Relevance vector machines using weighted expected squared distance for ore grade estimation with incomplete data

Accurate ore grade estimation is crucial to mineral resources evaluation and exploration. In this paper, we consider the borehole data collected from the Solwara 1 deposit, where the hydrothermal sulfide ore body is quite complicated with incomplete ore grade values. To solve this estimation problem, the relevance vector machine (RVM) and the expected squared distance (ESD) algorithm are incorporated into one regression model. Moreover, we improve the ESD algorithm by weighting the attributes of the data set and propose the weighted expected squared distance (WESD). In this paper, we uncover the symbiosis characteristics among different elements of the deposits by statistical analysis, which leads to estimating certain metal based on the data of other elements instead of on geographical position. The proposed WESD-RVM features high sparsity and accuracy, as well as the capability of handling incomplete data. Effectiveness of the proposed model is demonstrated by comparing with other estimating algorithms, such as inverse distance weighted method and Kriging algorithm which utilize only geographical spatial coordinates for inputs; extreme learning machine, which is unable to deal with incomplete data; and ordinary ESD based RVM regression model without entropy weighted distance. The experimental results show that the proposed WESD-RVM outperforms other methods with considerable predictive and generalizing ability.