the ternary relationship between objects, attributes, and modi is a matter of degree rather than a yes-or-no relationship. We present the basic notions for the new, ‘graded’ setting, an illustrative example, and generalize basic results including the basic theorem of triadic concept analysis.

N-closure systems and n-closure operators

It is very well known and permeating the whole of mathematics that a closure operator on a given set gives rise to a closure system, whose constituent sets form a complete lattice under inclusion, and vice-versa. Recent work of Wille on triadic concept analysis and subsequent work by the author on polyadic concept analysis led to the introduction of complete trilattices and complete n-lattices, respectively, that generalize complete lattices and capture the order-theoretic structure of the collection of concepts associated with polyadic formal contexts. In the present paper, polyadic closure operators and polyadic closure systems are introduced and they are shown to be in a relationship similar to the one that exists between ordinary (dyadic) closure operators and ordinary (dyadic) closure systems. Finally, the algebraic case is given some special consideration.

Polyadic Concept Analysis

The framework and the basic results of Wille on triadic concept analysis, including his Basic Theorem of Triadic Concept Analysis, are here generalized to n-dimensional formal contexts.

The Basic Theorem of triadic concept analysis

Experiences with applications of concept lattices and the pragmatic philosophy founded by Ch. S. Peirce have suggested a triadic approach to formal concept analysis. It starts with the notion of atriadic context combiningobjects, attributes, andconditions under which objects may have certain attributes.The Basic Theorem of triadic concept analysis clarifies the class of structures which are formed by thetriadic concepts of triadic contexts: These structures are exactly thecomplete trilattices up to isomorphism.