Using Hellinger and Bures metrics to construct two-dimensional quantum metric space for weather data fusion

Abstract

Motivated by obtaining more concise and reliable fusion results for relevant applications, such as, in sector monitoring, risk managing, early-warning, dynamic prediction, this paper explores the detection and fusion models of weather data from multiple perspectives. We represent the weather data as the collection of quantum states, and study construction of the quantum metric space in which the related weather data fusion method is developed. Since weather data usually contain raw (image or sensor) data, feature data, or decision data, the weather data fusion belongs to normal three levels of data fusion, i.e., pixel level, feature level or decision level. In this paper we represent weather data units as density matrixes, and take the quantified data units as the basis for constructing the two-dimensional quantum metric space consisting of Hellinger and Bures metrics. All the density matrix units in this space are transformed into the rectangle nodes for detection and fusion. Then, according to the neighborhood relationships between rectangle nodes and the density of rectangle nodes in a specified rectangle, the source weather dataset is divided into different subsets. The key to the fusion of the rectangle nodes in a subset is to calculate the presupposing central node in this subset's corresponding rectangle. And the corresponding object node depends on the areas of the rectangles including rectangle nodes and the central node. The experimental evaluation demonstrates that, compared with the already developed fusion methods, the proposed weather data fusion method can obtain more concise and reliable fusion results for decision applications.