=Paper= {{Paper |id=Vol-3308/paper11 |storemode=property |title=RCAviz: Visualizing and Exploring Relational Conceptual Structures |pdfUrl=https://ceur-ws.org/Vol-3308/Paper11.pdf |volume=Vol-3308 |authors=Emile Muller,Marianne Huchard,Pierre Martin,Pascal Poncelet,Arnaud Sallaberry |dblpUrl=https://dblp.org/rec/conf/cla/MullerH0PS22 }} ==RCAviz: Visualizing and Exploring Relational Conceptual Structures== https://ceur-ws.org/Vol-3308/Paper11.pdf 
RCAviz: Visualizing and Exploring Relational
Conceptual Structures
Emile Muller1,βˆ— , Marianne Huchard1 , Pierre Martin2 , Pascal Poncelet1 and
Arnaud Sallaberry1,3
1
  LIRMM, UniversitΓ© de Montpellier, CNRS, Montpellier, France
2
  CIRAD, UPR AIDA, F-34398 Montpellier, France; AIDA, Univ Montpellier, CIRAD, Montpellier, France
3
  AMIS, UniversitΓ© Paul-ValΓ©ry Montpellier 3, Montpellier, France


                                         Abstract
                                         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 RCAviz1 , 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.

                                         Keywords
                                         Formal Concept Analysis, Relational Concept Analysis, Visualization, Navigation, Concept Lattice




1. Introduction
Formal Concept Analysis (FCA) aims at classifying a set of objects described by Boolean
attributes as a concept lattice [1]. Other conceptual structures may also be produced, such
as AOC-poset or Iceberg lattice. FCA and its various extensions enable the extraction of
frequent patterns, attribute implications, mutual exclusions within attribute groups, and object
similarities. The survey of [2] shows the variety of applications where different knowledge
discovery methods based on FCA are successfully used [3].

1
    https://rcaviz.lirmm.fr/
Published in Pablo Cordero, Ondrej Kridlo (Eds.): The 16π‘‘β„Ž International Conference on Concept Lattices and Their
Applications, CLA 2022, Tallinn, Estonia, June 20–22, 2022, Proceedings, pp. 133–146.
βˆ—
    Corresponding author.
Envelope-Open emile.muller.contact@gmail.com (E. Muller); marianne.huchard@lirmm.fr (M. Huchard); ipierre.martin@cirad.fr
(P. Martin); pascal.poncelet@lirmm.fr (P. Poncelet); arnaud.sallaberry@lirmm.fr (A. Sallaberry)
Orcid 0000-0002-6309-7503 (M. Huchard); 0000-0002-4874-5795 (P. Martin); 0000-0002-8277-3490 (P. Poncelet);
0000-0001-7068-176X (A. Sallaberry)
                                       Β© 2022 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
    CEUR
    Workshop
    Proceedings
                  http://ceur-ws.org
                  ISSN 1613-0073
                                       CEUR Workshop Proceedings (CEUR-WS.org)
   Among the extensions of FCA, Relational Concept Analysis (RCA) supports multiple binary
relations between several sets of objects. As output, RCA builds conceptual structures (one
per object set) interconnected by relational attributes, that embed the inter-object relations
provided as input. Analyzing multi-relational datasets with RCA may benefit from exploring
these interconnected structures by navigating from one concept to another. This navigation
is therefore performed within the same conceptual 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.
   FCA and RCA present a strong interest when querying a dataset using a set of attributes.
In addition to the objects that respond to the query, they provide the classification of these
objects [4, 5, 6]. When some objects respond strictly to the query, these objects are part of the
extent of the concept, whose intent is constituted by the query attributes. The sub-concepts
of this concept then contain the objects having more attributes than those listed in the query.
Conversely, the super-concepts contain the objects having less attributes, corresponding to a
constraint release. This latter case is of particular interest to domain experts when the dataset
is likely to be incomplete, as constraint release may create hypotheses worth to be investigated.
Classification also helps to reformulate the query when the answer set is empty, as it shows the
concepts highlighting the partially answering objects.
   Several authors investigate the potential offered by the visualization for assisting exploring,
querying, and analyzing a classification produced by FCA [7, 6, 8]. For RCA, the most advanced
tools propose either a sophisticated visualization of the conceptual structure (e.g. Galicia1 ) or a
simple visualization of the conceptual structure with the ability to jump from one structure to
another through the relational links (e.g. RCAexplore2 ). These tools lack features enabling full
visualization support for gradually navigating between concepts without being overwhelmed
by the size of the structure. This paper addresses this need by introducing RCAviz3 , an online
tool which aims to support such navigation.
   Section 2 briefly introduces FCA and RCA basics, and a small RCA navigation example to
illustrate the main features expected for a navigation tool. Section 3 presents the visualization
and navigation features of RCAviz. in Section 4, we present related work on FCA and RCA
visualization and exploration. Section 5 concludes with a summary of the work and a few
perspectives.


