Artificial Neural Networks for Mineral-Potential Mapping: A Case Study from Aravalli Province,Western India

This paper describes a GIS-based application of a radial basis functional link net (RBFLN) to map the potential of SEDEX-type base metal deposits in a study area in the Aravalli metallogenic province (western India). Available public domain geodata of the study area were processed to generate evidential maps, which subsequently were encoded and combined to derive a set of input feature vectors. A subset of feature vectors with known targets (i.e., either known mineralized or known barren locations) was extracted and divided into (a) a training data set and (b) a validation data set. A series of RBFLNs were trained to determine the network architecture and estimate parameters that mapped the maximum number of validation vectors correctly to their respective targets. The trained RBFLN that gave the best performance for the validation data set was used for processing all feature vectors. The output for each feature vector is a predictive value between 1 and 0, indicating the extent to which a feature vector belongs to either the mineralized or the barren class. These values were mapped to generate a predictive classification map, which was reclassified into a favorability map showing zones with high, moderate and low favorability for SEDEX-type base metal deposits in the study area. The method demarcates successfully high favorability zones, which occupy 6% of the study area and contain 94% of the known base metal deposits.     

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 subset's 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.     

A Comparative Analysis of Favorability Mappings by Weights of Evidence,Probabilistic Neural Networks,Discriminant Analysis,and Logistic Regression

This study compares the performance of favorability mappings by weights of evidence (WOE), probabilistic neural networks (PNN), logistic regression (LR), and discriminant analysis (DA). Comparisons are made by an objective measure of performance that is based on statistical decision theory. The study further emphasizes out-of-sample inference, and quantifies the extent to which outcome is influenced by optimum variable discretization with classification and regression trees (CARTS).Favorability mapping methodologies are evaluated systematically across three case studies with contrasting scale and geologic information:

Application of Discriminant Analysis and Support Vector Machine in Mapping Gold Potential Areas for Further Drilling in the Sari-Gunay Gold Deposit,NW Iran

In this contribution, we used discriminant analysis (DA) and support vector machine (SVM) to model subsurface gold mineralization by using a combination of the surface soil geochemical anomalies and earlier bore data for further drilling at the Sari-Gunay gold deposit, NW Iran. Seventy percent of the data were used as the training data and the remaining 30 % were used as the testing data. Sum of the block grades, obtained by kriging, above the cutoff grade (0.5 g/t) was multiplied by the thickness of the blocks and used as productivity index (PI). Then, the PI variable was classified into three classes of background, medium, and high by using fractal method. Four classification functions of SVM and DA methods were calculated by the training soil geochemical data. Also, by using all the geochemical data and classification functions, the general extension of the gold mineralized zones was predicted. The mineral prediction models at the Sari-Gunay hill were used to locate high and moderate potential areas for further infill systematic and reconnaissance drilling, respectively. These models at Agh-Dagh hill and the area between Sari-Gunay and Agh-Dagh hills were used to define the moderate and high potential areas for further reconnaissance drilling. The results showed that the nu-SVM method with 73.8 % accuracy and c-SVM with 72.3 % accuracy worked better than DA methods.     

Nitrogen mineralization potential in rewetted soils from a semi-arid stream landscape,north-west Australia

Drying-rewetting pulses stimulate nitrogen (N) mineralization in semi-arid systems and enhance N availability. Intermittent stream landscapes encompass a mosaic of soils of different textures and composition, and may support intense N transformation after rainfall. We modelled N mineralization potential by measuring accumulation of inorganic N (KCl extractable NO₃^? and NH₄⁺) in response to sustained flooding in soils from a small intermittent stream in semi-arid, north-west Australia. To test the relative importance of landscape position compared to flood pulse size, we incubated soils and sediments from six landscape positions, including three riparian vegetation types, rewetted to four different water potentials. Selected water potentials represented a light rain, heavy rain, single flood and successive flood event for the study site. The total amount of N mineralized was significantly affected by landscape position but not by saturation level. Riparian soils produced the greatest mineralization flush – over 70% of the total amount of N mineralized accumulated within 48 h of rewetting – however there was no difference among riparian vegetation types in N mineralization potential. N mineralized was a half to two-thirds lower in channel, floodplain and bank soils in comparison with riparian soils. We conclude that in systems subject to prolonged drought, N mineralization is predominantly determined by soil characteristics rather than the size of the rewetting pulse.     

