The rising number of different kinds of data that can be used to describe a human trajectory (Such as GPS Coordinate, GSM, RFID, RSSI…) put in the spotlight the semantically rich trajectory. A semantic trajectory annotates semantic knowledge directly into raw data based on features of the studied area such as point of interest or weather conditions. One of the challenges of mobility studies nowadays is to find the right data model to shape all those data coming from different source into a framework flexible enough to multiply the contextual data that can be used; where contextual data are knowledge coming from external data source (public city dataset, web pages, national weather services etc….). Such data models are the key component of mobility studies, but oftentimes lose the computational aspect of trajectories. In this paper, we will use the semantically rich trajectory as a way to analyse behavioral data enriched by contextual knowledge as this issue has rarely been addressed in the state of the art. We will study the use of formal concept analysis and pattern mining as a way to compute complex sequential patterns in a dataset of semantic trajectories by using the NextPriorityConcept algorithm. This kind of formal concept analysis allows an interactive analysis between individuals path and contextual data resulting in a hierarchy of spatio-temporal clusters where each cluster contains a specific pattern depicting the trajectories within.
Formal Concept Analysis (FCA) and Rough Set Theory (RST) are two useful mathematical tools for extracting information, which have different philosophies. One important issue in data science is to obtain relationships among the main variables in the considered data set. Both theories, FCA and RST, independently study these relations by means of attribute implications in FCA and decision rules in RST. This paper introduces a preliminary comparison between these approaches, focused on the notions of valid attribute implication in FCA and true decision rule in RST.
Galois connections are useful to model solutions for both pure and application-oriented problems. Throughout the paper, the general framework is a complete fuzzy lattice over a Heyting algebra. We have established a fuzzy Galois connection between the fuzzy powerset lattice and the set of functions in 𝐴 . Furthermore, the fixed points, or formal concepts , of this fuzzy Galois connection are exactly the fuzzy closure systems and fuzzy closure operators on 𝐴 . The extension of this fuzzy Galois connection to the general framework is discussed but the study of the fixed points is still an open problem.
This paper establishes an ordering between partial formal contexts, which are trivalued contexts. We use three values to represent the presence or absence of a certain property or its unknown value. We establish a Galois connection between this ordered set and the Boolean algebra of attribute sets. Finally, we discuss the interpretation of this Galois connection.
An increasing number of cyberattacks puts a rising demand on the security analysts and teams for security incident response. In this paper, we focus on connections and relationships between digital evidence, which can help solve cybersecurity incidents. We can apply Formal concept analysis as a set of data analysis methods that are based on lattice theory. This particular biclustering method allows us to explore the meaningful groupings of digital objects (referred to as objects) regarding joint attributes. Moreover, we can visualize the concept lattice to consult its hierarchy with the experts in the field. In our paper, we describe the formal context based on digital evidence collected from the NTFS filesystem. We present several concept lattices on these data subsets and provide our tasks’ association rules.
Data cleaning is a process that precedes data mining. Particularly, in our dataset on pesticidal plant use, several types of anomalies were identified, ranging from incorrect values to a lack of data susceptible of causing users to draw wrong conclusions during its exploration. Literature presents three methods based on Formal Concept Analysis (FCA), i.e. implication rules computation, association rules computation, and attribute exploration, that may allow the detection and correction of anomalies. This paper evaluates 30 FCA-based software and their apposite features to the development of an anomaly detection and correction method applicable to our dataset. Results show that only ConExp and its reimplementations provide all three methods. Since the data model on plant use is relational but ConExp only allows formal contexts as input, this paper concludes on the importance of integrating Relational Concept Analysis (RCA) with ConExp in future work.
Partial formal contexts are trivalued contexts that, besides allowing to establish whether a property is satisfied or not, allow to represent situations in which there is ignorance about whether a property is satisfied. This can be useful, not only for the cases in which the modeled phenomenon has intrinsically unknown information, but also when summarizing information from a formal context by grouping similar rows. In this paper, we prospect for its extension including degrees of knowledge.
