## 1 Introduction  
Parallel Coordinates Plots (PCP) [1] is a well-known technique for the visualization and analysis of complex multidimensional datasets. However, it requires experience from the user in interpreting PCP output and often a deep domain knowledge in the subject of analysis in order to extract meaningful conclusions and new knowledge. Therefore, methods that aid experts and users in the process of analyzing the PCP visualization and developing a new understanding of a decision-making process are needed. Thus, in this paper, we present a refinement of a previously developed system called Immersive Parallel Coordinates Plots (IPCP) [2; 3; 4], which is now augmented with new and improved functionality. In our case, data visualization is presented to the user with the help of an interactive and fully immersive Virtual Reality (VR) interface. A previous exploratory and qualitative study carried out using the first version of IPCP demonstrated that users were able to successfully detect patterns in high-dimensional datasets visualized as-is [2; 3; 4], that is, without any prior analysis or data cleaning, using the IPCP system (see Figure 1) combined with a simple naive clustering algorithm applied to cross-dimensional 3D scatter plots data [2; 3; 4]. However, this basic IPCP system allowed users to rediscover the knowledge; specifically, patterns with the data items previously found by the domain experts and,more importantly, users were able to discover new knowledge in the dataset compared to original analyses carried out by experts using a more traditional 2D PCP system [3,4]. In comparison, the version presented in this paper has been extended with features and improvements of functionality bestowed by the IPCP [3,4] and supporting 3D scatter plots. Similar to prior work [3,4] we rely on two datasets to drive the system development process, which we will refer to as the Pareto front data (54 data items with 29 dimensions each) as dataset **DS1** and the S-duct design optimization study (166 data items with 39 dimensions each) as dataset **DS2**. There were two goals with the refinement of the system: (1) to better assist the user in the identification of clusters of data points in the scatter plots; (2) to help the user identify meaningful axes in the IPCP. For the first goal, the system assumes clustering is performed only in three dimensions selected by the user to generate the scatter plot. This assumption is justified by the fact that clustering over a scatter plot's data is meant to assist the user in inspecting the dataset, and, as a consequence, the clustering algorithm should not be applied to all dimensions as it causes interpretation problems if, for example, many axes contain merely noise or redundant data. We tested several clustering algorithms and concluded that only the Ordering Points to Identify Cluster Structure (OPTICS) [5], Density-Based Spatial Clustering of Applications with Noise (DBSCAN) [6], and Affinity Propagation [7] are sufficiently robust to work on our data, as they allow for automatic noise removal. Furthermore, we applied to our data another clustering method called Subspace Memory Clustering (SuMC) [8]. This novel clustering algorithm is based on lossy compression and the Minimal Description Length Principle (MDLP), i.e., inductive inference. It looks for low-dimensional subspaces by minimizing the squared error (MSE) while keeping the total amount of memory fixed that it can use to describe the data. For the second goal, we investigated two independent methods for generating explanations of axis importance.