Improved quantum clustering analysis based on the weighted distance and its application

Cluster analysis is widely used in fields such as economics, management and engineering. The distance and correlation are two of the most important and often used mathematics- and statistics-based similarity measures in cluster analysis. Many studies have been conducted to improve the distance and similarity in high-dimensional and overlapped data. However, these studies do not consider the degree of influence (weight) of different properties on different types of data. In practice, the weight of each property is different, so these methods cannot accurately analyze real data. First, this study proposes a new distance measure that can reflect the weight, so that non-spherical overlapping data in the Euclidean space can be projected onto a weighted Euclidean space to form non-overlapping data. Second, the Fuzzy-ANP method is used to determine the weight of each factor. Then, by applying the Fuzzy-ANP-Weighted-Distance-QC (FAWQC) method to weighted random data, the effectiveness of the method is verified. Finally, the method is applied to the 2015 Economics-Energy-Environment (3E) data for 19 provinces in China for a comparative study of the classification of the system structure and evaluation of the low-carbon economy development level. The experiment results show that the FAWQC method can more accurately analyze real-world data than other methods.