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  • Articles  (13)
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  • cluster analysis  (13)
  • 2005-2009
  • 1975-1979  (13)
  • Geosciences  (13)
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  • Articles  (13)
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  • 1
    Electronic Resource
    Electronic Resource
    The sampling distribution of theW statistic of disjunction for the arbitrary division of a random rectangular distribution (1979)
    Springer
    Mathematical geology 11 (1979), S. 423-429 
    Details
    ISSN: 1573-8868
    Keywords: cluster analysis ; significance tests ; overlap measures
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The sampling distribution of the Wstatistic of disjunction has been estimated by Monte Carlo simulation for the case where the underlying distribution is a random rectangular (Poisson) variable that is divided into two groups at an arbitrary position. A transformation to sinh −1 log e Wgave a variable that was acceptably normal, and from this a simple approximation for the distribution is given, together with a diagram of confidence limits of Wfor this case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01029298
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  • 2
    Electronic Resource
    Electronic Resource
    Data manipulation in cluster analysis and the concept of zero presence (1978)
    Springer
    Mathematical geology 10 (1978), S. 335-345 
    Details
    ISSN: 1573-8868
    Keywords: cluster analysis ; ecology ; zero presence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A zero presence results from mathematical manipulation of a zero datum due to centering and normalizing the data for each site. Ecologically it can be interpreted as having the same importance as any other presence, where any presence results from the interaction of environmental factors.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01031738
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  • 3
    Electronic Resource
    Electronic Resource
    An empirical assessment and illustration of some multivariate morphometric techniques (1978)
    Springer
    Mathematical geology 10 (1978), S. 111-139 
    Details
    ISSN: 1573-8868
    Keywords: classification ; cluster analysis ; principal components ; morphometrics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract An artificial data set is used to illustrate the morphologic properties of some common multivariate techniques and consideration of three common situations. The first concerns a sample showing no obvious groupings. In this situation principal components (or coordinates) and factor analyses give a logical ordination of form variation; cluster analysis produces sizedominated groups. The second situation considers an homogeneous sample where size and shape have important implications. Principal components are tested for association with size and shape, both of which can be isolated if isometry exists; if allometry is present, isolation of shape is possible only by size elimination, e.g., conversion to ratios. The third situation examines a sample of unknown groupings in which shape variation is the only interest. Aside from ratios, two other methods which produce shape-dominant clusters are assessed. Some of the options available in cluster analysis are also examined.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01032861
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  • 4
    Electronic Resource
    Electronic Resource
    Deposit modeling of a nickel belt in Finland (1978)
    Springer
    Mathematical geology 10 (1978), S. 543-554 
    Details
    ISSN: 1573-8868
    Keywords: deposit modeling ; Ni−Cu deposits ; cluster analysis ; characteristic analysis ; factor analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Data from 34 Ni−Cu deposits of the 315c-striking, 420-km long, and 10–40-km wide Kotalahtinickel belt have been recorded in the previously described system of the Ore Data File of Finland. For comparison data from four Ni−Cu deposits outside the belt have been collected. The statistical treatment of the data begins with cluster analysis and four classes are distinguished on the basis of 303 data elements. These classes form eight groups within the linear belt. Two groups containing the largest deposits, Hitura and Kotalahti, are processed by characteristic analysis, and factor analysis is applied to test the interdependence of the characteristics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02461984
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  • 5
    Electronic Resource
    Electronic Resource
    A method for testing the distinctness of clusters: A test of the disjunction of two clusters in Euclidean space as measured by their overlap (1977)
    Springer
    Mathematical geology 9 (1977), S. 123-143 
    Details
    ISSN: 1573-8868
    Keywords: classification ; cluster analysis ; numerical taxonomy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A method is described for testing the distinctness of two clusters in Euclidean space. One first calculates the projections, q,of the N1 and N2 members of the clusters onto the line joining the cluster centroids. From the distributions of qan index of disjunction, W,is calculated, which corresponds to an index of overlap, VG.The quantity W√(N1+N2)is distributed as noncentral tsubject to assumptions on the multivariate normal distribution of the clusters. This allows a test of whether the observed disjunction is significantly greater than a chosen figure, which is equivalent to testing whether the overlap of the clusters is significantly less than a corresponding value of VG.Two clusters that appear distinct may be produced simply by the partitioning of a homogeneous swarm into two contiguous regions. Provided that the clusters form a dichotomy in a dendrogram, and that the clustering method yields geometrically convex clusters, a conservative test of this situation can be derived by determining the excess of Wover the value expected for a rectangular distribution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02312508
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  • 6
    Electronic Resource
    Electronic Resource
    Sequence in Australian coal seams (1976)
    Springer
    Mathematical geology 8 (1976), S. 529-547 
    Details
    ISSN: 1573-8868