2. RCA Navigation at a glance
This section briefly introduces FCA and RCA through an example inspired by the Knomana
project [9] which motivated the tool presented in this paper. The Knomana dataset deals with
the control of pests using plants in agriculture. We then develop the needs addressed by our
proposed tool on a small example.



1
  http://www.iro.umontreal.ca/~galicia/
2
  http://dataqual.engees.unistra.fr/logiciels/rcaExplore/
3
  http://rcaviz.lirmm.fr/
FCA in a nutshell FCA input is a formal context (FC) which includes a binary relation that
connects each object with each of the attributes it has. E.g. the FC Plant presented in Table 1
describes four plants by their family and a few characteristics like being aromatic or comestible.
FCA builds formal concepts on top of the FC and organizes these concepts as a conceptual
structure. A formal concept is a maximal group of objects (extent) sharing a maximal group of at-
tributes (intent). For instance, in Table 1, as all the plants of the group 𝐸9 = {π‘β„Žπ‘Ÿπ‘œπ‘šπ‘œπ‘™π‘Žπ‘’π‘›π‘Žπ‘‚π‘‘π‘œπ‘Ÿπ‘Žπ‘‘π‘Ž
π‘Žπ‘ π‘π‘–π‘™π‘–π‘Žπ΄π‘“ π‘Ÿπ‘–π‘π‘Žπ‘›π‘Ž, π‘Žπ‘”π‘’π‘Ÿπ‘Žπ‘‘π‘’π‘šπΆπ‘œπ‘›π‘¦π‘§π‘œπ‘–π‘‘π‘’, } share all the attributes 𝐼9 = { π‘Žπ‘ π‘‘π‘’π‘Ÿπ‘Žπ‘π‘’π‘Žπ‘’, π‘Žπ‘Ÿπ‘œπ‘šπ‘Žπ‘‘π‘–π‘, π‘‘π‘œπ‘₯𝑖𝑐,
π‘’π‘£π‘’π‘Ÿπ‘”π‘Ÿπ‘’π‘’π‘›, π‘Žπ‘π‘π‘™π‘–π‘πΈπ‘ π‘ π‘’π‘›π‘‘π‘–π‘Žπ‘™π‘‚π‘–π‘™, π‘Žπ‘π‘π‘™π‘–π‘πΈπ‘₯π‘‘π‘Ÿπ‘Žπ‘π‘‘}, 𝐢𝑃𝑙9 = (𝐸9 , 𝐼9 ) is a concept. The conceptual struc-
ture reflects group inclusion and highlights concept specialization. The top right part of Figure
1 presents an example of specialization of plant concepts. Concept 𝐢𝑃𝑙11 , which associates
𝐸11 = {π‘Žπ‘”π‘’π‘Ÿπ‘Žπ‘‘π‘’π‘šπΆπ‘œπ‘›π‘¦π‘§π‘œπ‘–π‘‘π‘’} with its common attributes 𝐼11 = 𝐼9 βˆͺ {π‘Žπ‘›π‘‘π‘–π‘‘π‘¦π‘ π‘’π‘›π‘‘π‘’π‘Ÿπ‘–π‘} is a subconcept
of 𝐢𝑃𝑙9 , with 𝐼11 βŠ‡ 𝐼9 and 𝐸11 βŠ† 𝐸9 . This figure also presents relational attributes, specific to
RCA (i.e. initiated using the quantifier βˆƒ), which are explained here after.