Comparing models of debris-flow susceptibility in the alpine environment

Debris-flows are widespread in Val di Fassa (Trento Province, Eastern Italian Alps) where they constitute one of the most dangerous gravity-induced surface processes. From a large set of environmental characteristics and a detailed inventory of debris flows, we developed five models to predict location of debris-flow source areas. The models differ in approach (statistical vs. physically-based) and type of terrain unit of reference (slope unit vs. grid cell). In the statistical models, a mix of several environmental factors classified areas with different debris-flow susceptibility; however, the factors that exert a strong discriminant power reduce to conditions of high slope-gradient, pasture or no vegetation cover, availability of detrital material, and active erosional processes. Since slope and land use are also used in the physically-based approach, all model results are largely controlled by the same leading variables.Overlaying susceptibility maps produced by the different methods (statistical vs. physically-based) for the same terrain unit of reference (grid cell) reveals a large difference, nearly 25% spatial mismatch. The spatial discrepancy exceeds 30% for susceptibility maps generated by the same method (discriminant analysis) but different terrain units (slope unit vs. grid cell). The size of the terrain unit also led to different susceptibility maps (almost 20% spatial mismatch). Maps based on different statistical tools (discriminant analysis vs. logistic regression) differed least (less than 10%). Hence, method and terrain unit proved to be equally important in mapping susceptibility.Model performance was evaluated from the percentages of terrain units that each model correctly classifies, the number of debris-flow falling within the area classified as unstable by each model, and through the metric of ROC curves. Although all techniques implemented yielded results essentially comparable; the discriminant model based on the partition of the study area into small slope units may constitute the most suitable approach to regional debris-flow assessment in the Alpine environment.     

Radial Basis Function Network for Ore Grade Estimation

This paper highlights the performance of a radial basis function (RBF) network for ore grade estimation in an offshore placer gold deposit. Several pertinent issues including RBF model construction, data division for model training, calibration and validation, and efficacy of the RBF network over the kriging and the multilayer perceptron models have been addressed in this study. For the construction of the RBF model, an orthogonal least-square algorithm (OLS) was used. The efficacy of this algorithm was testified against the random selection algorithm. It was found that OLS algorithm performed substantially better than the random selection algorithm. The model was trained using training data set, calibrated using calibration data set, and finally validated on the validation data set. However, for accurate performance measurement of the model, these three data sets should have similar statistical properties. To achieve the statistical similarity properties, an approach utilizing data segmentation and genetic algorithm was applied. A comparative evaluation of the RBF model against the kriging and the multilayer perceptron was then performed. It was seen that the RBF model produced estimates with the R ² (coefficient of determination) value of 0.39 as against of 0.19 for the kriging and of 0.18 for the multilayer perceptron.     

Mineral Prospectivity Prediction from High-Dimensional Geoscientific Data Using a Similarity-Based Density Estimation Model

Assuming a study region in which each cell has associated with it an N-dimensional vector of values corresponding to N predictor variables, one means of predicting the potential of some cell to host mineralization is to estimate, on the basis of historical data, a probability density function that describes the distribution of vectors for cells known to contain deposits. This density estimate can then be employed to predict the mineralization likelihood of other cells in the study region. However, owing to the curse of dimensionality, estimating densities in high-dimensional input spaces is exceedingly difficult, and conventional statistical approaches often break down. This article describes an alternative approach to estimating densities. Inspired by recent work in the area of similarity-based learning, in which input takes the form of a matrix of pairwise similarities between training points, we show how the density of a set of mineralized training examples can be estimated from a graphical representation of those examples using the notion of eigenvector graph centrality. We also show how the likelihood for a test example can be estimated from these data without having to construct a new graph. Application of the technique to the prediction of gold deposits based on 16 predictor variables shows that its predictive performance far exceeds that of conventional density estimation methods, and is slightly better than the performance of a discriminative approach based on multilayer perceptron neural networks.     

Mapping Mineralization Probabilities using Multilayer Perceptrons

Mineral-potential mapping is the process of combining a set of input maps, each representing a distinct geo-scientific variable, to produce a single map which ranks areas according to their potential to host mineral deposits of a particular type. The maps are combined using a mapping function that must be either provided by an expert (knowledge-driven approach), or induced from sample data (data-driven approach). Current data-driven approaches using multilayer perceptrons (MLPs) to represent the mapping function have several inherent problems: they are highly sensitive to the selection of training data; they do not utilize the contextual information provided by nondeposit data; and there is no objective interpretation of the values output by the MLP. This paper presents a new approach by which MLPs can be trained to output values that can be interpreted strictly as representing posterior probabilities. Other advantages of the approach are that it utilizes all data in the construction of the model, and thus eliminates any dependence on a particular selection of training data. The technique is applied to mapping gold mineralization potential in the Castlemaine region of Victoria, Australia, and results are compared with a method based on estimating probability density functions.     

