Most of the traditional clustering algorithms are poor for clustering more complex structures other than the convex spherical sample space. In the past few years, several spectral clustering algorithms were proposed to cluster arbitrarily shaped data in various real applications. However, spectral clustering relies on the dataset where each cluster is approximately well separated to a certain extent. In the case that the cluster has an obvious inflection point within a non-convex space, the spectral clustering algorithm would mistakenly recognize one cluster to be different clusters. In this paper, we propose a novel spectral clustering algorithm called HSC combined with hierarchical method, which obviates the disadvantage of the spectral clustering by not using the misleading information of the noisy neighboring data points. The simple clustering procedure is applied to eliminate the misleading information, and thus the HSC algorithm could cluster both convex shaped data and arbitrarily shaped data more efficiently and accurately. The experiments on both synthetic data sets and real data sets show that HSC outperforms other popular clustering algorithms. Furthermore, we observed that HSC can also be used for the estimation of the number of clusters.
Main aim of the study was to determine the temporal and spatial patterns of relations between monthly and annual average river flow (RF) and water temperature (WT) for 53 rivers in Poland. The research made use of monthly and annual WT and RF for 88 water gauges for the period 1971–2015. Correlations were established using the Spearman’s rank correlation coefficient and the similarity of RF–WT relations was determined using the Ward’s hierarchical grouping. It was demonstrated that correlations between average annual RF and WT were negative (for >85% of water gauges) and statistically significant (p<0.05) only for 30% of water gauges. It was confirmed that the studied RF–WT relations underwent seasonal changes. Positive correlations were clearly predominant in the winter months, while from April to September these relations were negative and statistically significant. The RF–WT relations were also characterized by spatial differences and this had been confirmed by separation of seven groups of water gauge profiles distinguished with the help of the Ward's hierarchical grouping method. The strongest RF–WT relations were apparent in the case of mountainous rivers, for which snow melt supply and summer rainfall supply were predominant, and lakeland rivers, which had a considerable share of groundwater supply. These were classified as cold rivers, as opposed to the cool rivers in the lowland belt, for which the RF–WT relations were the weakest. The results obtained may contribute to the elaboration of an appropriate management strategy for river ecosystems, which are assigned important economic and environmental functions.