RCA in a nutshell RCA extends FCA to datasets that conform to the entity-relationship
model [10]. The top left part of Figure 1 shows such a model presented using the UML syntax: A
plant treats (controls) a pest; A pest is found in a country; A country possesses plants. As input,
RCA takes a set of FCs and a set of relational contexts (RC) connecting objects of two FCs. FCs
correspond to the classes of the UML model (i.e. π‘ƒπ‘™π‘Žπ‘›π‘‘, 𝑃𝑒𝑠𝑑, πΆπ‘œπ‘’π‘›π‘‘π‘Ÿπ‘¦), while RCs correspond to
the associations (i.e. π‘‘π‘Ÿπ‘’π‘Žπ‘‘π‘ , 𝑖𝑠𝐹 π‘œπ‘’π‘›π‘‘πΌ 𝑛, π‘π‘œπ‘ π‘ π‘’π‘ π‘ π‘’π‘ ). Each FC is computed as a conceptual structure,
which has incorporated iteratively the object clustering of the other FCs thanks to the relational
attributes. Object clustering propagation applies when a RC (denoted by π‘Ÿ) connects objects of a
source FC (denoted by 𝐹 𝐢𝑠 ) to objects of a target FC (denoted by 𝐹 𝐢𝑑 ). E.g. The RC π‘Ÿ = π‘‘π‘Ÿπ‘’π‘Žπ‘‘π‘ 
connects objects of FC 𝐹 𝐢𝑠 = π‘ƒπ‘™π‘Žπ‘›π‘‘ to objects of FC 𝐹 𝐢𝑑 = 𝑃𝑒𝑠𝑑. Once a concept 𝐢𝑑 is built in 𝐹 𝐢𝑑 ,
some objects in 𝐹 𝐢𝑠 may be connected to objects of 𝐢𝑑 using π‘Ÿ. Different schemes of connection
can be adopted, e.g. the connection of an object π‘œπ‘  of 𝐹 𝐢𝑠 by π‘Ÿ to π‘Žπ‘‘ π‘™π‘’π‘Žπ‘ π‘‘ π‘œπ‘›π‘’ object of 𝐢𝑑 , the
connection of π‘œπ‘  to π‘Žπ‘™π‘™ objects of 𝐢𝑑 , or half of π‘œπ‘  connections by π‘Ÿ are with some objects of 𝐢𝑑 . For
example in Figure 1, the concept 𝐢𝑃𝑒13 groups π‘Žπ‘ π‘π‘’π‘Ÿπ‘”π‘–π‘™π‘™π‘’π‘ π‘‚π‘β„Žπ‘Ÿπ‘Žπ‘π‘’π‘’π‘  and π‘Žπ‘ π‘π‘’π‘Ÿπ‘”π‘–π‘™π‘™π‘’π‘ π‘ƒπ‘Žπ‘Ÿπ‘Žπ‘ π‘–π‘‘π‘–π‘π‘’π‘ ,
two pests that attack peanuts. In addition, π‘Žπ‘ π‘π‘–π‘™π‘–π‘Žπ΄π‘“ π‘Ÿπ‘–π‘π‘Žπ‘›π‘Ž and π‘β„Žπ‘Ÿπ‘œπ‘šπ‘œπ‘™π‘Žπ‘’π‘›π‘Žπ‘‚π‘‘π‘œπ‘Ÿπ‘Žπ‘‘π‘Ž control
respectively π‘Žπ‘ π‘π‘’π‘Ÿπ‘”π‘–π‘™π‘™π‘’π‘ π‘ƒπ‘Žπ‘Ÿπ‘Žπ‘ π‘–π‘‘π‘–π‘π‘’π‘  and π‘Žπ‘ π‘π‘’π‘Ÿπ‘”π‘–π‘™π‘™π‘’π‘ π‘‚π‘β„Žπ‘Ÿπ‘Žπ‘π‘’π‘’π‘ . Thus both plants control at least
one pest of 𝐢𝑃𝑒13. The selection of the scheme is captured in the relational attributes that
include a quantifier (e.g. βˆƒ, βŠ‡, βˆ€β‰₯50% ), the relation π‘Ÿ and the target concept 𝐢𝑑 . The use of the
quantifier βˆƒ in Figure 1 conducts to express the relational attribute β€œtreats at least one pest
of 𝐢𝑃𝑒13” as follow: βˆƒπ‘‘π‘Ÿπ‘’π‘Žπ‘‘π‘ (𝐢𝑃𝑒13). Relational attributes are added to the description of the
objects to respect FCA principle. E.g. π‘Žπ‘ π‘π‘–π‘™π‘–π‘Žπ΄π‘“ π‘Ÿπ‘–π‘π‘Žπ‘›π‘Ž and π‘β„Žπ‘Ÿπ‘œπ‘šπ‘œπ‘™π‘Žπ‘’π‘›π‘Žπ‘‚π‘‘π‘œπ‘Ÿπ‘Žπ‘‘π‘Ž both receive
βˆƒπ‘‘π‘Ÿπ‘’π‘Žπ‘‘π‘ (𝐢𝑃𝑒13) as an attribute. During the conceptual structure computation, existing concepts
may be enriched by these relational attributes or new concepts may be built to group objects that
share some of them. In our example 𝐢𝑃𝑙21 is built to factorize βˆƒπ‘‘π‘Ÿπ‘’π‘Žπ‘‘π‘ (𝐢𝑃𝑒13). The propagation
thus follows the paths and cycles of the entity-relationship model until a fix-point is reached.
RCA algorithm and theoretical details can be found in [10].
Table 1
Example of relational dataset made of the Formal Contexts (FC) plants (FC Plant), pests (FC Pest)
and countries (FC Country). Plants are described by their family and a few characteristics. Pests are
described by their family and entities they attack. Countries are described by their place in a continent.
Relational Contexts (RC) connect objects of two FCs. RC treats connects FC Plant and FC Pest. RC
isFoundIn indicates in which country is found a pest. RC possesses indicates which country possesses a
plant.
            FC Plant            lauraceae     asteraceae      aromatic       comestible     toxic       evergreen   contraceptive    antidysenteric   applicOil   applicEssentialOil   applicExtract
    cinnamomumZeylanicum            x                            x               x                          x                                            x
      chromolaenaOdorata                            x            x                            x             x                                                             x                 x
         aspiliaAfricana                            x            x                            x             x                x                                            x                 x
      ageratumConyzoides                            x            x                            x             x                              x                              x                 x
                              Pest                attacksPeanuts      attacksCheese         attacksRice        aspergillus          Country      australAfrica westernAfrica
                        aspergillusFlavus                                   x                                      x                Namibia            x
                     aspergillusParasiticus             x                                                          x            SouthernAfrica         x
                     aspergillusOchraceus               x                                                          x                 Nigeria                         x
                       aspergillusTamarii                                        x                  x              x                  Benin                          x
                                       RC treats                  aspergillusFlavus         aspergillusParasiticus           aspergillusOchraceus aspergillusTamarii
                               cinnamomumZeylanicum                       x                                                                                 x
                                 chromolaenaOdorata                                                                                    x
                                    aspiliaAfricana                                                        x
                                 ageratumConyzoides                          x
         RC isFoundIn        Namibia   SouthernAfrica       Nigeria   Benin           RC possesses       cinnamomumZeylanicum         chromolaenaOdorata    aspiliaAfricana   ageratumConyzoides
       aspergillusFlavus       x                                                        Namibia
    aspergillusParasiticus                                               x           SouthernAfrica
    aspergillusOchraceus                                      x                         Nigeria                                                                    x
      aspergillusTamarii                      x                                          Benin                                                 x




