基于GIS的NMF算法在矿产资源定量预测中的应用研究
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摘要
矿产资源定量预测是地质学和数学、信息技术、计算机技术相结合的产物,它建立矿产资源与地质条件之间的定量关系,从而使矿产资源预测更加客观、更加准确,效率也大幅提升,同时定量预测也是定性预测的深化和具体化,定量预测更成为资源预测的发展方向。随着矿产资源发现难度的不断增加和现代科学理论及方法技术的发展与渗透,GIS技术的应用形成了新一代的矿产资源评价方法,将其引入地质找矿行业是充分利用已有数据、提取潜在信息以及提高矿产资源预测水平的重要途径。
非负矩阵分解理论是近年来才提出的一种矩阵分解方法,它增加了非负限制,以保证分解后矩阵数据的非负特性,非负结果更容易解释。非负矩阵分解算法简单,易于实现,并且具有降维、收敛和稀疏等特性。因此,该算法已被广泛地应用于多个领域中。
本文主要是论述稀疏非负矩阵分解算法在矿产资源定量预测中的应用研究。在讨论了非负矩阵分解算法的原理与应用条件下,在基于GIS的空间信息集成功能,对内蒙古东部地区1:20万地质、物探和化探信息进行集成的基础上,采用稀疏非负矩阵分解算法对内蒙古东部地区1:20万银矿产资源进行了定量预测。该算法在预测过程中实现了对集成变量矩阵的稀疏化,节约了存储空间;利用稀疏非负矩阵分解算法,对集成变量矩阵中的主要特征向量进行了提取,采用稀疏非负矩阵分解算法进行定量预测处理,取得了较为符合实际的结果。论文最后通过聚类分析、加权丰度预测模型、稀疏非负矩阵分解算法所得结果的比较分析,验证了这三种不同预测方法结果的一致性,得出在矿产预测中使稀疏非负矩阵分解算法,可以得到较为理想的预测结果。
Quantitative prediction of mineral resources is the product of the combination of geology, mathematics, information and computer technology. It builds the quantitative relationship between mineral resources and geological conditions in order to make the prediction of mineral resources more objective and accurate and efficiency dramatically increased. Meanwhile, quantitative prediction extends and further specifies of qualitative prediction. It has become the trend of predictable resources. With the increasing difficulty of the discovery of mineral resources and the development of modern scientific theories and technological methods, GIS technology application becomes a new evaluation method of mineral resource. Introduction the GIS to geological prospecting industry is an important way to make full use of existing data, extract potential information and develop the level of mineral resources prediction.
Theory of non-negative matrix factorization (Non-Negative Matrix Factorization, NMF) is a matrix decomposition method proposed in recent years. It increases the non-negative constraints to ensure that the data matrix decomposition characteristics of non-negative and non-negative result are more easily to be explained. Moreover, NMF algorithm is simple and easy to implement and it has features such as dimension-lowering and sparse convergence. Therefore, it has been widely used in many fields.
In this article, the sparse non-negative matrix factorization algorithm is applied to quantitative predict the mineral resources. The principle and application seditions of non-negative matrix factorization algorithm are discussed. Based on the integrated function of GIS space information and 1:200,000 scale information of geology, geophysical and geochemical in the east of Inner Mongolia, the sparse non-negative matrix factorization algorithm is adopt to quantitatively predict 1:200,000 scale silver mineral prediction in the east of Inner Mongolia. The algorithm realizes the sparse of original data and saves the storage space. Main features of the matrix vectors are extracted by using the sparse non-negative matrix factorization algorithm. The results relatively conform to reality. Comparative analysis of the results of cluster analysis, the weighted abundance estimate algorithm and sparse non-negative matrix factorization algorithm is given. The results show that the predictions of the three methods have consistency.Applying the sparse non-negative matrix factorization algorithm to predict the geology and mineral resources can get a better result.
