Ryoichi Kouda

Application of a feedforward neural network in the search for Kuroko deposits in the Hokuroku district, Japan

A feedforward neural network with one hidden layer and five neurons was trained to recognize the distance to kuroko mineral deposits. Average amounts per hole of pyrite, sericite, and gypsum plus anhydrite as measured by X-rays in 69 drillholes were used to train the net. Drillholes near and between the Fukazawa, Furutobe, and Shakanai mines were used. The training data were selected carefully to represent well-explored areas where some confidence of the distance to ore was assured. A logarithmic transform was applied to remove the skewness of distance and each variable was scaled and centered by subtracting the median and dividing by the interquartile range. The learning algorithm of annealing plus conjugate gradients was used to minimize the mean squared error of the scaled distance to ore. The trained network then was applied to all of the 152 drillholes that had measured gypsum, sericite, and pyrite. A contour plot of the neural net predicted distance to ore shows fairly wide areas of 1 km or less to ore; each of the known deposit groups is within the 1 km contour. The high and low distances on the margins of the contoured distance plot are in part the result of boundary effects of the contouring algorithm. For example, the short distances to ore predicted west of the Shakanai (Hanaoka) deposits are in basement. However, the short distances to ore predicted northeast of Furotobe, just off the figure, coincide with the location of the Nurukawa kuroko deposit and the Omaki deposit, south of the Shakanai-Hanaoka deposits, seems to be on an extension of short distance to ore contour, but is beyond the 3 km limit from drillholes. Also of interest are some areas only a few kilometers from the Fukazawa and Shakanai groups of deposits that are estimated to be many kilometers from ore, apparently reflecting the networks recognition of the extreme local variability of the geology near some deposits.

A comparison of the weights-of-evidence method and probabilistic neural networks

The need to integrate large quantities of digital geoscience information to classify locations as mineral deposits or nondeposits has been met by the weights-of-evidence method in many situations. Widespread selection of this method may be more the result of its ease of use and interpretation rather than comparisons with alternative methods. A comparison of the weights-of-evidence method to probabilistic neural networks is performed here with data from Chisel Lake-Andeson Lake, Manitoba, Canada. Each method is designed to estimate the probability of belonging to learned classes where the estimated probabilities are used to classify the unknowns. Using these data, significantly lower classification error rates were observed for the neural network, not only when test and training data were the same (0.02 versus 23%), but also when validation data, not used in any training, were used to test the efficiency of classification (0.7 versus 17%). Despite these data containing too few deposits, these tests of this set of data demonstrate the neural networks ability at making unbiased probability estimates and lower error rates when measured by number of polygons or by the area of land misclassified. For both methods, independent validation tests are required to ensure that estimates are representative of real-world results. Results from the weights-of-evidence method demonstrate a strong bias where most errors are barren areas misclassified as deposits. The weights-of-evidence method is based on Bayes rule, which requires independent variables in order to make unbiased estimates. The chi-square test for independence indicates no significant correlations among the variables in the Chisel Lake–Andeson Lake data. However, the expected number of deposits test clearly demonstrates that these data violate the independence assumption. Other, independent simulations with three variables show that using variables with correlations of 1.0 can double the expected number of deposits as can correlations of −1.0. Studies done in the 1970s on methods that use Bayes rule show that moderate correlations among attributes seriously affect estimates and even small correlations lead to increases in misclassifications. Adverse effects have been observed with small to moderate correlations when only six to eight variables were used. Consistent evidence of upward biased probability estimates from multivariate methods founded on Bayes rule must be of considerable concern to institutions and governmental agencies where unbiased estimates are required. In addition to increasing the misclassification rate, biased probability estimates make classification into deposit and nondeposit classes an arbitrary subjective decision. The probabilistic neural network has no problem dealing with correlated variables—its performance depends strongly on having a thoroughly representative training set. Probabilistic neural networks or logistic regression should receive serious consideration where unbiased estimates are required. The weights-of-evidence method would serve to estimate thresholds between anomalies and background and for exploratory data analysis.