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 network's 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.     

Using geovisual analytics to compare the performance of geographically weighted discriminant analysis versus its global counterpart,linear discriminant analysis

Geographically weighted spatial statistical methods are a family of spatial statistical methods developed to address the presence of non-stationarity in geographical processes, the so-called spatial heterogeneity. While these methods have recently become popular for analysis of spatial data, one of their characteristics is that they produce outputs that in themselves form complex multi-dimensional spatial data sets. Interpretation of these outputs is therefore not easy, but is of high importance, since spatial and non-spatial patterns in the results of these methods contain clues to causes of underlying non-stationarity. In this article, we focus on one of the geographically weighted methods, the geographically weighted discriminant analysis (GWDA), which is a method for prediction and analysis of categorical spatial data. It is an extension of linear discriminant analysis (LDA) that allows the relationship between the predictor variables and the categories to vary spatially. This produces a very complex data set of GWDA results, which include on top of the already complex discriminant analysis outputs (e.g. classifications and posterior probabilities) also spatially varying outputs (e.g. classification function parameters). In this article, we suggest using geovisual analytics to visualise results from LDA and GWDA to facilitate comparison between the global and local method results. For this, we develop a bespoke visual methodology that allows us to examine the performance of global and local classification method in terms of quality of classification. Furthermore, we are also interested in identifying the presence (or absence) of non-stationarity through comparison of the outputs of both methods. We do this in two ways. First, we visually explore spatial autocorrelation in both LDA and GWDA misclassifications. Second, we focus on relationships between the classification result and the independent variables and how they vary over space. We describe our visual analytic system for exploration of LDA and GWDA outputs and demonstrate our approach on a case study using a data set linking election results with a selection of socio-economic variables.     

Supergene and exotic Cu mineralization occur during periods of landscape stability in the Centinela Mining District,Atacama Desert

The Centinela Mining District (CMD), Atacama Desert (northern Chile), includes several mid‐late Eocene porphyry Cu deposits that contains supergene mineralization and provides access to a record of gravel deposits that host syn‐sedimentary exotic Cu mineralized bodies. By studying these gravels, we reconstruct the unroofing history and constrain the geomorphological conditions that produced supergene and exotic Cu mineralization. We present an integrated study based on stratigraphic and sedimentological data, lithology clast counts, ⁴⁰Ar/³⁹Ar and U/Pb ages from interbedded tuff layers and U/Pb detrital zircon geochronology data. To relate the gravel deposition episodes to the timing of the supergene mineralization, we provide in‐situ and exotic supergene mineral ages (40Ar/39Ar and K‐Ar). Six gravel units were deposited between the mid‐Eocene and the mid‐Miocene. The Esperanza gravels were deposited concurrently with the emplacement of porphyry Cu deposits at depth. The subsequent Tesoro I, II and III and Atravesado gravels register the unroofing of these deposits, from the advanced argillic zone to the sericitic and prophylitic hypogene zones. The Arrieros gravels register landscape pediplanation, that is, denudational removal and wear of the landscape to base level on a relatively stable tectonic regime, occurring roughly contemporaneous with supergene activity. The supergene mineral ages of the CMD define a time span (ca. 25–12 Ma) during which most of the supergene ages cluster in northern Chile. This time span corresponds with a period of warm and humid climate conditions in the southern hemisphere. We conclude that landscape pediplanation favours supergene mineralization and helps preserve the former supergene mineralized zones from significant erosion. Low erosion rates during pediplanation may constitute a necessary condition for the efficiency of the supergene processes in such semi‐arid climate.     

Application of Artificial Neural Network for Gold–Silver Deposits Potential Mapping: A Case Study of Korea