非负矩阵分解理论是近年来才提出的一种矩阵分解方法,它增加了非负限制,以保证分解后矩阵数据的非负特性,非负结果更容易解释。非负矩阵分解算法简单,易于实现,并且具有降维、收敛和稀疏等特性。因此,该算法已被广泛地应用于多个领域中。
本文主要是论述稀疏非负矩阵分解算法在矿产资源定量预测中的应用研究。在讨论了非负矩阵分解算法的原理与应用条件下,在基于GIS的空间信息集成功能,对内蒙古东部地区1:20万地质、物探和化探信息进行集成的基础上,采用稀疏非负矩阵分解算法对内蒙古东部地区1:20万银矿产资源进行了定量预测。该算法在预测过程中实现了对集成变量矩阵的稀疏化,节约了存储空间;利用稀疏非负矩阵分解算法,对集成变量矩阵中的主要特征向量进行了提取,采用稀疏非负矩阵分解算法进行定量预测处理,取得了较为符合实际的结果。论文最后通过聚类分析、加权丰度预测模型、稀疏非负矩阵分解算法所得结果的比较分析,验证了这三种不同预测方法结果的一致性,得出在矿产预测中使稀疏非负矩阵分解算法,可以得到较为理想的预测结果。
Quantitative prediction of mineral resources is the product of the combination of geology, mathematics, information and computer technology. It builds the quantitative relationship between mineral resources and geological conditions in order to make the prediction of mineral resources more objective and accurate and efficiency dramatically increased. Meanwhile, quantitative prediction extends and further specifies of qualitative prediction. It has become the trend of predictable resources. With the increasing difficulty of the discovery of mineral resources and the development of modern scientific theories and technological methods, GIS technology application becomes a new evaluation method of mineral resource. Introduction the GIS to geological prospecting industry is an important way to make full use of existing data, extract potential information and develop the level of mineral resources prediction.
Theory of non-negative matrix factorization (Non-Negative Matrix Factorization, NMF) is a matrix decomposition method proposed in recent years. It increases the non-negative constraints to ensure that the data matrix decomposition characteristics of non-negative and non-negative result are more easily to be explained. Moreover, NMF algorithm is simple and easy to implement and it has features such as dimension-lowering and sparse convergence. Therefore, it has been widely used in many fields.
In this article, the sparse non-negative matrix factorization algorithm is applied to quantitative predict the mineral resources. The principle and application seditions of non-negative matrix factorization algorithm are discussed. Based on the integrated function of GIS space information and 1:200,000 scale information of geology, geophysical and geochemical in the east of Inner Mongolia, the sparse non-negative matrix factorization algorithm is adopt to quantitatively predict 1:200,000 scale silver mineral prediction in the east of Inner Mongolia. The algorithm realizes the sparse of original data and saves the storage space. Main features of the matrix vectors are extracted by using the sparse non-negative matrix factorization algorithm. The results relatively conform to reality. Comparative analysis of the results of cluster analysis, the weighted abundance estimate algorithm and sparse non-negative matrix factorization algorithm is given. The results show that the predictions of the three methods have consistency.Applying the sparse non-negative matrix factorization algorithm to predict the geology and mineral resources can get a better result.
引文
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[7]余生晨,叶水盛,刘光胜,王世称.利用地理信息系统(GIS)进行综合信息矿产资源预测[J].世界地质, 1996, 15(3): 91-96.
[8]陈毓川,裴荣富,王登红.三论矿床的成矿系列问题[J].地质学报, 2006, 80(10):1501-1508.
[9]胡平昭,侯景儒.多元空间信息统计分析计算机系统[J].遥感信息, 1998, 2:2-5.
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[11]朱裕生.矿产预测理论—区域成矿学向矿产勘察延伸的理论体系[J].地质学报, 2006, 80(10):1518-1527.
[12]毕伏科,肖文暹,阎同生.成矿系列的缺位问题及其在成矿预测中的应用[J].矿床地质, 2006, 25(6):735-742.
[13]李裕伟,赵精满,李晨阳.基于GMS、DSS和GIS的潜在矿产资源评价方法[M].地震出版:2007, 7-10.
[14]张原庆,王世称等.地球化学信息在综合信息矿产预测中的应用[J].地学前缘, 2005, (3):323-324.
[15]《国家中长期科学和技术发展规划纲要》发布, http://news.xinhuanet. com/st/2006-02/09/content_4155229. htm ,浏览日期:2009.3.7,刷新日期:2006.2.9,责任编辑:陈淑君.
[16]国家科技计划进行调整能源等放首位.人民日报2006年01月13日第十一版,责任编辑:石希.
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[19]美国地质调查局.美国本土矿产资源评价计划系列报告之一[M].地理信息系统及其在地学领域中的应用译文集,地矿部科技司计算机办公室, 1993.
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[22]刘驰.地理信息系统(GIS)在矿产资源评价中的应用[J].辽宁地质. 1999, 16(3):234-237.
[23]朱创业.地理信息系统在矿产预测中的应用—以华蓥山锶矿带为例[J].成都大学学报:自然科学版, 1999, 18(4):36-38.
[24]矫东风,吕新彪.基于GIS空间分析的成矿预测[J].地质找矿论丛, 2003, 18(4):269-274.
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[27]Pohl C., Van Genderen J. L., Multisensor image fusion in remote sensing: concepts. Methods and applications International Journal of Remote Sensing [J]. 1998, 19(5): 823-854.
[28] P. Paatero, U. Tapper, Positive Matrix Factorization: A non-negative factor model with optimal utilization of error estimates of data values [J]. Environ metrics, 1994, 5:111-126.