Navigating within linked conceptual structures The above example is used to reveal the
gradual navigation needs of the RCA outputs4 . Let us suppose the user wants information about
the pests that attack peanuts. Pest Concept 𝐢𝑃𝑒13 introduces π‘Žπ‘‘π‘‘π‘Žπ‘π‘˜π‘ƒπ‘’π‘Žπ‘›π‘’π‘‘π‘  and is therefore
the natural entry point. Pests of 𝐢𝑃𝑒13 extent are Aspergillus ochraceus and Aspergillus
parasiticus. To know the localization of these pests, the user needs to follow the relational
attribute βˆƒπ‘–π‘ πΉ π‘œπ‘’π‘›π‘‘πΌ 𝑛(𝐢𝐢20). This attribute leads to Country concept 𝐢𝐢20 which groups
Western Africa countries, i.e. Benin and Nigeria. In 𝐢𝐢20, the relational attributes containing
π‘π‘œπ‘ π‘ π‘’π‘ π‘ π‘’π‘  point to plant concepts. Going towards the Plant concept 𝐢𝑃𝑙21 indicates that 𝐢𝐢20
countries host Aspilia africana or Chromolaena odorata. 𝐢𝑃𝑙21 comports the relational attribute
βˆƒπ‘‘π‘Ÿπ‘’π‘Žπ‘‘π‘ (𝐢𝑃𝑒13), meaning that its plants treat at least one of the Aspergillus pest species that
attack peanuts. It can be interpreted that way: Aspergillus species that attack peanuts are
observed in Western Africa countries and are treated by plants that can be found in the countries
of this region. It can be interesting here, for the user, to go back by choosing Concept 𝐢𝐢20
to look at relational attributes βˆƒπ‘π‘œπ‘ π‘ π‘’π‘ π‘ π‘’π‘ πΆπ‘ƒπ‘™6 or βˆƒπ‘π‘œπ‘ π‘ π‘’π‘ π‘ π‘’π‘ πΆπ‘ƒπ‘™9. Choosing βˆƒπ‘π‘œπ‘ π‘ π‘’π‘ π‘ π‘’π‘ πΆπ‘ƒπ‘™9 and
going to 𝐢𝑃𝑙9, the user can see that these Western Africa countries possess plants that have
characteristics that are close to the plants treating Aspergillus species attacking peanuts. This
is the case of Ageratum conizoΓ―des which is analyzed by going to sub-concept 𝐢𝑃𝑙11. This
plant is toxic and has an antidysenteric effect, it may have antibacterial properties. These
characteristics may suggest that common chemical compounds could be shared between these
3 plant species. This navigation therefore brings a research hypothesis that domain experts
may study through new experimental research: can Ageratum conizoΓ―des be used to control
Aspergillus species (i.e. Aspergillus ochraceus and Aspergillus parasiticus) attacking peanuts?

4
    A navigation for this example using RCAviz is presented at https://rcaviz.lirmm.fr/documentation.html#examples.
    A video on YouTube is also proposed.
                                                                                    CPl6
                                                                                  aromatic
           treats                isFoundIn
   Plant                  Pest                Country                            evergreen
                                                                              βˆƒtreats(CPe12)

                         possesses
                                                                                              CPl9
                                                                    CPl22
                                                                                           asteraceae
                                                               βˆƒtreats(CPe15)
                                                                                              toxic
                                                                                        applicEssentialOil
                                                                                          applicExtract
                                                   CPl7
                                                lauraceae                CPl11
                                               comestible            antidysenteric                      CPl21
                                                 applicOil        ageratumConyzoides                βˆƒtreats(CPe13)
                                             βˆƒtreats(CPe16)
                                        cinnamomumZeylanicum                          CPl10
                      CC17                                                        contraceptive                     CPl25
                                                                                 βˆƒtreats(CPe27)                βˆƒtreats(CPe24)
                                                                                 aspiliaAfricana             chomolaenaOdorata
                                    CC20
                                westernAfrica
      CC18                    βˆƒpossesses(CPl6)                  CPl8
                              βˆƒpossesses(CPl9)             βˆƒtreats(CPe14)                CPe12
   australAfrica
                              βˆƒpossesses(CPl21)                                        aspergillus
     Namibia
                                                                                   βˆƒisFoundIn(CC17)
  SouthernAfrica

