Minimal implications base for social network analysis

Abstract

Purpose Currently, social network (SN) analysis is focused on the discovery of activity and social relationship patterns. Usually, these relationships are not easily and completely observed. Therefore, it is relevant to discover substructures and potential behavior patterns in SN. Recently, formal concept analysis (FCA) has been applied for this purpose. FCA is a concept analysis theory that identifies concept structures within a data set. The representation of SN patterns through implication rules based on FCA enables the identification of relevant substructures that cannot be easily identified. The authors’ approach considers a minimum and irreducible set of implication rules (stem base) to represent the complete set of data (activity in the network). Applying this to an SN is of interest because it can represent all the relationships using a reduced form. So, the purpose of this paper is to represent social networks through the steam base. Design/methodology/approach The authors’ approach permits to analyze two-mode networks by transforming access activities of SN into a formal context. From this context, it can be extracted to a minimal set of implications applying the NextClosure algorithm, which is based on the closed sets theory that provides to extract a complete, minimal and non-redundant set of implications. Based on the minimal set, the authors analyzed the relationships between premises and their respective conclusions to find basic user behaviors. Findings The experiments pointed out that implications, represented as a complex network, enable the identification and visualization of minimal substructures, which could not be found in two-mode network representation. The results also indicated that relations among premises and conclusions represent navigation behavior of SN functionalities. This approach enables to analyze the following behaviors: conservative, transitive, main functionalities and access time. The results also demonstrated that the relations between premises and conclusions represented the navigation behavior based on the functionalities of SN. The authors applied their approach for an SN for a relationship to explore the minimal access patterns of navigation. Originality/value The authors present an FCA-based approach to obtain the minimal set of implications capable of representing the minimum structure of the users’ behavior in an SN. The paper defines and analyzes three types of rules that form the sets of implications. These types of rules define substructures of the network, the capacity of generation users’ behaviors, transitive behavior and conservative capacity when the temporal aspect is considered.

Exploring Different Paradigms to Extract Proper Implications From High Dimensional Formal Contexts

“…As mentioned in [16], the Impec -most popular algorithm to extract proper implications sets -was proposed in order to extract all proper implications from a formal context, but it does not perform well for larger datasets. A similar algorithm was proposed by [18], named PropIm, which is based on the Impec algorithm, but only identifies proper implications with support greater than zero, meaning all the implications found have at least one occurrence in the dataset. The algorithm was used to identify the relationships between professional skills of LinkedIn user profiles through proper implications.…”

“…Implications from this set are useful because they provide a minimum data representation -especially for applications that require a minimum set of attributes to reach a specific conclusion. In [18], the authors used the proper implications set to identify relationships between professional skills of LinkedIn users. From the set of proper implications, the authors identified the minimum set of skills (premise) required for a certain professional competence (conclusion).…”

“…Another example of algorithm that generates a set of proper implications from a set of attributes M is the PropIm algorithm [18], which differs from the Impec mainly by only generating implications with a support value greater than 0. Although implications with support equal to 0 are valid implications, most of the time, analysts are more interested in implications with support greater than 0, as those indicate characteristics explicitly represented by the data.…”

“…In this article, we propose a solution to efficiently extract proper implications on highdimensional formal contexts. Considering a high dimensional context, with a large number of objects (up to 100,000), in which the main goal is to find proper implications with support greater than 0, and given a subset of desirable conclusions to describe a specific domain, we propose two algorithms based on the original proposal of [18]: I) the first algorithm, ImplicP, contains a heuristic to avoid the generation of unnecessary premise sets, evaluated based on the notion of monotonic constraints; II) the second algorithm, named PImplicPBDD, includes a Binary Decision Diagram (BDD) structure to represent and manipulate the formal context efficiently, and a parallel computing model to process several conclusions simultaneously. The modifications and approaches presented in this article were more efficient, when compared to the solutions present in the literature, for the following reasons: a) In applications where the user desires a set of proper implications with only a subset of the attributes as viable conclusions, it is not necessary to generate all the implications, for all the attributes, in order to extract the desired conclusions; b) it also becomes unnecessary to generate and evaluate all sets of premises; c) the use of BDDs to represent and manipulate data from the formal context is useful for efficiently handling high-dimensional datasets.…”

“…Using our proposed modified algorithms, we were able to manipulate a high dimensional dataset (e.g., 100,000 objects and 23 attributes), which no one of the algorithms found in the literature was able to process. In our experiments, we used both synthetic and real-world datasets (LinkedIn dataset used in [18]), varying the number of attributes and context density, and compared the time taken by our approaches and the ImplicP and PImplicPBDD algorithms.…”