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A new algorithm has been developed by J. W. Sammon for the nonlinear-point mapping of high-dimensional data in two dimensions such that the inherent structure of the data is approximately preserved. This paper describes results using several sets of geologic data including stratigraphic thickness, petrographic modal analysis, and morphological or geochemical measurements. Comparisons are made with hierarchical cluster analysis using dendrogram representation. Initial results are encouraging and suggest that the technique could have widespread geological applications. [ABSTRACT FROM AUTHOR]

This paper presents a technique for evaluating the similarity of ore deposits utilizing several geological variables. Information on tungsten mines in North America, taken from published literature, was used for a cluster analysis to group samples according to their similarity based on a simple matching coefficient. It was possible to interpret and evaluate different ore environments that clustered according to age, mineralogy, and other variables. Cluster analysis may be important in mineral exploration where considerable amounts of data are available for analysis. Subtle relationships that might be overlooked because the data are too voluminous can be isolated using this technique. It also can be used to establish exploration priority in unknown areas on the basis of similarity to known metallogenetic provinces. [ABSTRACT FROM AUTHOR]

This paper embodies petrographical and statistical investigations of three gabbro occurrences. The Mangaon and Kunkeri gabbros are similar in petrography and petrochemistry, whereas they are completely different from the Vajrat gabbro. Application of recently developed statistical tests help in classifying these gabbros by using three oxides, CaO, FeO, and KO. This study shows that the evolution of the Mangaon and Kunkeri gabbros probably proceeded along different lines as compared to the Vajrat gabbro. [ABSTRACT FROM AUTHOR]

Copyright of Archiv für Psychiatrie und Nervenkrankheiten is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Factor analysis utilizing textural data from 81 bottom samples was used to analyze the surficial sediments covering a 40,000-sq km area, which is one input data point per 500 km. On the other hand, the surficial geology of the area studied is complex as some map units are only 1 km wide in places. Under these circumstances it is interesting to determine that factor analysis nonetheless aims toward a reasonable geological solution. If the premise is accepted that factor analysis provides a solution 'best-fitted' to the data, the geologist has carried his research one step further and is left with the problem of interpreting the results of factor analysis correctly. In this experiment, the interpretation of the factors representing the gravel and the mud is relatively simple, although the two factors representing sands are more difficult to explain. The proper interpretation of factors leads naturally to an inquiry on the optimum number of factors to use, but this problem can be solved objectively by considering the factor loadings. [ABSTRACT FROM AUTHOR]

The article focuses on the effect of classification errors upon statistical inference. All data collected by census or a special sample survey contain errors of classification and that the goal of attaining complete accuracy is unattainable. This article undertakes to establish a model within which this problem can be discussed. It then uses this model to arrive at some principles which are worthy of consideration by those who conduct censuses and sample surveys. Classification errors occur when a response is made to a question, but there is an error either in the response or in its recording of such a nature that the person is placed in a different category from that in which he belongs. Those who are most tolerant of errors emphasize the surprising but widely observed phenomenon that errors of classification tend to cancel each other. The results obtained here suggest most strongly that the correlation of the errors in direction and degree can powerfully affect the inferences drawn. Second, these results underline and support the principle that it is of utmost importance to reduce not only net errors but also gross errors in all types of data-collecting because the pattern of association between gross errors has such a substantial effect upon inference.

The article presents information about a statistic for random model testing. Very often testing for the random model becomes important in the social sciences. For instance, if one has three categories of classification, he would be interested to know whether the chance of an individual falling into these categories is the same. Conventionally the test statistic used for this type of analysis is the contingency x2. Authors show here that the notion of variance, if applied to relative frequencies, yields a simple statistic for random model testing. Further-more, it is shown that the few statistic, viz. variance of relative frequencies, is related to the contingency x2. As indicated, the social scientist frequently encounters in his research the problem of testing for the random model as well as for the degree of dispersion of responses or other attributes of individuals and aggregates involving nominal data. The variance of relative frequencies can be of significant aid to the researcher in reducing his data to a convenient single measure expressing dispersion and a test for randomness. The following case should exemplify the utility of the statistic. One of the important dimensions of the division of labor in science including the social sciences, is the pattern of scientific foci or interest within different scientific disciplines.