                             CC23                   CC26                  CPe15                         CPe13
                       βˆƒpossesses(CPl10)      βˆƒpossesses(CPl25)       attacksCheese                 attacksPeanuts
                            Nigeria                 Benin           βˆƒisFoundIn(CC18)               βˆƒisFoundIn(CC20)
                                                                    aspergillusFlavus


                          CC19                                           CPe16                  CPe24                       CPe27
                    βˆƒpossesses(CPl7)                                  attacksRice         βˆƒisFoundIn(CC23)            βˆƒisFoundIn(CC26)
                    βˆƒpossesses(CPl8)                               aspergillusTamarii    aspergillusOchraceus        aspergillusParasiticus
                    βˆƒpossesses(CPl11)
                    βˆƒpossesses(CPl22)
                                                                                                  CPe14
                                                                                             βˆƒisFoundIn(CC19)

Figure 1: UML model (top left). Classification with RCA of plants (top right), pests (bottom right) and
countries (bottom left) of Table 1.


If the answer is true, this then would mean that farmers in Western Africa have an additional
local plant that can be used for controlling Aspergillus ochraceus and Aspergillus parasiticus.
   This brief navigation example illustrates the main needs of a user: (i) selecting an attribute
(or an object) to initiate the navigation, (ii) visualizing the neighborhood of a concept to be
able to choose the next step and do not end with an empty solution, (iii) moving from one
concept to a sub-concept (or a super-concept) in the same conceptual structure, (iv) jumping to
a neighboring conceptual structure using a relational attribute, and (v) backtracking easily.


3. Visualization
In the previous section, we presented the extracted data structure using an RCA classification.
As can be seen in Figure 1, this structure can be modeled as a set of Directed Acyclic Graphs
(DAG), each DAG corresponding to a context (here, one DAG for plants, one for pests and one
for countries). There is an extensive literature on the visualization of DAG (see [11] for an
introduction). Most articles present algorithms for positioning vertices and drawing edges to
limit the number of edge crossings. This type of approach is particularly interesting for small
datasets, like the one presented in Figure 1. However, when datasets have hundreds of vertices,
visualizing the entire structure induces visual cluttering issues. Moreover, in our context, it can
be useful to be able to switch from one DAG to another interactively via the relational attributes.
This is why we opted for a local visualization system with a step-by-step navigation.

Requirement analysis Generally, visualization design is done by iterating a process con-
sisting of (1) defining needs and suitable data structures, (2) proposing visual encodings and
interactive features meeting these needs, (3) providing the results to the users so that they
can refine their needs, etc. (see for instance [12, 13]). In our case, we designed RCAviz by
organizing regular meetings with the three visualization experts in charge of providing the
visual platform, an RCA expert and a dataset expert. Here is the final list of the needs identified
during these meetings: [R1] Selection of a concept. A step-by-step navigation requires a
starting point. Our tool must therefore initially allow the selection of a concept, depending on
the objects and attributes of interest for the user. [R2] Visualization of a concept and its
neighbors. The user must be able to see a concept (with its objects and attributes) as well as its
neighbors, i.e. the lower and higher level concepts in the DAG and the neighboring concepts in
the other DAGs. [R3] Navigation step-by-step. The user must be able to explore neighboring
concepts of the displayed concept (whether they belong to the same DAG or to another one).
[R4] History. The users must be able to keep a history of their navigation, i.e. the list of the
previously explored concepts. They must also be able to navigate through this history and to
save a state to be able to resume their exploration later.
   RCAviz is designed to meet these requirements. The visualization consists of an initial view
allowing to select the starting concept, the Concept Selector, and two coordinated views: (1) the
Explorer allows to navigate step-by-step and (2) the History allows to visualize the navigation
history.

Concept Selector The Concept Selector is the first view displayed when one launches RCAviz.
It is designed to meet the requirement [R1]. It first allows to upload a data file. Once the file is
uploaded, the user can choose a context, i.e. one of the DAGs of the dataset. Then appears the
list of objects, the list of attributes and the list of concepts, as shown in Figure 2. The user can
select one or more objects and one or more attributes. The selection of these elements updates
the other lists according to the logical operators used, and in particular updates the list of the
corresponding concepts on the right. One can for example display the concepts containing
(object A and object B) and (attribute C or attribute D). When the list of objects and attributes
is long, a search field allows the user to easily find the elements. The user also can select or
deselect all the elements of each list. The list of selected items is displayed when hovering
over Selected. When an object or an attribute is selected, the corresponding introducer concept
number on the right panel appears in bold face. Once the user has found an interesting concept,
they can select it from the list on the right and launch the Explorer and the History. It may seem
critical to select a concept according to its index number and the selected associated objects
and attributes. Thus, in a future work, we plan to show additional information on the listed
concepts, such as their introduced objects and introduced attributes, or their whole extent and
intent.