The aim of this study is to analyze hydrothermal gold–silver mineral deposits potential in the Taebaeksan mineralized district, Korea, using an artificial neural network (ANN) and a geographic information system (GIS) environment. A spatial database considering 46 Au and Ag deposits, geophysical, geological, and geochemical data was constructed for the study area using the GIS. The geospatial factors were used with the ANN to analyze mineral potential. The Au and Ag mineral deposits were randomly divided into a training set (70%) to analyze mineral potential using ANN and a test set (30%) to validate predicted potential map. Four different training datasets determined from likelihood ratio and weight of evidence models were applied to analyze and validate the effect of training. Then, the mineral potential index (MPI) was calculated using the trained back-propagation weights, and mineral potential maps (MPMs) were constructed from GIS data for the four training cases. The MPMs were then validated by comparison with the test mineral occurrences. The validation results gave respective accuracies of 73.06, 73.52, 70.11, and 73.10% for the training cases. The comparison results of some training cases showed less sensitive to training data from likelihood ratio than weight of evidence. Overall, the training cases selected from 10% area with low and high index value of MPM_L and MPM_W gave higher accuracy (73.52 and 73.10%) for MPMs than those (73.06 and 70.11%, respectively) from known deposits and 10% area with low index value of MPI_L and MPI_W.     

科尔沁沙地不同生境土壤氮矿化/硝化作用研究

利用顶盖埋管原位培育法测定了科尔沁沙地不同生境（丘间低地、固定、半固定、半流动和流动沙丘）土壤氮素矿化/硝化速率的月际动态及净矿化/硝化量。结果表明：①沙地土壤无机氮主要以NO^-₃-N的形式存在,各类生境土壤NH⁺₄-N平均含量比NO^-₃-N低58.2%~79.7%;②土壤氮素矿化/硝化速率随植被与土壤条件的恶化呈现递减的趋势,从丘间低地到流动沙丘,净矿化速率分别为61.0、43.4、29.1、5.3 mg·m^-2·d^-1和2.7 mg·m^-2·d^-1,净硝化速率分别为61.8、46.2、30.1、6.2 mg·m^-2·d^-1和3.4 mg·m-2·d-1;③从丘间低地到固定、半固定、半流动和流动沙丘,矿化氮总量分别减少28.8%、52.3%、91.4%和95.5%,硝化总量分别减少25.3%、51.3%、90.0%和94.5%;④不同类型生境土壤净硝化氮占净矿化氮的比例都为100%,表明沙地土壤中植物可利用氮素易于淋溶或氨挥发损失。     

温度对武夷山不同海拔土壤有机碳矿化的影响

采用碱吸收法测定武夷山不同海拔土壤分别在15℃、25℃、35℃下培养35d时土壤有机碳矿化速率及矿化量的变化．结果表明,土壤有机碳矿化速率随培养时间延长而逐渐降低,尤以培养3d～7d时下降最为明显．各海拔土壤累积矿化量均随培养温度升高而逐渐增加．培养35d时15℃和35℃下土壤累积矿化量随海拔升高而增加,但25℃下黄红壤的累积矿化量高于红壤和黄壤而低于山地草甸土．各培养温度下,土壤有机碳平均矿化速率均以山地草甸土最高,红壤最低．而对于各海拔土壤,不同温度下土壤有机碳平均矿化速率大小顺序为：15℃〈25℃〈35℃．培养3d时温度为15℃／25℃黄壤的Q10值显著高于其他海拔土壤（P〈0．05）,但培养35d时15℃／25℃下的土壤Q10值以黄红壤的最高．培养3d和35d时,25℃／35℃下不同海拔土壤Q10值差异均不显著（P〉0．05）．根据土壤平均矿化速率计算的Q10值在温度范围为15℃／25℃时以黄壤的最高,但25℃／35℃时红壤的Q10值最大．     

Mineral-Potential Mapping for MVT Deposits with Limited Data Sets Using Landsat Data and Geological Evidence in the Borden Basin, Northern Baffin Island, Nunavut, Canada

Posterior probabilities of occurrence for Zn-Pb Mississippi Valley Type (MVT) mineralization were calculated based on evidence maps derived from regional geology, Landsat-TM, RADARSAT-1, a digital elevation model and aeromagnetic data sets in the Borden Basin of northern Baffin Island, Canada. The vector representation of geological contacts and fault traces were refined according to their characteristics identified in Landsat-TM, RADARSAT-1, DEM, slope, aspect, and shaded relief data layers. Within the study area, there is an association between the occurrence of MVT mineralization and proximity to the contact of platformal carbonates and shale units of the adjacent geological formation. A spatial association also tends to exist between mineralization and proximity to E-W and NW-SE trending faults. The relationships of known MVT occurrences with the geological features were investigated by spatial statistical techniques to generate evidence maps. Supervised classification and filtering were applied to Landsat-TM data to divide the Society Cliffs Formation into major stratigraphic subunits. Because iron oxides have been observed at some of the MVT occurrences within the Borden Basin, Landsat-TM data band ratio (3/1) was calculated to highlight the potential presence of iron-oxides as another evidence map. Processed Landsat-TM data and other derived geological evidence maps provided useful indicators for identifying areas of potential MVT mineralization. Weights of evidence and logistic regression were used independently to integrate and generate posterior probability maps showing areas of potential mineralization based on all derived evidence maps. Results indicate that in spite of the lack of important data sets such as stream or lake sediment geochemistry, Landsat-TM data and regional geological data can be useful for MVT mineral-potential mapping.     