The purpose of the article is to demonstrate how entropy and some theorems of the theory of information may be useful in the domain of classification, both for class formation and for class identification. Starting from a sample of subjects who have given different answers to a battery of tests or items, researchers see that there can be two kinds of approaches. Firstly, on the basis of entropy one can sort out the tests that have higher information content and on this basis form classes of subjects whose homogeneity can be appraised. In this case the problem is therefore to form a certain number of homogeneous classes with the minimum number of tests. Secondly, once the classification of subjects has been made, it is possible, according to the theory of information, to see whether the typical sequence of subjects of the different classes can be established also through fewer tests, being it then possible also to recognize a distance between the different classes. With this method researchers try to arrive at homogeneous classes on the basis of the smallest possible number of tests, that is in effect choosing variables with the greatest discriminating power.

Numerical methods for the examination of multivariate soil samples are presented in geometric terms. Techniques of coordinate representation by principal components, by nonmetric scaling, and by a new method are discussed, as are techniques for agglomerative hierarchic cluster analysis. These are illustrated by two sets of previously published data. [ABSTRACT FROM AUTHOR]

Copyright of Rock Mechanics (00357448) is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A multivariate analytical strategy is proposed for aiding the investigator in extracting maximum information from environmental data. Data are carefully coded and scaled and are tested for redundancy using R-mode cluster analysis. The samples are partitioned into environmental classes using Q-mode cluster analysis. Q-mode ordination facilitates interpretations, which usually can be verified by comparison with field relationships. Discriminant analysis serves as an identification procedure for extending the classification to unknown samples. The strategy is demonstrated by application to Cape Hatteras microorganism distributions and Devonian sedimentary facies. [ABSTRACT FROM AUTHOR]

Coefficients of association have been widely employed in cluster analysis. However, their use has been, for the most part, restricted to binary data. This limitation can be overcome by redefining positive and negative matches and mismatches in terms of minimum and maximum values of paired elements of parallel vector arrays. Rewriting the algorithms of coefficients of association with these new components gives the new 'quantified' coefficients general utility for binary, ordered multistate, and quantitative data, while retaining their original analytic properties. Quantified coefficients of association avoid several problems of shape and size that are associated with correlation coefficients and measures of Euclidean distance. However, when measuring similarity, quantified coefficients weight each attribute of an object by that attribute's magnitude. A related set of similarity indices termed 'mean ratios' is introduced; these indices give each attribute equal weight in all situations. Both quantified coefficients of association and mean ratios are related to a number of measures of similarity introduced to various fields of scientific research during the past 50 years. A review of this literature is included in an attempt to consolidate methodology and simplify nomenclature. [ABSTRACT FROM AUTHOR]

An iterative method of adaptive pattern recognition is used to allocate unclassified individuals to an a priori classification. The model is similar in form to a linear discriminant function, but the coefficient vector is determined by iteration. The method can be used with binary data, and with variables whose statistical distributions are not normal; it is therefore a useful technique for geologists. [ABSTRACT FROM AUTHOR]

Four generalizations are made. 1/ Despite the varying interpretations made by the respective authors, previous studies indicate that urban growth in Latin America is caused by both rural-urban migration and a positive rate of urban natural increase. Thus to ascribe Latin American urban growth to a single prime causal factor is a misleading oversimplification. 2/ Net in-migration apparently plays a larger role in determining the rate of growth of large metropolitan centers than is the case with smaller urban areas. 3/ A significant portion of urban growth in a given intercensal period may be attributed to the growth of localities previously too small to be classified as "urban". 4/ Urban natural increase is the weighted sum of the natural increase of in-migrants (after their arrival) and urban natives. Improper recognition of this last point may lead to an overstatement of the relative importance of urban natural increase as a component of urban growth. [ABSTRACT FROM AUTHOR]

This article presents information regarding classification in social science. Basically, a "modern" system of classification can be considered as the result of two kinds of choices: one, concerning how to classify objects, i.e., how to define "similarity" among objects, how to choose the discriminating criteria etc., the other, concerning the system to be chosen, i.e., what is the justification for our preference, etc. Furthermore, it should be said that these two problems can hardly be distinguished, since the one influences the other; and, while the first choice is probably relatively independent from the "history" of the systems of classification, the second one is the result, in a very weak sense, of an evolution of the systems themselves. In conclusion, it is important to point out that neither the evolution of the systems nor the choice concerning the way to define similarity among objects, happen to operate by themselves, they are both correlated and in a sense dependent on the specific "aims" that the classification is supposed to achieve.

