# Exploring Variability of Visual Accessibility Options in Operating Systems
## 4 Data Mining Method
### RCA Basics  
Relational Concept Analysis (RCA) has been designed to deal with multi-relational datasets [21]. In the present study, the different relations represent either the systems, or the different implementations of the mechanisms in the systems, or they connect the systems to their mechanism implementation. RCA input, i.e., a relational context family (RCF), is formally a pair (K,R) with: \(\text{K}=\{K_{i}\}_{i=1,\ldots,n}\) a set of formal contexts \(K_{i}=(O_{i},A_{i},I_{i})\) and a set of relational contexts \(\text{R}=\{r_{j}\}_{j=1,\ldots,p}\), \(r_{j}\subseteq O_{k}\times O_{l}\) for \(k,l\in\{1,\ldots,n\}\). RCA groups objects (e.g., operating systems), not only by their intrinsic attributes, but also by the relations they share to other objects or object groups (concepts). This is highlighted through relational attributes. From a relation \(r_{j}\subseteq O_{k}\times O_{l}\), relational attributes for \(K_{k}\) are built using relations between objects of \(O_{k}\) and concepts built upon objects of \(O_{l}\). A relational attribute is similar to a formula in Description Logics. It is composed of a quantifier (e.g., \(\exists\), \(\exists\forall\)), a relation (e.g., \(os2 Contrast\)), and a concept (e.g., \(Concept\_Contrast\_3\)) [34]. For example, using _Relational Context os2 Contrast_ from Table 5 and _contrast concept lattice_ from Figure 7 (right): The relational attribute \(\exists os2 Contrast(Concept\_Contrast\_3)\) is associated with \(SOcaM\) and \(SOi\) because they have at least one link for \(os2 Contrast\) with an object of the \(Concept\_Contrast\_3\) extent.  
As previously shown, in our framework, the RCF is composed of a central formal context, describing operating systems, together with four formal contexts describing the different mechanisms and relations connecting the operating systems to the mechanism implementations. This is reproduced at the level of lattices. The central concept lattice, shown in Figure 8, combines information given in the different concept lattices defined for the different mechanisms. Its top concept (\(Concept\_Systems\_0\)) shows the relational attributes that are common to all studied systems. One example is relational attribute _exist os2 contrast_(\(Concept\_Contrast\_6\)) which indicates that all operating systems have atleast one \(os2 contrast\) link towards an object in \(Concept\_Contrast\_6\). This means that all operating systems have accessibility options that concern the contrast mechanism. More informative relational attributes will be presented hereafter.  
The data mining output method is summarized below (Box 4). Its results are interpreted in the next section for the target domain in the software product line paradigm.  
Figure 8: Concept lattice of Operating System accessibility options. In figures that correspond to RCAexplore tool output, quantifiers appear as plain text (e.g., \(exist\)) rather than symbols (e.g., \(\exists\)) to avoid encoding issues.  
Figure 7: Concept lattices on zoom and contrast.  
**RCA output.** From the formal and relational contexts, we generate, through the _RCAexplore_ tool, one concept lattice for each formal context:  
One central _system lattice_, which structures information about all systems on all mechanisms, e.g., Figure 8.  
Several _mechanism lattices_, each focusing on a mechanism, e.g., Figure 6(a),b for zoom and contrast.