# Visual Assessment of Cluster Tendency with Variations of Distance Measures
## 2 Materials and Methods
The considered distance measures included: Euclidean distance, squared Euclidean distance, standardized Euclidean distance, Manhattan distance, Mahalanobis distance, Bray-Curtis dissimilarity, Canberra distance, Chebyshev distance, distance correlation, cosine similarity. For the experiments, we used synthetic (artificial) datasets (with cluster labels) [49], as well as from samples of industrial products [50; 51] and from a set of some taxation characteristics of forest stands [52]:

1. _Long2_ is an artificial dataset that contains the collection of two clusters (1000 data points, 2 dimensions) (Figure 1a). 2. _Sizes1_ is an artificial dataset contains the collection of four clusters (1000 data points, 2 dimensions) (Figure 1b). 3. _Longsquare_ is an artificial dataset contains the collection of six clusters (1000 data points, 2 dimensions) (Figure 1c). 4. _Microhips_ are two sets of results of test effects on electrical and radio products for monitoring the current-voltage characteristics of input and output circuits of microcircuits: Microchips 140 UD25 AS1 VK (46 data points, 9 dimensions, 2 clusters) and 1526 IE10_002 (3987 data points, 67 dimensions, 4 clusters) [50; 51]. For microchip 1526 IE10_002, we used the following batch combinations: mixed lots from four (62 parameters), three (41 parameters), and two batches (41 parameters). 5. _Siberian Forest Compartments Dataset_[52] is a set of some taxation characteristics of forest stands, on which outbreaks of mass reproduction of the Siberian silkworms were recorded at a certain time (15,523 data points, 150 dimensions). The Siberian Forest Compartments Dataset contains three forestry strands: Irbey forestry (2330 data points), Chunsky forestry (3271 data points), and Lower Yenisei forestry (3619 data points). In our experiments, the following test system was used: Intel (R) Core (TM) i5-8250U CPU, 16 GB RAM, while Python was also used to implement the algorithms. ### Synthetic Datasets

The computational experiment showed that the resulting iVAT images more clearly showed the number of clusters than the resulting VAT images (Appendix A, Figure A1) for Long2. In addition, it can be noted that the Mahalanobis distance and squared Euclidean distance had an advantage over the other distances (Appendix A, Figure A1). The VAT and iVAT algorithms with Canberra distance did not cope with the task. The VAT and iVAT images showed four clusters. The VAT image with Bray-Curtis dissimilarity and cosine similarity showed no clusters (Appendix A, Figure A1). For the Sizes1 dataset, the computational experiment showed that the resulting iVAT images more clearly showed the number of clusters than the resulting VAT images (Appendix A, Figure A2). In addition, the Canberra distance and cosine similarity had an advantage over the other distances (Appendix A, Figure A2). The VAT and iVAT algorithms with distance correlation did not cope with the task. The VAT and iVAT images showed no clusters (Appendix A, Figure A2). For LongSquare, the computational experiment showed that the resulting iVAT images more clearly showed the number of clusters than the resulting VAT images (Appendix A, Figure A3). In addition, the Mahalanobis distance and squared Euclidean distance had an advantage over the other distances (Appendix A, Figure A3). The VAT and iVAT algorithms with Bray-Curtis dissimilarity, distance correlation, Canberra distance, and cosine similarity did not cope with the task. The VAT and iVAT images with distance correlation and iVAT images with cosine similarity showed two clusters, while the VAT image with Bray-Curtis dissimilarity showed no clusters (Appendix A, Figure A3). ### Microchips Datasets

For Microchips 140 UD25 AS1 VK, the computational experiment showed that the resulting iVAT images more clearly showed the number of clusters than the resulting VAT images. The VAT and iVAT algorithms with Mahalanobis distance did not cope with the task. The VAT and iVAT images with Mahalanobis distance did not cope with the task.