[29]D. Lee, H. S. Seung, Unsupervised learning by convex and conic coding [J]. Advances in Neural Information Processing Systems, 1997, 9:515-521.
[30]D. Lee, H. S. Seung, learning the parts of objects by non-negative matrix factorization [J], Nature, 1999, 401:788-791.
[31]Luo. R. C., Michael G. K. Edited. Multi-sensor Integration and Fusion for Intelligent Machines and Systems [M]. Ablex Publishing Corporation, 1995.
[32]卢进军,杨杰,梁栋等,基于非负矩阵分解的相关反馈图像检索算法[J].上海交通大学学报, 2005, 39(4):578-581.
[33]Dong Liang, Jie Yang, Yuchou Chang, Supervised Non-negative Matrix Factorization Based Latent Semantic Image Indexing [J]. chinese optics letters, 2006, 4(5):272-274.
[34]Lee J S, Lee D, Choi S, ET.al., Non-negative matrix factorization of dynamic images in nuclear medicine[C]. Proceedings of IEEE Nuclear Science Symposium Conference Record, San Diego, California, 2001, 4:2027-2030.
[35]Sajda P., Du S., Brown T. R., ET.al., Nonnegative matrix factorization for rapid recovery of constituent spectra in magnetic resonance chemical shift imaging of the brain[C]. IEEE Transactions on Medical Imaging, 2004, 23(12):1453-1465.
[36]Xiaoxiang Wang, Jie Tian, Xingfeng Li, ET. al., Detecting brain activations by constrained non-negative matrix factorization from task-related BOLD fMRI [C]. Proceedings of the SPIE - The International Society for Optical Engineering, 2004, 5369(1):675-682.
[37]Yuan Gao, George Church, Improving molecular cancer class discovery through sparsenon-negative matrix factorization [J]. Bioinformatics, 2005, 21(21):3970-3975.
[38]A. Pascual-Montano, F. Tirado, P. Carmona-Sáez, ET. al., Two-way clustering of gene expression profiles by sparse matrix factorization[C]. 2005 IEEE Computational Systems Bioinformatics Conference - Workshops (CSBW'05), 2005, 103-104.
[39]Shahnaz, Farial, Berry, Michael W., Pauca V. Paul, Plemmons, Robert J. Document clustering using nonnegative matrix factorization [J]. Information Processing and Management March, 2006, 42(2):373-386.
[40]F. Sha, L. K. Saul, Real-time pitch determination of one or more voices by nonnegative matrix factorization [J]. Advances in Neural Information Processing Systems, 2005, 1233-1240.
[41]张鹏,鲍长春,郭莉莉,基于非负矩阵分解的2kb/s波形内插语音编码算法[J].电子学报, 2008, 4(36):632-638.
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[49]叶水盛,王世称,刘万菘等. GIS基本原理与应用开发[M].长春:吉林大学出版社, 2004, 439-483.
[50]矿产工业要求参考手册(第二版)[M].北京:地质出版社, 1987, 26-46.
[2]陈永清,成秋明,夏庆霖.矿产资源潜力快速评价技术成果报告. 2006.
[3]赵鹏大.“三联式”资源定量预测与评价-数字找矿理论与实践探讨[J].地球科学-中国地质大学学报, 27 (5):482-489.
[4]赵鹏大,陈建平,张寿庭.“三联式”成矿预测新进展[J].地学前缘, 2003, 10 (2):455-463.
[5]王世称,陈永良,夏立显.综合信息矿产预测理论与方法[M].北京:科学出版社, 2000, 291-294.
[6]赵震宇,王世称,孟令顺.陕南地区金矿床综合信息预测[J].吉林大学学报:地球科学版, 2004, 2(34): 287-291.
[7]余生晨,叶水盛,刘光胜,王世称.利用地理信息系统(GIS)进行综合信息矿产资源预测[J].世界地质, 1996, 15(3): 91-96.
[8]陈毓川,裴荣富,王登红.三论矿床的成矿系列问题[J].地质学报, 2006, 80(10):1501-1508.
[9]胡平昭,侯景儒.多元空间信息统计分析计算机系统[J].遥感信息, 1998, 2:2-5.
[10]侯景儒,李飞跃.地质统计学(空间信息统计学)及其在地质勘查及找矿中的应用[J].冶金地质动态, 1997, 10:26-29.
[11]朱裕生.矿产预测理论—区域成矿学向矿产勘察延伸的理论体系[J].地质学报, 2006, 80(10):1518-1527.
[12]毕伏科,肖文暹,阎同生.成矿系列的缺位问题及其在成矿预测中的应用[J].矿床地质, 2006, 25(6):735-742.
[13]李裕伟,赵精满,李晨阳.基于GMS、DSS和GIS的潜在矿产资源评价方法[M].地震出版:2007, 7-10.