Some Simple Guides to Finding Useful Information in Exploration Geochemical Data

Most regional geochemistry data reflect processes that can produce superfluous bits of noise and, perhaps, information about the mineralization process of interest. There are two end-member approaches to finding patterns in geochemical data—unsupervised learning and supervised learning. In unsupervised learning, data are processed and the geochemist is given the task of interpreting and identifying possible sources of any patterns. In supervised learning, data from known subgroups such as rock type, mineralized and nonmineralized, and types of mineralization are used to train the system which then is given unknown samples to classify into these subgroups.To locate patterns of interest, it is helpful to transform the data and to remove unwanted masking patterns. With trace elements use of a logarithmic transformation is recommended. In many situations, missing censored data can be estimated using multiple regression of other uncensored variables on the variable with censored values.In unsupervised learning, transformed values can be standardized, or normalized, to a Z-score by subtracting the subsets mean and dividing by its standard deviation. Subsets include any source of differences that might be related to processes unrelated to the target sought such as different laboratories, regional alteration, analytical procedures, or rock types. Normalization removes effects of different means and measurement scales as well as facilitates comparison of spatial patterns of elements. These adjustments remove effects of different subgroups and hopefully leave on the map the simple and uncluttered pattern(s) related to the mineralization only.Supervised learning methods, such as discriminant analysis and neural networks, offer the promise of consistent and, in certain situations, unbiased estimates of where mineralization might exist. These methods critically rely on being trained with data that encompasses all populations fairly and that can possibly fall into only the identified populations.

Typing mineral deposits using their grades and tonnages in an artificial neural network

A test of the ability of a probabilistic neural network to classify deposits into types on the basis of deposit tonnage and average Cu, Mo, Ag, Au, Zn, and Pb grades is conducted. The purpose is to examine whether this type of system might serve as a basis for integrating geoscience information available in large mineral databases to classify sites by deposit type. Benefits of proper classification of many sites in large regions are relatively rapid identification of terranes permissive for deposit types and recognition of specific sites perhaps worthy of exploring further.Total tonnages and average grades of 1,137 well-explored deposits identified in published grade and tonnage models representing 13 deposit types were used to train and test the network. Tonnages were transformed by logarithms and grades by square roots to reduce effects of skewness. All values were scaled by subtracting the variables mean and dividing by its standard deviation. Half of the deposits were selected randomly to be used in training the probabilistic neural network and the other half were used for independent testing. Tests were performed with a probabilistic neural network employing a Gaussian kernel and separate sigma weights for each class (type) and each variable (grade or tonnage).Deposit types were selected to challenge the neural network. For many types, tonnages or average grades are significantly different from other types, but individual deposits may plot in the grade and tonnage space of more than one type. Porphyry Cu, porphyry Cu-Au, and porphyry Cu-Mo types have similar tonnages and relatively small differences in grades. Redbed Cu deposits typically have tonnages that could be confused with porphyry Cu deposits, also contain Cu and, in some situations, Ag. Cyprus and kuroko massive sulfide types have about the same tonnages. Cu, Zn, Ag, and Au grades. Polymetallic vein, sedimentary exhalative Zn-Pb, and Zn-Pb skarn types contain many of the same metals. Sediment-hosted Au, Comstock Au-Ag, and low-sulfide Au-quartz vein types are principally Au deposits with differing amounts of Ag.Given the intent to test the neural network under the most difficult conditions, an overall 75% agreement between the experts and the neural network is considered excellent. Among the largestclassification errors are skarn Zn-Pb and Cyprus massive sulfide deposits classed by the neuralnetwork as kuroko massive sulfides—24 and 63% error respectively. Other large errors are the classification of 92% of porphyry Cu-Mo as porphyry Cu deposits. Most of the larger classification errors involve 25 or fewer training deposits, suggesting that some errors might be the result of small sample size. About 91% of the gold deposit types were classed properly and 98% of porphyry Cu deposits were classes as some type of porphyry Cu deposit. An experienced economic geologist would not make many of the classification errors that were made by the neural network because the geologic settings of deposits would be used to reduce errors. In a separate test, the probabilistic neural network correctly classed 93% of 336 deposits in eight deposit types when trained with presence or absence of 58 minerals and six generalized rock types. The overall success rate of the probabilistic neural network when trained on tonnage and average grades would probably be more than 90% with additional information on the presence of a few rock types.

Introduction to Special Issue on the Symposium on the Application of Neural Networks to the Earth Sciences

Papers in this issue of Natural Resources Research are from the “Symposium on the Application of Neural Networks to the Earth Sciences,” held 20–21 August 2002 at NASA Moffet Field, Mountain View, California. The Symposium represents the Seventh International Symposium on Mineral Exploration (ISME-02). It was sponsored by the Mining and Materials Processing Institute of Japan (MMIJ), the US Geological Survey, the Circum-Pacific Council, and NASA. The ISME symposia have been held every two years in order to bring together scientists actively working on diverse quantitative methods applied to the earth sciences. Although the title, International Symposium on Mineral Exploration, suggests exclusive focus on mineral exploration, interests and presentations always have been wide-ranging—talks presented at this symposium are no exception.