Figure 2: The Concept Selector. The user can select Objects and Attributes of interest. Then, the list
of the available Concepts is updated on the right, and the user can select one of them to launch the
Explorer and the History. Concept 20 is in bold face as it introduces the selected attribute westernAfrica.



Explorer Figure 3 shows the History (top panel) and the Explorer (bottom). The Explorer
consists of three sub-views. The central panel displays the selected concept in the center and its
neighborhood above (children in the DAG) and below (parents in the DAG) [R2]. Each concept
is represented as a colored rectangle composed of stacked boxes. The id is shown at the left
corner of the top box. The introduced objects are presented in the box entitled β€œObjects”. Simple
(i.e. non relational) introduced attributes appear in another box. The introduced relational
attributes, when they exist, appear in the box at the bottom of the concept. When there are
several relational attributes with the same relation, they are grouped by relation. In addition,
when there are many relational attributes with the same relation, only their number is shown
in order to save space, and thus they are not clickable.
    For example, the concept 20 in the country DAG in Figure 3 has links to the concepts 6, 9,
and 21 in the plant DAG and 13 in the pest DAG. The user can navigate step-by-step by clicking
on the concepts [R3]. For example, if they click on the concept 23, it is positioned in the middle
of the view and its parents and children are displayed below and above. ⊀, for the top (resp. βŠ₯
for the bottom) at the top right of a concept means that it has no parents (resp. no children).
To facilitate the navigation, an opposite link, e.g. β€œisFoundIn-opposite”, is provided for each
relational attribute. These opposite links do not correspond to a isFoundIn-opposite formal
context which would be the reverse of isFoundIn . In a future work, additional information on
each concept (intent, extent, etc.) will be provided to make the navigation easier.
   Each DAG is represented by a color. We use a categorical color scale adapted to the repre-
sentation of nominal variables [14]. In our example, the country DAG is shown in blue, the
plant DAG in red, and the pest DAG in green. When the user hovers over a link, the concept in
the corresponding DAG is displayed on the right panel. In Figure 3, the mouse is positioned
on the red link 21, the corresponding concept is displayed with its neighborhood on the right
panel. When the user clicks on the link, the left DAG is positioned in the central panel [R3]
and that of the central panel is positioned in the right panel. We thus keep track of the previous
exploration step [R4].
   The concepts that have already been explored appear with lower brightness than the other
concepts [R4]. In Figure 3, we can see that all the concepts have already been explored except
one of the red DAG at the bottom left.
   Finally, it is common to have a high number of parents or children. Showing all of them
induces visualization and navigation issues. Therefore, if the number exceeds 5, we display
a single ”super-concept”. When the user clicks on it, a pop-up displays a view similar to the
Concept Selector. The user can then select one or more concepts which, after validation, are
displayed in the central panel. In this release, we choose a top to bottom representation of the
specialization relation as this is the common representation of partial orders by Hasse diagrams.
Alternatively, we may explore a left to right representation, where a concept will be on the left
of its sub-concepts, to show more sibling concepts as they will be vertically organized.

History We have seen that a part of the path leading to the concept displayed is available in
the left panel of the Explorer. The brightness of the concepts also makes it possible to know
if a concept has already been explored. However, these functionalities do not fully meet the
requirement [R4]. We therefore complete them with a view entirely dedicated to [R4]: the
History. As shown in Figure 3, the history consists of two parts: a colored line at the top and a
list of concepts below.
   The colored line is made up of segments, each segment representing an explored concept.
The color represents the DAG of the concept. The length of the line adapts to the width of
the visualization so that all the concepts explored are visible. Therefore, the more concepts
the user has explored, the smaller the segments representing those concepts are. The user
can see if the current concept of the Explorer has already been explored with a small triangle
placed above each segment representing this concept. For example, in Figure 3, we see two
triangles, one on the last segment representing the concept displayed in the Explorer and one
on a previous segment: this means that the current concept has already been explored once
during the navigation.
   The list of concepts explored with their id is displayed under the colored line. This list can be
long, a horizontal slider is therefore activated when the available space is not enough to display
all of them in the view. The concepts are represented by colored rectangles according to the
DAG they belong to. An arrow connects two concepts if the user has moved from one to the
other by navigating step-by-step. If the user clicks, in the History, on a previously explored
concept, it is displayed in the Explorer and a vertical bar is used in the History to show that
the sequence was not produced by a navigation step-by-step. When the user hovers over a
concept, a small red cross appears at the corner. It can be used to remove this concept from the
History. As selecting a concept only according to its id may be tricky, additional information
(e.g. intent/extent) will be presented in a future release.
   Finally, the user can save the state of their navigation as well as the history by clicking on the
save button in the top bar. They can then load the file thus produced to resume their exploration.

Implementation RCAviz is a web platform developed in HTML, CSS and JavaScript. The
panels and the visualizations are made using the D3.js5 [15] library. Saving the history file
is made possible with the FileSaver6 library. The tool is available online7 . An extensive
documentation containing sample datasets is available to allow anyone to use the tool with the
samples or with their own datasets.


