# Outlier Recognition via Linguistic Aggregation of Graph Databases
## 6 Conclusions  
In this paper, we introduce a novel method of outlier detection and recognition in graph datasets, when only linguistic and/or imprecise knowledge is available to differ suspected objects on the background of regular, typical data. The method is applicable when no quantitative or measurable information is accessible (and, thus, outlier definitions by [PERSON], [PERSON], etc. would not work), but when it is possible to create fuzzy models, i.e., fuzzy representations of expert knowledge, based on raw numerical data (which is a common practice in fuzzy computations). Specific processing of graph databases is taken into account, to make it readable for fuzzy methods. An illustrative implementation example is provided to show how graph data can be processed by fuzzy representations of linguistic information and, finally, to point at particular objects as recognized outliers. In other words, we show how the question \"which objects are outliers in \(\mathcal{D}\)?\" can be answered, and not only \"are there outliers in \(\mathcal{D}\) or not?\".  
Algorithms 1 or 2 can confirm that outliers are present in \(\mathcal{D}\), and the subsets of outlying observations \(\mathcal{D}_{\mbox{out}}\) in the analyzed \(\mathcal{D}\) are determined by Algorithms 3 or 4 taken into account the degrees of truth of linguistically quantified statements generated by Algorithms 1 or 2 as their side effects, see (19) and (21). Finally, we would like to underline that the approach proposed to the issue of detecting and recognizing outliers in datasets, especially, its novelty based on linguistically quantified statements interpreted in terms of fuzzy sets, were not applied, up to now, to graph datasets.  
Currently, our further research on recognizing outliers is in progress, mostly using multi-subject linguistic summaries, cf. [29], and analyzing other non-relational databases.  
Conceptualization, A.N. and A.D.; methodology, A.D.; software, M.B.; validation, A.N., A.D. and M.B.; formal analysis, A.N. and A.D.; resources, M.B.; data curation and processing, M.B.; implementation, M.B.; writing--original draft preparation, A.N. and A.D.; writing--review and editing, A.N., A.D. and M.B.; supervision, A.N. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**No.** & **Neighbors** & **Leafsize** & **Metric** & **Contamination** & **Number of Outliers** \\ \hline
1. & 20 & 30 & Minkovsky & auto & 3206 \\
2. & 50 & 30 & Minkovsky & auto & 2989 \\
3. & 50 & 100 & Jaccard & auto & 0 \\
4. & 20 & 30 & dice & auto & 0 \\
5. & 20 & 30 & correlation & 0.0050 & 132 \\
6. & 20 & 30 & correlation & 0.0012 & 33 \\
7. & 20 & 30 & correlation & 0.0004 & 11 \\
8. & 20 & 30 & correlation & 0.0002 & 6 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Parameters of the LOF algorithm and number of outliers detected in the \(\mathcal{D}\) dataset.  
Data Availability Statement: Publicly available datasets were analyzed in this study. This data can be found here: [20].  
This publication was completed while the third author was the Doctoral Candidate in the International Doctoral School at Lodz University of Technology, Lodz, Poland.  
The authors declare no conflict of interest.  
Samples of the compounds of the proposed algorithms are available from the authors.