The correlation of the set of attributes is a crucial statistical value for the measuring of prediction potential present in a dataset. The correlation coefficient, which measures the correlation between the values of two attributes, can be used in order to measure the prediction potential between two-element subsets of a dataset containing a high number of attributes. In this way two common summary visualizations of prediction potential in datasets are formed—correlation matrices and correlation heatmaps. Both of these visualizations are focused on the presentation of correlation between pair of attributes but not much more regarding the context of correlations in the dataset. The main objective of this article is the design and implementation of graphical models usable in a visual representation of data prediction potential—correlation graphs and correlation chains—which emphasize the pseudo-transitivity of prediction potential in a dataset.

This article presents methods for correct decomposition for high performance computations related to large sets of graphs. These computations contain large number of calls of sequential, recursive algorithm for NP-complete problem - proper edge coloring of graph. Decomposition of this computational problem is not trivial, since the number of recursions in various parts of the computation is different and causes a high load and time imbalance. We designed, implemented and experimentally verified a new decomposition method that significantly reduces the computational time for a large set of graphs (up to 404 million graphs). This method ensures the same duration of computational time for partial subtasks and thus eliminates the need to wait for synchronization of parallel computations.

To efficiently store data where the relationships between individual objects are essential, the use of a graph database model is recommended. After storing the data, it is necessary to further analyze it using statistical methods or visualize it within the context of exploratory data analysis. Such visualization is crucial for understanding the structure and content of the database. However, commonly used visualization tools often fall short in terms of interactivity and effectiveness. The main objective of the presented work is the design and implementation of a novel model for the visualization of data structures stored in graph databases with the use of two natural graphical models—the standard topological layout of the database and the so-called clustered layout of a graph database. The presented graphical models are focused on interactive visualization, mainly scaling of visualization and development of database objects, and principles of effective visualization. Implementation of the proposed approach was evaluated via case studies on three model graph databases of various sizes—Messaging database (16 objects, 16 relationships), Library database (16 objects, 32 relationships) and Movie database (171 objects, 253 relationships). Compared to the standard Neo4j tool for the visual representation of property graphs in graph databases, the proposed model presents improvement in terms of the number of visualization models, effectivity of the visualization, and development of objects in the visualized database.

In data analysis, there is a natural connection between correlation and visual analysis. Correlation analysis enables the identification of relationships between attribute pairs in multidimensional datasets, while visual data analysis focuses on representing the data and the models that process it in a comprehensible visual form. A notable model that integrates these two approaches is the correlation structure—a graphical and visual model based on correlation graphs and correlation chains. However, traditional correlation structures are parametric, requiring an attribute of interest as an input to guide the analysis. This presents a major challenge when analyzing unfamiliar datasets or domains, where the attributes of interest are not known in advance. To address this limitation, this study proposes the design and implementation of non-parametric correlation structures—specifically, non-parametric correlation graphs and non-parametric correlation chains—that eliminate the dependency on predefined input attributes. These models are implemented in Python language to ensure broad accessibility and integration into existing data analysis pipelines. Once implemented, the concept of embedding non-parametric correlation chains within non-parametric correlation graphs is explored to enhance the interpretability of correlation structures of a dataset. The proposed approach is evaluated through case studies on five open-access datasets, varying in size from 6 to 149 attributes, and tested using five regression analysis models. Finally, the advantages and disadvantages of the proposed model are determined.

Among statistical methods used in data analysis processes, correlation analysis holds one of the most significant places. Using correlation, analysts measure prediction potential between values of a pair of attributes of a dataset which can be summarized into a correlation matrix for any multidimensional dataset. Such matrices are usually sizable, and hard to read. Pruning of the correlation matrix for the precise selection of attribute pairs of a considered dataset which bear strong prediction potential is conventionally conducted via correlation matrix masks. Since these masks are commonly designed as crisp borders for the acceptability of values in the matrix, there is a strong lack of nuance in this approach. The work presented in the scope of this study focuses on the design and implementation of fuzzy masks for correlation matrices. This objective is divided into three main tasks - firstly, the visualization of correlation coefficient value frequency and its relationship to fuzzy membership function is designed and implemented, then visualisation of basic regression analysis and correlation context of attribute pairs in the fuzzy area of a studied dataset is designed and implemented, and lastly, the proposed approach is evaluated via case studies on three benchmarking datasets. The results obtained with the fuzzy approach to correlation matrix masks show a qualitative improvement in the matrix pruning task and a more appropriate identification of the relevant parts of the dataset compared to the conventional, crips approach.