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.