The article focuses on a classification of marine microorganisms by numerical taxonomy. The role, which marine heterotrophic organisms play in the sea and in marine radiocontamination is very imperfectly understood, since, despite numerous attempts, it has not been possible to study more than a small fraction of the heterotrophic microorganisms present in the sea. This is due to the fact that in order to study the characteristics of heterotrophic microorganisms researchers have to study their metabolism characteristic, since there are not enough morphological features to classify them. Unfortunately at present no method is known which will enable researchers to culture all heterotrophic organisms present in the sea. In fact only 0.1% to 1% of the number of bacteria determined by direct microscopic counts can be cultivated in the laboratory. From the knowledge of this small fraction and from analogy to the function that bacteria perform in the terrestrial environment, researchers can assume that the function of the bacteria in the sea is mainly concerned with the mineralization of organic substances produced by marine organisms.

A simple, semiobjective method is described to reduce the number of groups in a classification to an arbitrary level without losing contact with the geologic information contained in the evolving groups. The method, operated in a stepwise or cyclic manner, employs some of the commonly used numerical techniques, but avoids strict adherence to them to obtain geologically more meaningful results. The method is illustrated in a facies study of the upper Paleozoic rocks of southeastern Utah. [ABSTRACT FROM AUTHOR]

Spatially distributed soil data possess a short-range erratic variation, an irregular longer range pattern, and maybe multivariate. In order to reveal a pattern or meaning in them, they are usually classified by drawing boundaries. A method is described for determining boundaries automatically on transects. A small portion of a sampled transect is taken and divided about its midpoint, and Mahalanobis' generalized distance, D or D, between the two halves calculated from the sample data. The procedure is repeated for portions of the same length at positions one-sampling interval apart along the transect. High peaks on the resultant series of D identify the boundaries. The length of portions is set equal to, or somewhat less than, the expected average distance between boundaries, and is determined by constructing correlograms of principal components. The lag distance over which fairly steady decay occurs is related closely to the distance between boundaries. The procedure is illustrated with data from a 6-km transect in Oxfordshire and shows good agreement with boundaries drawn by combined air-photo interpretation and field judgment. A means of extending the procedure to two dimensions is suggested. [ABSTRACT FROM AUTHOR]

The definition of objectives and question of interpretation must be considered when setting up data banks. The objective will determine the type of data to be collected. A hierarchy of data-processing systems exists where the amount of interpretation in the data increases as the order of the system increases. The remarkable continuity of basic data can be embodied in the axiom: 'Any fundamental data free of interpretation cannot be discontinuous.' The measurement of space and time remain invariant for all orders of data systems and are essential for relating data containing various amounts of interpretation. In general, only basic data should be exchanged. Where this is not feasible the object described should be clearly defined in space and time. [ABSTRACT FROM AUTHOR]

Relative percentages of sand, silt, and clay from samples of the same till unit are not identical because of different lithologies in the source areas, sorting in transport, random variation, and experimental error. Random variation and experimental error can be isolated from the other two as follows. For each particle-size class of each till unit, a standard population is determined by using a normally distributed, representative group of data. New measurements are compared with the standard population and, if they compare satisfactorily, the experimental error is not significant and random variation is within the expected range for the population. The outcome of the comparison depends on numerical criteria derived from a graphical method rather than on a more commonly used one-way analysis of variance with two treatments. If the number of samples and the standard deviation of the standard population are substituted in a t-test equation, a family of hyperbolas is generated, each of which corresponds to a specific number of subsamples taken from each new sample. The axes of the graphs of the hyperbolas are the standard deviation of new measurements (horizontal axis) and the difference between the means of the new measurements and the standard population (vertical axis). The area between the two branches of each hyperbola corresponds to a satisfactory comparison between the new measurements and the standard population. Measurements from a new sample can be tested by plotting their standard deviation vs. difference in means on axes containing a hyperbola corresponding to the specific number of subsamples used. If the point lies between the branches of the hyperbola, the measurements are considered reliable. But if the point lies outside this region, the measurements are repeated. Because the critical segment of the hyperbola is approximately a straight line parallel to the horizontal axis, the test is simplified to a comparison between the means of the standard population and the means of the subsample. The minimum number of subsamples required to prove significant variation between samples caused by different lithologies in the source areas and sorting in transport can be determined directly from the graphical method. The minimum number of subsamples required is the maximum number to be run for economy of effort. [ABSTRACT FROM AUTHOR]