## 4 Data-Science Analytics
### Goal 1--Cluster Identification
Figure 2: Comparison of clustering results obtained with selected algorithms: (**a**) DBSCAN; (**b**) OPTICS; (**c**) Affinity Propagation. The top row presents the 2D plots, whereas the bottom one shows 3D scatter plots as the headset wearer sees them. The selected clusters are marked gray hulls (in 2D) and green (in 3D), respectively. These clustering examples were done over the **DS1**. desired. Figure 3a shows the 2D projection of clustering results in 3D space after applying PCA and selecting three main components. In addition to these clustering results, we have also employed a state-of-the-art SuMC [8] clustering solution that belongs to the class of methods called subspace clustering [31]. The poor performance of the standard clustering algorithms applied to high-dimensional datasets is usually caused by _curse of dimensionality_[32]. The typical attempt in solving this issue is the application of some form of dimension reduction on the given dataset. These can be grouped in the feature selection and feature extraction methods. A well-known example of the latter is the PCA [30] method that we have previously applied in order to test other clustering algorithms on our datasets (see Figure 3a). In comparison, the SuMC method was specifically designed to deal with high-dimensional data without relying on dimension reduction as one of its steps. This method belongs to the so-called _hard subspace clustering_ techniques whose main goal is to indicate the explicit subspaces to which the identified clusters belong. We have deployed the SuMC method on various hand-selected subsets of **DS1** and **DS2** choosing 3, 5, and 7 as the number of desired clusters. As the SuMC is designed to operate on high-dimensional datasets we have run the method on the full datasets, as well as on subsets consisting only of criteria or design parameters for each dataset. In the case of both datasets, the criteria parameters are the objective functions, i.e., the last three right-most dimensions in Figure 1, whereas the design parameters are the remaining dimensions on the left. This choice of sub-datasets was dictated by the standard methodology of dataset analysis in the case of the 2D and 3D PCP users. Similar to the popular clustering method K-means, this technique starts with the random assignment of points to clusters. Using an iterative refinement technique (i.e., [PERSON]'s method), it shifts points between clusters to optimize the cost function and obtain potential candidates for the patterns. The most illustrative example of the SuMC application to our data can be seen in Figure 4. Here, the results of clustering for both 3 and 5 desired number of clusters carried out over only the 26 design parameters are compared against the patterns fund by the domain-experts in **DS1**. This result shows that that patterns identified by the human experts overlap substantially with clusters identified by the SuMC method. For instance, at the bottom of Figure 4 the whole pattern is embedded in one of the clusters (in light green). Such preselection of the pattern candidates can substantially trim the search space for the user. For instance, the IPCP system could, on-demand, carry out the clustering and automatically split the main plot into subsections in the 3D space or allow the user to select grouped data items in which the user can search for patterns by selecting or deselecting individual elements. For the detail information of the interaction interface bestowed by the IPCP please see [2; 3; 4]. Figure 3: (**a**) DBSCAN clustering after dimensionality reduction with PCA to 3 components. ; (**b**) feature importances obtained with random forest classifier. Difficulties in proper cluster identification on the correlated axis are shown in (**c**). Choosing the set of the uncorrelated axis (**d**) allows for a better overview of data. The presented clustering was done over the **DS1**.