4. Related Work
Visualizing and exploring in FCA tools There have been a lot of proposals to visualize
and explore the conceptual structures. For space reasons, we only mention some of them to
highlight the main followed directions. Some proposals visualize the structure itself such as
Conexp [16], Latviz [17], Carve (based on a decomposition tree) and DAnCe (with concept
enumeration guided by the user) [18], and the approach by expandable and collapsible concept
trees [19]. Additional views can be provided, like in RV-xplorer [20], with pie-charts showing
local view on a concept, its content and its neighboring, and statistics on the next levels to
guide the user. Other approaches do not disclose the DAG structure, such as CREDO [21] or
SearchSleuth [22] for web queries which show links and terms that can be clicked to navigate on
the underlying lattice, e.g. for specializing or generalizing the query; SORTeD [18] where terms
can be added or removed; SPARKLIS [23] for RDF data which uses lists of urls, types, operators;
or ConceptCloud [8] which represents a focus concept by a tag cloud showing objects and
attributes (with size and colors for highlighting importance and categories) and tag selection to
change the focus concept. Some approaches use objects representations other than terms, such
as photos [24] or movie posters [25]. As presented in this paper, RCAviz shows the structure,
enables selecting a focus concept from initial objects or attributes, enables going step-by-step
towards sub-concepts and super-concepts, and backtracks to a previous step.




5
  https://d3js.org/
6
  https://github.com/eligrey/FileSaver.js/
7
  https://rcaviz.lirmm.fr/
Visualizing in RCA tools Only four tools implement RCA: Galicia, eRCA8 improved in
Galatea9 , RCAexplore, and a Cogui10 plugin. This last plugin was also converted as a Java
library named FCA4J11 . RCAexplore and Cogui have the largest functional features regarding
the number of input/output and accepted quantifiers. Regarding the visualization, Galicia
provides an advanced lattice representation (tridimensional, graph layout built with a force
algorithm) but no specific operators to navigate within a structure or from one structure to
another. RCAexplore provides a visualization tool relevant for navigating small-size structures.
Compared to Galicia, eRCA/Galatea, and Cogui, RCAexplore provides a browser enabling the
navigation between concepts textually described (no visualization), shows the whole structure
but does not enable zooming. Concepts and relational attributes are clickable to go from one
structure to a neighboring structure, but selecting a focus concept and going step-by-step using
local views is not proposed. Finaly eRCA/Galatea, RCAexplore, and Cogui produce outputs
in the dot file format, which can be visualized or transformed using Graphviz12 . In RCAviz,
several visualization panels show local views, and allow the user to know which neighboring
structure has been previously accessed or can be accessed through relational attributes. The
step-by-step navigation is done by clicking on the relational attributes. The colors help to
distinguish the different sets of objects. Table 2 synthesizes the main features of RCA tools
regarding our requirements.

Table 2
Comparison with other RCA tools on the visualization requirements.
                             R1                      R2                        R3                    R4
                      Initial concept          Local visu with          Step-by-step nav.          History
                     selection by O/A      only concept neighbors   among concepts with clicking
       Galicia
    eRCA/Galatea
     RCAexplore                              Textual descr. only      In concept browser and
                                             (concept browser)         Along relational attr.
                                                                           in global visu.
       RCAviz                x                       x                            x                  x




5. Conclusion
This paper presents RCAviz, a web platform devoted to visualize and navigate within relational
conceptual structures computed using RCA. First uses showed the relevance of the features
adopted to navigate within and between conceptual structures. These uses also enabled to
identify a need for additional features to be integrated, e.g. specifying the path length to be
shown, presenting the complete conceptual structures when they are small, local computation
as in [26], visualizing the ER model, showing a larger concept neighborhood, or expressing

8
 https://code.google.com/archive/p/erca/
9
 https://github.com/jrfaller/galatea
10
   http://www.lirmm.fr/cogui/
11
   https://www.lirmm.fr/fca4j/
12
   https://graphviz.org/
complex queries to initiate the exploration. Additional testings will be conducted to consolidate
the reliability of the software.
   This release is a first step in the building of a general platform to support exploratory search in
relational datasets. To this end, future development will also focus on considering implications
visualization. Large user experiments will be carried out in the context of the Knomana project.


Acknowledgments
The authors wish to thank the anonymous reviewers for their valuable comments that helped
improving the paper. They also warmly thank Alain Gutierrez for his strong support during
this work and for enabling FCA4J to generate output files with the JSON data format as required
by RCAviz. This work was supported by the French National Research Agency under the
Investments for the Future Program, referred as ANR-16-CONV-0004.


