RCAExplore, a FCA based Tool to Explore Relational Data

Abstract

Relational Concept Analysis (RCA) is one variant of Formal Concept Analysis for multi-relational dataset exploration. The tool RCAExplore is an implementation of the RCA process where several choices can be made before each iteration: the structure to be used (concept lattice, AOC-Poset, Iceberg lattice), the scaling quanti er (exist, forall, contains, percentage-quanti ers, etc.), and the considered formal and relational contexts. RCAExplore was developed during Fresqueau ANR 11 MONU 14 project, in order to explore relational hydroecological data, and has also been used on several datasets in di erent other domains. The source code and a standalone jar application are available online. An integration of the tool is ongoing within a platform for data exploration and knowledge representation.

Keywords

• Data exploration
• Concept Analysis
• Formal Concept Analysis
• Relational

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traits of life traits taxons taxons presence of taxons [1..19] presence of taxons [20..99]

presence of taxons [100..+∞[ physico-chemical characters lvl 1 physico-chemical characters lvl 2 stations watercourse kind physico-chemical characters watercourse characteristics

Exploring such a relational dataset allows to answer several questions, e.g. what are the links between life traits of the taxons and values of physico-chemical parameters on river stations? Answers can take several forms, such as extracting rules that involve the relations, or grouping objects from the di erent categories (like physico-chemical parameters, or taxons) depending on their attributes and on the objects of another category they are connected with.

RCA can be used for such tasks. First, the user has to build object-attribute contexts, here, life traits, taxons, stations, physico-chemical characters and watercourse characteristics. Relations between objects are then formalised into seven object-object contexts, e.g. presence of taxons1-19 goes from taxons to stations: a taxon is linked to a station, if the sample size for this taxon on this station is between 1 and 19 (see RCAExplore editor open on this relation, in Fig. 3).

The principle of RCA consists in integrating object-object relations as new attributes (called relational attributes ) in formal contexts thanks to scaling quanti ers, such as the existential (exist ) and universal strict (exist+forall ) scaling quanti ers. It produces iteratively a set of concept lattices (one lattice per object category) interconnected through relational information. The concepts in a given lattice group objects according to the shared attributes and to the connections they have with objects of another category. The result is a family of concept lattices where concepts of a lattice are linked to concepts of another lattice, as sketched out in Fig. 2: a concept Cs reveal a group of stations (1) where at least one physico-chemical value from a group of physico-chemical characteristics (concept Cp) has been measured with level 2, (2) being in a kind of watercourse from a watercourse characteristics group (concept Cw), (3) hosting more than 60% of numerous (100+) taxon types from a group (concept Ct) whose elements have at least one trait from a group of life traits (concept Cl).

The process is as follows: rst, lattices are built on the object-attribute contexts Ki; second, object-attribute contexts are extended with new attributes built using the object-object relations and the concept sets of the lattices; third, new lattices are built on the extended contexts. For instance let K = fK1; K2g, R = fRg, where K1 = (G1; M1; I1), K2 = (G2; M2; I2) and R = (G1; G2; r). Let C = (X; Y ) be a concept of the K2 lattice (i.e. X G2); 9 is the existential quanti er. A relational attribute 9r(C) is added to the K1 context, and is owned by an object g 2 G1 if r(g) \ X 6= ;. A whole construction process consists in building a nite sequence of contexts and concept lattices based on (K; R) and chosen scaling quanti ers. The last sequence is obtained when the xed point is reached. Details about RCA are given in [ 6 ]. 2

RCAExplore

RCAExplore1 is a reference implementation of RCA o ering new ways of dealing with relations. RCAExplore is developed in Java. It proposes a relational context family editor (see Fig. 3, highlighting an object-object context linking taxons and stations), an interactive concept lattice family generator (see Fig. 4), and a concept lattice family browser. The tool is developed under the LGPL license.

The novelty behind RCAExplore, with respect to other RCA tools such as Galicia2, is to provide, besides an automatic mode, a manual mode where it is possible to modify the data considered before each new iteration step of the RCA process. At each step of the process, the user can choose (Fig. 4):

1 http://dataqual.engees.unistra.fr/logiciels/rcaExplore

2 http://www.iro.umontreal.ca/ galicia/ { the conceptual structure (concept lattice, AOC-poset, Iceberg lattice), { the scaling quanti er (in f9, 98, 9 , 98 n%, 9 n%g, n = 30 and n = 60), { the considered contexts (among the available object-attribute and objectobject contexts), { if they want the simpli ed or the full intents and extents, and other options. The tool checks whether the choices made by the user are consistent. For example, a user cannot choose at step n a relational context with the target formal context K, if K has not been chosen at step n 1. Files are generated at each step, that contain all the conceptual structures of this step in a format (.svg and .dot, from Graphviz3) which is readable and exploitable by other programs, and it is possible to also see the extended contexts in LATEX and HTML. A trace le records the choices made during the process, and can be used to replay the same con guration in automatic mode, namely without again manually selecting structures, quanti ers or contexts. A visualization option also allows to see graphically, at the end of the process, the conceptual structures that have been generated at all steps.

The concept lattice family browser allows, from a given step number, a given context and a given concept name, to look at the parents, children, intent, simpli ed intent and extent of a concept. If two attributes are selected in the simpli ed intent and the intent respectively, the corresponding implication rule is displayed. 3

Application examples

As previously introduced, RCAExplore has been primarily used to explore hydroecological data in the framework of Fresqueau ANR 11 MONU 14 project. The question was to link the characteristics (traits) of taxons to the physicochemical state of a river station where they live. Data have been explored according to di erent paths: focusing on river stations and trying to characterize them both with taxon traits and physico-chemical parameters, focusing on speci c relations (e.g. presence of rare taxons in river stations) by varying and combining

3 https://www.graphviz.org/

Fig. 4. Choosing the conceptual structure and scaling operators to be used the scaling operators, etc. Rules have been computed [ 3 ], e.g. a straightforward rule4, could be (meaning that if a station hosts many of numerous taxon types that appreciate slow current, then the river has calm water): 9 ! 60% presence[100;::+1[(9traits of taxons(appreciate slow current)) 9watercourse kind(calm water)

The features of RCAExplore have been useful to support FCA and several research experiences, to mention just a few: e ect of varying the scaling quanti ers on a subset of the Fresqueau dataset is shown in [ 1 ], assessing the relevance of using AOC-posets during gradual class model refactoring has been shown in [ 7 ] on industrial UML and Java class models. In [ 2 ], the authors use RCAExplore to assess the scalability of RCA on connected product comparison matrices. RCAExplore has also been used to analyse spatio-temporal data characterizing river networks [ 8 ] and is currently used to teach FCA and RCA at Montpellier and Strasbourg Universities. It is under integration in the COGUI platform5 under the guidance of Alain Gutierrez. 4 Such straightforward rules are useful to understand and to build con dence on other, more informative, rules. 5 https://www.lirmm.fr/cogui/3/

References

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