Block generation in a two-dimensional space constructed by Hellinger metric and affinity for weather data fusion and learning inputs

Abstract The concise and reliable representation of a given source dataset is available for data based learning and decision-making, which can be obtained through a controllable data fusion process within a formatted space. Based on the density matrix representation of a given source weather dataset, this paper first calculates the Hellinger distances and affinities between different density matrices, and then takes them to construct a two-dimensional metric space using the longest Hellinger metric and affinity paths. Within this space, the given source data units are converted into the corresponding rectangle nodes which are determined by the minimum horizontal and vertical distances between different data units. According to a predefined detection size in this space, the basic blocks centred by different rectangle nodes are classified into different subset blocks for fusion. Each subset block is jointed by the basic blocks with overlapped areas. During the detection process, the detection size keeps increasing until a predefined reference variable, such as the relative density for all subset blocks, reaches a predefined turning point. The fusion of the rectangle nodes in a subset block depends on the distances between the included rectangle nodes’ positions and this subset block’s centre position which is calculated according to the included rectangle nodes’ weights and positions. The experimental analysis shows that the proposed weather data fusion method is controllable and stable and can obtain concise and reliable fusion results for learning inputs and decision-making.