References
 [1] B. Ganter, R. Wille, Formal Concept Analysis: Mathematical Foundations, Springer, 1999.
 [2] J. Poelmans, D. I. Ignatov, S. O. Kuznetsov, G. Dedene, Formal concept analysis in knowledge
     processing: A survey on applications, Expert Syst. Appl. 40 (2013) 6538–6560.
 [3] J. Poelmans, S. O. Kuznetsov, D. I. Ignatov, G. Dedene, Formal concept analysis in knowledge
     processing: A survey on models and techniques, Expert Syst. Appl. 40 (2013) 6601–6623.
 [4] N. Messai, M. Devignes, A. Napoli, M. SmaΓ―l-Tabbone, Querying a bioinformatic data
     sources registry with concept lattices, in: ICCS, volume 3596 of Lecture Notes in Computer
     Science, Springer, 2005, pp. 323–336.
 [5] Z. Azmeh, M. Huchard, A. Napoli, M. Rouane-Hacène, P. Valtchev, Querying Relational
     Concept Lattices, in: CLA’11, 2011, pp. 377–392.
 [6] S. FerrΓ©, Reconciling Expressivity and Usability in Information Access, Habilitation Γ 
     diriger des recherches, UniversitΓ© de Rennes 1, 2014. URL: https://hal.inria.fr/tel-01100292.
 [7] C. Carpineto, G. Romano, Concept data analysis - theory and appl., Wiley, 2005.
 [8] G. J. Greene, M. Esterhuizen, B. Fischer, Visualizing and exploring software version control
     repositories using interactive tag clouds over formal concept lattices, Information and
     Software Technology 87 (????).
 [9] P. Silvie, P. Martin, P. Marnotte, M. Huchard, Projet Knomana. KNOwledge MANAgement
     on pesticidal plants in Africa for a safer food and a better environmental health. Rapport
     d’extractions, Technical Report, MΓ©taprog. Glofoods INRA-CIRAD, 2019.
[10] M. R. Hacene, M. Huchard, A. Napoli, P. Valtchev, Relational concept analysis: mining
     concept lattices from multi-relational data, Ann. Math. Artif. Intell. 67 (2013) 81–108.
[11] P. Healy, N. S. Nikolov, Hierarchical drawing algorithms, in: R. Tamassia (Ed.), Handbook
     on Graph Drawing and Visualization, Chapman and Hall/CRC, 2013, pp. 409–453.
[12] T. Munzner, A nested process model for visualization design and validation, IEEE Trans-
     actions on Visualization and Computer Graphics 15 (2009) 921–928.
[13] M. Sedlmair, M. D. Meyer, T. Munzner, Design study methodology: Reflections from the
     trenches and the stacks, IEEE Transactions on Visualization and Computer Graphics 18
     (2012) 2431–2440.
[14] T. Munzner, Visualization Analysis and Design, A.K. Peters visualization series, A K Peters,
     2014.
[15] M. Bostock, V. Ogievetsky, J. Heer, D3 data-driven documents, IEEE Transactions on
     Visualization and Computer Graphics 17 (2011) 2301–2309.
[16] S. A. Yevtushenko, Conexp, 2018. URL: http://conexp.sourceforge.net/.
[17] M. Alam, T. N. N. Le, A. Napoli, Latviz: A new practical tool for performing interactive
     exploration over concept lattices, in: CLA’16, 2016, pp. 9–20.
[18] T. Pattison, Interactive visualization of formal concept lattices, in: ED/GViP@Diagrams,
     volume 1244 of CEUR Workshop Proceedings, CEUR-WS.org, 2014, pp. 78–89.
[19] S. Andrews, L. Hirsch, A tool for creating and visualising formal concept trees, in:
     CSTIW@ICCS, volume 1637 of CEUR Workshop Proceedings, 2016, pp. 1–9.
[20] M. Alam, M. Osmuk, A. Napoli, RV-Xplorer: A Way to Navigate Lattice-Based Views over
     RDF Graphs, in: CLA’15, 2015, pp. 23–34.
[21] C. Carpineto, G. Romano, Exploiting the Potential of Concept Lattices for Information
     Retrieval with CREDO, J. UCS 10 (2004) 985–1013.
[22] J. Ducrou, P. Eklund, SearchSleuth: The conceptual neighbourhood of an Web query, in:
     CLA’07, ????, p. 14.
[23] S. FerrΓ©, Sparklis: An expressive query builder for SPARQL endpoints with guidance in
     natural language, Semantic Web 8 (2017) 405–418.
[24] S. FerrΓ©, CAMELIS: Organizing and Browsing a Personal Photo Collection with a Logical
     Information System, in: CLA’07, Montpellier, France, 2007, pp. 112–123.
[25] M. Crampes, M. PlantiΓ©, Visualizing and Interacting with Concept Hierarchies, in: Proc.
     of WIMS14, ACM, 2014.
[26] A. Bazin, J. Carbonnel, M. Huchard, G. Kahn, P. Keip, A. Ouzerdine, On-demand relational
     concept analysis, in: ICFCA 2019, volume 11511 of LNCS, Springer, 2019, pp. 155–172.
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Figure 3: The History. The top panel shows the History containing the list of the previous explored
concepts. The Explorer. On the center panel, the view shows a concept and its neighborhood. The
user can navigate through the concepts by clicking on them. The left panel shows the previous DAG
displayed. When the user hovers over a link of another DAG, the last is displayed on the right panel.