A link key between two RDF datasets 𝐷 1 and 𝐷 2 is a set of pairs of properties allowing to identify pairs of individuals 𝑥 1 and 𝑥 2 through an identity link such as x 1 owl ∶ sameAs x 2 . In this paper, relying on and extending previous work, we introduce an original formalization of link key discovery based on the framework of Partition Pattern Structures (pps). Our objective is to study and evaluate the redundancy of link keys based on the fact that owl:sameAs is an equivalence relation. In the pps concept lattice, every concept has an extent representing a link key candidate and an intent representing a partition of instances into sets of equivalent instances. Experiments show three main results. Firstly redundancy of link keys is not so significant in real-world datasets. Nevertheless, the link key discovery approach based on pps returns a reduced number of non redundant link key candidates when compared to a standard approach. Moreover, the pps-based approach is efficient and returns link keys of high quality.
A central notion in Formal Concept Analysis is the concept lattice. This lattice allows describing a hierarchical biclustering between objects and attributes of a formal context, whose hierarchy is defined by an order that expresses the specialisation-generalisation relationship between concepts. It is a fundamental way of representing the knowledge implicit in the context. Therefore, in practice, due to its theoretical complexity, it is necessary to define computationally efficient algorithms for its calculation. In the literature, several algorithms, using different approaches, have been proposed for the computation of the lattice in the classical framework, where the presence of an attribute in an object is modelled as a binary value, indicating that the attribute is either present or absent. However, it is possible to extend this framework to take into account the different degrees to which an attribute could be present in an object. Through this extension, it is possible to model fuzzy situations where the attribute is not 100% present in an object, giving flexibility to the model. In this paper, we review the best known algorithms for the calculation of the concept lattice in the binary version, and we extend them for the calculation of the fuzzy concept lattice, presenting the most significant differences with respect to the original binary versions. In addition, we will present examples of the execution of these new versions of the algorithms.
Since its first formalization, the Formal Concept Analysis (FCA) field has shown diverse extensions of the FCA paradigm. A recent example is Graph-FCA, an extension of FCA to graphs. In the context of Graph-FCA, a notion of concept of neighbors has been introduced to support a form of nearest neighbor search over the nodes of a graph. Concepts of neighbors have been used for diverse tasks, such as knowledge graph completion and relation classification in texts. In this paper, we present CONNOR, a Java library for the computation of concepts of neighbors on RDF graphs.
Formal Concept Analysis (FCA) and its extensions have shown their efficacy and relevance in various application domains. We recently conducted a set of experiments using Relational Concept Analysis and FCA in the domain of agro-ecology. This motivated the development of a library named FCA4J, which includes Java implementation of algorithms to build structures and implications and to manage data, in particular relational context families. This paper presents the main features of FCA4J, its ecosystem, and a few use cases.
Noting certain limitations of fuzzy concept lattices in rough set theory in terms of their possible applications, we present here a more flexible notion of a graded fuzzy concept lattice in rough set theory. We establish initial facts about the object-oriented version of graded fuzzy concept lattice and illustrate them with some examples, of both theoretical and practical nature.
Graph-FCA is an extension of formal concept analysis for multi-relational data. In this paper, we discuss the freedom of representation offered by Graph-FCA, in particular by its support of n-ary relations, considering natural language syntax as a use case.
Formal concept analysis (FCA) has become a mature tool for extracting helpful knowledge for real problems based on solid mathematical foundations rooted in logic and lattice theory. However, in areas such as machine learning, big data, artificial intelligence, database, etc. remains a stranger. The R language is one of the main languages used in data science, and this work describes an R package called fcaR that implements FCA’s core notions and techniques. One of the main goals is to spread FCA to the rest of the world. The main facilities of the tool are shown with a running example.
