Weighted Weights of Evidence and Stepwise Weights of Evidence and Their Applications in Sn-Cu Mineral Potential Mapping in Gejiu, Yunnan Province, China
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摘要:
鉴于水系沉积物地球化学数据可以表示为非负矩阵, 这使得利用非负矩阵分解(NMF) 方法处理该类数据成为可能.介绍了非负矩阵分解方法的基本原理和方法, 讨论了基于非负矩阵分解方法处理水系沉积物地球化学数据的可能和效果.以个旧水系沉积物地球化学数据为例, 运用NMF方法和主成分分析(PCA) 方法对其进行异常分析, 并对这两种方法的处理结果进行了比较, 发现NMF方法对于处理水系沉积物地球化学数据是一种有效的方法.尽管这两种方法各自有其优越性, 但就本实例数据而言, NMF方法优于PCA方法.
Abstract:This paper explores the possibility of applying non-negative matrix factorization (NMF) to process stream sediment geochemical data for mineral exploration. The brief introduction of principle of NMF is followed by detailed comparison of the results obtained by NMF and principal component analysis (PCA) applied to a dataset of 813 samples with six trace elements from Gejiu mineral district, Yunnan, China. It is shown that the NMF is not only suitable for processing geochemical data which are usually of positive values but also provides superior results than that by PCA in the case study introduced in the paper. The example indicates that NMF might become a useful method for processing other types of geochemical data.
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图 1 NMF方法r=1, 2, 3时6个基向量分别取对数后的6个图层
a.r=1时的第一个基向量取对数; b.r=2时的第一个基向量取对数; c.r=3时的第一个基向量取对数; d.r=2时的第二个基向量取对数; e.r=3时的第二个基向量取对数; f.r=3时的第3个基向量取对数
Fig. 1. Six basis vectors obtained using NMF when r=1, 2, 3
图 3 主成分分析得到的3个主成分的因子得分
Fig. 3. Scores of three principal components
a. log(PCA1+0. 7);b. log(PCA2 +7);c. log(PCA3+ 7)
表 1 r=1, 2, 3时NMF权值矩阵
Table 1. Encodings using NMF when r=1, 2, 3
表 2 NMF基向量和PCA的3个主成分之间的相关系数
Table 2. Correlations among six basis vectors using NMF and three principal components using PCA
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[1] Cheng, Q. M., Zhao, P. D., Chen, J. G., et al., 2009. Application of singularity the oryin prediction of tin and coppermineral deposits in Gejiu district, Yunnan, China: Weak information extraction and mixing information decomposition. Earth Science—Journal of China University of Geosciences, 34 (2): 232-242 (in Chinese with Eng-lish abstract). doi: 10.3799/dqkxzx.2009.021 [2] Donoho, D., Stodden, V., 2004. When does non-negative matrix factorization give a correct decomposition into parts? In: Thrun, S., Saul, L., Scholkopf, B., eds., Advances in neural information processing systems16. MIT Press, Cambridge, MA. [3] Feng, T., Li, S., Shum, H., et al., 2002. Local non-negative matrix factorization as a visual representation. In: Proceedings of the2ndinternational conference on development and learning. IEEE, Cambridge. U. K., 178-183. DOI: 10.1109/DEVLRN.2002.1011835. [4] Guillamet, D., Bressan, M., Vitria, J., 2001. A weighted non-negative matrix factorization for local representations. In: Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition V1, Kauai, HI, 942-947. DOI: 10.1109/CVPR.2001.990629. [5] Guillamet, D., Vitria, J., Schiele, B., 2003. Introducing a weighted non-negative matrix factorization for image classification. Pattern Recognition Letters, 24 (14): 2447-2454. doi: 10.1016/S0167-8655(03)00089-8 [6] Juvela, M., Lehtinen, K., Paatero, P., 1994. The use of positive matrix factorization in the analysis of molecular line spectra from the thumbprint nebula. In: Clemens, D. P., Barvainis, R., eds., Clouds, cores, and low mass star. ASP Conference Series, 65: 176-180. [7] Juvela, M., Lehtinen, K., Paatero, P., 1996. The use of positive matrix factorization in the analysis of molecular linespectra. Mon. Not. R. Astron. Soc. , 280: 616-626. https://ui.adsabs.harvard.edu/abs/1996MNRAS.280..616J/abstract [8] Lee, D. O., Seung, H. S., 1999. Learning the parts of objects by non-negative matrix factorization. Nature, 401: 788-791. doi: 10.1038/44565 [9] Lee, D., Seung, H., 2000. Algorithms for non-negative matrix factorization. In: Leen, T., Dietterich, T., Tresp, V., eds., Advances in neural information processing systems. MIT Press, Cambridge, MA, 556-562. [10] Paatero, P., 1997. Least squares formulation of robust non-negative factor analysis. Chemometrics and Intelligent Laboratory Systems, 37 (1): 23-35. doi: 10.1016/S0169-7439(96)00044-5 [11] Paatero, P., Tapper, U., 1994. Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values. Environmetrics, 5 (2): 111-126. doi: 10.1002/env.3170050203 [12] Wei, L., 2004. Blind sources separation based on non-negative matrix factorization. Electronics Optics & Control, 11 (2): 38-41, 53 (in Chinese with English abstract). [13] Xu, W., Liu, X., Gong, Y., 2003. Document-clustering based on non-negative matrix factorization. In: Proceedings ofSIGIR'03, July28-August1.267-273, Toronto, CA. [14] 成秋明, 赵鹏大, 陈建国, 等, 2009. 奇异性理论在个旧锡铜矿产资源预测中的应用: 成矿弱信息提取和复合信息分解. 地球科学——中国地质大学学报, 34 (2): 232-242. https://www.cnki.com.cn/Article/CJFDTOTAL-DQKX200902001.htm [15] 魏乐, 2004. 基于非负矩阵分解算法进行盲信号分离. 电光与控制, 11 (2): 38-41, 53. https://www.cnki.com.cn/Article/CJFDTOTAL-DGKQ200402011.htm -
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