[14]张原庆,王世称等.地球化学信息在综合信息矿产预测中的应用[J].地学前缘, 2005, (3):323-324.
[15]《国家中长期科学和技术发展规划纲要》发布, http://news.xinhuanet. com/st/2006-02/09/content_4155229. htm ,浏览日期:2009.3.7,刷新日期:2006.2.9,责任编辑:陈淑君.
[16]国家科技计划进行调整能源等放首位.人民日报2006年01月13日第十一版,责任编辑:石希.
[17]刘承祚.地质专家系统与成矿预测[M].北京:地震出版社, 1999.
[18]王世称,叶水盛等.综合信息成矿系列预测专家系统[M].长春出版社, 1999.
[19]美国地质调查局.美国本土矿产资源评价计划系列报告之一[M].地理信息系统及其在地学领域中的应用译文集,地矿部科技司计算机办公室, 1993.
[20]李新中,赵鹏大,胡光道.基于规则知识表示的模型单元选择专家系统的实现[J].地球科学-中国地质大学学报, 1995, 20(2):173-178.
[21]美国地质调查局.美国本土矿产资源评价计划系列报告之二[M].地理信息系统及其在地学领域中的应用译文集,地矿部科技司计算机办公室, 1993.
[22]刘驰.地理信息系统(GIS)在矿产资源评价中的应用[J].辽宁地质. 1999, 16(3):234-237.
[23]朱创业.地理信息系统在矿产预测中的应用—以华蓥山锶矿带为例[J].成都大学学报:自然科学版, 1999, 18(4):36-38.
[24]矫东风,吕新彪.基于GIS空间分析的成矿预测[J].地质找矿论丛, 2003, 18(4):269-274.
[25]赵鹏大,胡旺亮,李紫金.矿床统计预测(第二版)[M].北京:地质出版社, 1994.
[26]刘安洲,范兴业,刘少华.成矿信息论与大比例尺矿产靶区定量预测[M].长春:吉林大学出版社, 1991:182-187.
[27]Pohl C., Van Genderen J. L., Multisensor image fusion in remote sensing: concepts. Methods and applications International Journal of Remote Sensing [J]. 1998, 19(5): 823-854.
[28] P. Paatero, U. Tapper, Positive Matrix Factorization: A non-negative factor model with optimal utilization of error estimates of data values [J]. Environ metrics, 1994, 5:111-126.
[29]D. Lee, H. S. Seung, Unsupervised learning by convex and conic coding [J]. Advances in Neural Information Processing Systems, 1997, 9:515-521.
[30]D. Lee, H. S. Seung, learning the parts of objects by non-negative matrix factorization [J], Nature, 1999, 401:788-791.
[31]Luo. R. C., Michael G. K. Edited. Multi-sensor Integration and Fusion for Intelligent Machines and Systems [M]. Ablex Publishing Corporation, 1995.
[32]卢进军,杨杰,梁栋等,基于非负矩阵分解的相关反馈图像检索算法[J].上海交通大学学报, 2005, 39(4):578-581.
[33]Dong Liang, Jie Yang, Yuchou Chang, Supervised Non-negative Matrix Factorization Based Latent Semantic Image Indexing [J]. chinese optics letters, 2006, 4(5):272-274.
[34]Lee J S, Lee D, Choi S, ET.al., Non-negative matrix factorization of dynamic images in nuclear medicine[C]. Proceedings of IEEE Nuclear Science Symposium Conference Record, San Diego, California, 2001, 4:2027-2030.
[35]Sajda P., Du S., Brown T. R., ET.al., Nonnegative matrix factorization for rapid recovery of constituent spectra in magnetic resonance chemical shift imaging of the brain[C]. IEEE Transactions on Medical Imaging, 2004, 23(12):1453-1465.
[36]Xiaoxiang Wang, Jie Tian, Xingfeng Li, ET. al., Detecting brain activations by constrained non-negative matrix factorization from task-related BOLD fMRI [C]. Proceedings of the SPIE - The International Society for Optical Engineering, 2004, 5369(1):675-682.
[37]Yuan Gao, George Church, Improving molecular cancer class discovery through sparsenon-negative matrix factorization [J]. Bioinformatics, 2005, 21(21):3970-3975.
[38]A. Pascual-Montano, F. Tirado, P. Carmona-Sáez, ET. al., Two-way clustering of gene expression profiles by sparse matrix factorization[C]. 2005 IEEE Computational Systems Bioinformatics Conference - Workshops (CSBW'05), 2005, 103-104.
[39]Shahnaz, Farial, Berry, Michael W., Pauca V. Paul, Plemmons, Robert J. Document clustering using nonnegative matrix factorization [J]. Information Processing and Management March, 2006, 42(2):373-386.
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