Relevance vector machines using weighted expected squared distance for ore grade estimation with incomplete data
- PDF / 1,783,212 Bytes
- 12 Pages / 595.276 x 790.866 pts Page_size
- 51 Downloads / 142 Views
ORIGINAL ARTICLE
Relevance vector machines using weighted expected squared distance for ore grade estimation with incomplete data Yukui Zhang1 • Shiji Song1 • Keyou You1 • Xunan Zhang1 • Cheng Wu1
Received: 18 January 2016 / Accepted: 15 April 2016 Ó Springer-Verlag Berlin Heidelberg 2016
Abstract 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. Keywords Grade estimation Relevance vector machine Incomplete data Weighted expected squared distance Entropy weight & Shiji Song [email protected] 1
Department of Automation, Tsinghua University, Beijing 100084, People’s Republic of China
1 Introduction With limited mineral resources on land, people pay more attention to deep ocean, where exists tremendous resources including poly-metallic nodules, cobalt-rich crusts and hydrothermal sulfide deposits. The later one has great exploitation value for it contains large amounts of metals, such as Cu, Fe, Mn, Ag, and Au. Seafloor massive sulfide (SMS) deposits form where hot hydrothermal fluids rise and mix with cold sea water. Most of them are currently forming in the deep ocean around submarine volcanic arc, mid-ocean ridge systems, and back-arc spreading systems. However, the complexity of the deep-marine environment and high risks make it difficult to explore the ore deposits. What’s more, during the process of resource evaluation, the feasibility of exploring a mining project depends mainly on the accurate estimation of the ore grade [13, 18]. Hence, it is of utmost importance to choose an appropriate model, which can provide powerful data analysis and support for mining a hydrothermal sulfide deposit. Generally, the reliability of an ore g
Data Loading...