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 variable's 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.     

Classification of mineral deposits into types using mineralogy with a probabilistic neural network

In order to determine whether it is desirable to quantify mineral-deposit models further, a test of the ability of a probabilistic neural network to classify deposits into types based on mineralogy was conducted. Presence or absence of ore and alteration mineralogy in well-typed deposits were used to train the network. To reduce the number of minerals considered, the analyzed data were restricted to minerals present in at least 20% of at least one deposit type. An advantage of this restriction is that single or rare occurrences of minerals did not dominate the results. Probabilistic neural networks can provide mathematically sound confidence measures based on Bayes theorem and are relatively insensitive to outliers. Founded on Parzen density estimation, they require no assumptions about distributions of random variables used for classification, even handling multimodal distributions. They train quickly and work as well as, or better than, multiple-layer feedforward networks. Tests were performed with a probabilistic neural network employing a Gaussian kernel and separate sigma weights for each class and each variable. The training set was reduced to the presence or absence of 58 reported minerals in eight deposit types. The training set included: 49 Cyprus massive sulfide deposits; 200 kuroko massive sulfide deposits; 59 Comstock epithermal vein gold districts; 17 quartzalunite epithermal gold deposits; 25 Creede epithermal gold deposits; 28 sedimentary-exhalative zinc-lead deposits; 28 Sado epithermal vein gold deposits; and 100 porphyry copper deposits. The most common training problem was the error of classifying about 27% of Cyprus-type deposits in the training set as kuroko. In independent tests with deposits not used in the training set, 88% of 224 kuroko massive sulfide deposits were classed correctly, 92% of 25 porphyry copper deposits, 78% of 9 Comstock epithermal gold-silver districts, and 83% of six quartzalunite epithermal gold deposits were classed correctly. Across all deposit types, 88% of deposits in the validation dataset were correctly classed. Misclassifications were most common if a deposit was characterized by only a few minerals, e.g., pyrite, chalcopyrite,and sphalerite. The success rate jumped to 98% correctly classed deposits when just two rock types were added. Such a high success rate of the probabilistic neural network suggests that not only should this preliminary test be expanded to include other deposit types, but that other deposit features should be added     

STEPWISE CANONICAL DISCRIMINANT ANALYSIS OF CONTINUOUS DIGITALIZED SIGNALS:APPLICATION TO CHROMATOGRAMS OF WHEAT PROTEINS

Continuous digitalized signals such as spectra,electrophoregrams or chromatograms generally have alarge number of data points and contain redundant information.It is therefore troublesome performingdiscriminant analysis without any preliminary selection of variables.A procedure for the application ofcanonical discriminant analysis(CDA)on this kind of data is studied.CDA can be presented as asuccession of two principal component analyses(PCAs).The first is performed directly on the raw dataand gives PC scores.The second is applied on the gravity centres of each qualitative group assessed onthe normalized PC scores.A stepwise procedure for selection of the relevant PC scores is presented.Themethod has been tested on an illustrative collection of 165 size-exclusion high-performance(SE-HPLC)chromatograms of proteins of wheat belonging to 55 genotypes and grown in three locations.Thediscrimination of the growing locations was performed using seven to nine PC scores and gave more than86% accurate classifications of the samples both in the training sets and the verification sets.Thegenotypes were also rather well identified,with more than 85% of the samples correctly classified.Thestudied method gives a way of assessing relevant mathematical distances between digitalized signalsaccording to qualitative knowledge of the samples.     

INFLUENCES ON COUNTY FARMLAND PROTECTION EFFORTS IN CALIFORNIA: A DISCRIMINANT ANALYSIS*

County-level policies and programs to conserve farmland in California are examined through discriminant analysis. Based on 1981 state planning data, four degrees of farmland protection effort are established. A two-function discriminant analysis using 17 agricultural, socioeconomic, and political-ideological variables correctly predicts the fourfold classification of 88 percent of the counties. The propensity to enact protective actions is associated with the intensity of agricultural development, local government spending and taxing practices, demographic characteristics, ideological and political party voting traditions.