Formal Concept Analysis (FCA) aims at classifying a set of objects described by Boolean attributes as a concept lattice. Among the various FCA extensions, Relational Concept Analysis (RCA) supports multiple binary relationships between several sets of objects. Using such relational data, RCA builds interconnected conceptual structures, i.e. concept lattices or AOC-posets. Analyzing data can benefit from exploring these interconnected structures by navigating from one concept to another. Navigation can be performed within the same structure through the classification links or from one concept of a conceptual structure to a concept of another one through one of the relations linking the lattices. This paper presents RCAviz 1 , an online tool which aims to support such navigation. Once the user has selected a subset of objects and attributes as a starting point for navigation, RCAviz presents the associated concept and its close neighbors. Each concept includes the objects and attributes it introduces. The user can then navigate, i.e. zoom and pan the current view, and move from one concept to another. Additional views show the previous and next conceptual structures. The history allows the user to browse its navigation.
Knowledge Graphs (KG) have become a widespread knowledge representation. When different KGs exist for some domain, it is valuable to merge them into a richer KG. This is known as the problem of KG alignement, which encompasses related problems such as entity alignement or ontology matching. Although most recent approaches rely on supervised representation learning, Formal Concept Analysis (FCA) has also been proposed as a basis for symbolic and unsupervised approaches. We here explore the application of Graph-FCA, an extension of FCA for KGs, to different scenarios of KG alignments: (A) when the two KGs have common values, and (B) when pre-aligned pairs are known. We show that, compared to previous FCA-based approaches, Graph-FCA allows for a more natural and scalable representation of the KGs to be aligned, and makes it simpler to extract alignments from the concepts. It also features flexibility w.r.t. different alignment scenarios.
In a recent paper, we presented a new pattern discovery algorithm, NextPriorityConcept, in order to take into account complex and heterogeneous data using Formal Concept Analysis. We implemented this algorithm and developed a python 3 library whose acronym GALACTIC means Ga lois La ttices, C oncept T heory, I mplicational systems and C losures. It is opened to the community using a BSD-3 license and its architecture allows the writing of plugins to take into account new datatypes. In this article we will present the architecture of our software solution, we will explain how to add new plugins to the core of our system by giving the UML diagram of each kind of plugins and we will give some examples of plugins developed within our team.
We propose a generalization of decision jungles from a binary decision directed acyclic graph to a generalized decision directed acyclic graph. We describe the classification method based on a generalized decision directed acyclic graph. Moreover, we explore the properties of our proposed method and illustrate it by example. We present our experiments on several datasets and provide the comparison of our results with related studies. The comparison of the generalized decision directed acyclic graph with the concept lattice of approval for a loan concludes our paper.
In this paper we set out to understand the cognitive basis of Formal Concept Analysis used as an Exploratory Data Analysis framework under the guise of the Landscapes of Knowledge metaphor introduced by Wille. We show that it can be re-interpreted and extended in the framework of the Theory of Affordances from Ecological Psychology to provide not only different affordances for different flavours of formal analysis of the information captured by a formal context, but also a theory that sheds light on how we learn to do it, Perceptual Learning. This raises the issue of what it is that a formal analysis of a formal context provides. We introduce the concept of formal qualia as basic, incomparable, privative items of information afforded by each possible analysis and illustrate these concepts by the formal qualia provided by Formal Concept, Independence and Equivalence Analysis.
In this paper we are interested in studying concise representations of concepts and dependencies, i.e., implications and association rules. Such representations are based on equivalence classes and their elements, i.e., minimal generators, minimum generators including keys and passkeys, proper premises, and pseudo-intents. All these sets of attributes are significant and well studied from the computational point of view, while their statistical properties remain to be studied. This is the purpose of this paper to study these singular attribute sets and in parallel to study how to evaluate the complexity of a dataset from an FCA point of view. In the paper we analyze the empirical distributions and the sizes of these particular attribute sets. In addition we propose several measures of data complexity, such as distributivity, linearity, size of concepts, size of minimum generators, for the analysis of real-world and synthetic datasets.