    Keywords: cycles ; Markov processes ; cluster analysis ; time-trend analysis ; coal petrology ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract An embedded Markov model is used to test microlithotype analyses of subsections of a wide range of Australian coal seams for the presence of nonrandom sequences of lithologies. The data for individual seams, transformed to give five states (four states if dirt bands are excluded),were summed into geologically and geographically distinct groupings. The results suggest that dirt bands form an essential part of the sequences and that partial or complete cyclicity is present in many seam groupings. The cyclicity is either asymmetric or partially symmetric with the vitrite +clarite content of the coal decreasing upwards within each cycle. A new cycle is marked either by a sharp reversion, or by a slightly gradational reversion, to a vitrite +clariterich lithology. This reversion may or may not be preceded by a dirt band. In virtually all groupings, a vitrite +clarite-rich lithology is the most likely type after a dirt band. The sequences are similar to those that have been described in European coals and it seems probable that the presence of intraseam, cyclic sequences is a normal, rather than an unusual condition, within coal seams. This cyclicity is a response to changes in the sedimentation balance. These changes are probably due in large part to processes originating within the peat-forming environment but processes external to this environment are also likely to produce cyclic sequences of coal lithologies.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01042992
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  • 7
    Electronic Resource
    Electronic Resource
    Delineation and analysis of clusters in orientation data (1976)
    Springer
    Mathematical geology 8 (1976), S. 9-23 
    Details
    ISSN: 1573-8868
    Keywords: cluster analysis ; statistics ; numerical taxonomy ; structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract This paper presents a technique for (1) clustering orientation data with minimum constraint on resulting partitions, and (2) testing clusters against a probability distribution defined on the unit sphere which admits elliptical symmetry about its mean. The use of an objective function to highlight certain features of the data is discussed. The technique for delineation and analysis of clusters is applied to an example problem through use of a computer code.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01039681
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  • 8
    Electronic Resource
    Electronic Resource
    Implementation of criteria for partitioning a dendrogram (1976)
    Springer
    Mathematical geology 8 (1976), S. 75-84 
    Details
    ISSN: 1573-8868
    Keywords: classification ; cluster analysis ; entropy ; facies analysis ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Criteria have been suggested for the optimal partitioning of a dendrogram into sample clusters. The implementation of these criteria by means of statistical and graphical measures is considered for two dendrograms. It is shown that the optimization of criteria is conditioned by research aims.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01039686
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  • 9
    Electronic Resource
    Electronic Resource
    Binary coefficients: A theoretical and empirical study (1976)
    Springer
    Mathematical geology 8 (1976), S. 137-150 
    Details
    ISSN: 1573-8868
    Keywords: cluster analysis ; binary coefficients ; biostratigraphy ; paleoecology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Binary coefficients can be assigned to several categories on the basis of algebraic and conceptual properties. The phi coefficient of association is related algebraically to the chi-square statistic for 2-by-2 contingency tables, and use of this coefficient in cluster analysis permits the objective, nonarbitrary partitioning of objects among groups on the basis of previously selected levels of significant, positive association. Similarity, matching, and distance coefficients possess neither conceptual nor operational statistical meaning for many geological data sets. The weighted pair group method and flexible clustering strategy may give an overly conservative partitioning of objects among groups. Clustering by the unweighted pair group method, using the phi coefficient, is recommended for the analysis of biostratigraphic and paleoecologic presence—absence data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01079031
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  • 10
    Electronic Resource
    Electronic Resource
    A multivariate sedimentary environmental analysis of Great South Bay and South Oyster Bay, New York (1976)
    Springer
    Mathematical geology 8 (1976), S. 283-304 
    Details
    ISSN: 1573-8868
    Keywords: classification ; cluster analysis ; discriminant analysis ; ordination analysis ; grain size ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A multivariate statistical strategy for classifying paleoenvironments is effective for studying modern sedimentary processes in western Great South Bay and South Oyster Bay, New York. The 13 whole phi weight percent variables were tested for redundancy with R-mode cluster analysis. The samples were partitioned statistically into five environmentally significant facies using Q-mode cluster analysis: (A)sandy gravel, (B)sandy silt, (C)silty sand, (D)slightly gravelly sand, and (E)fine sand. An ordination depicted gradational relationships among the samples and the facies. It was used to evaluate the environmental and textural parameter gradients within the sample space. Interpretations obtained in this manner and by examination of the grain-size curves suggest that these sediments were deposited by waves and currents on beaches and in wave zones (facies C and E),shoal areas (facies B),and tidal channels (facies A and D).Tidal currents, wave action, and eelgrass control the distribution of sediments within the two bays.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01029274
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  • 11
    Electronic Resource
    Electronic Resource
    Analysis of multivariate point distributions and chemical grouping of rocks (1975)
    Springer
    Mathematical geology 7 (1975), S. 191-214 
    Details
    ISSN: 1573-8868
    Keywords: classification ; cluster analysis ; mapping ; multivariate analysis ; pattern recognition ; point-density analysis ; geochemistry ; ore-bearing districts
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Large sets of rock compositions can be grouped by the analysis of corresponding point distributions in multidimensional space, where the separate dimensions represent the chemical variables. The point density around each composition is estimated in a small, multivariate, rectangular interval. Establishment of the identity of specimens contained in the interval, and systematic comparison of the point densities surrounding each of them, leads to the recognition of density maxima, which represent the statistical modes of the rock types present in the set. The remaining specimens by the same operations can be assigned to the groups formed. Experimental results are given for two sets, one comprising a wide variety of metasedimentary and metavolcanic rocks from the ore-bearing Skellefte district and adjacent parts of Västerbotten, Sweden, and the other representing a less variable population of basic rocks from Norrbotten, Sweden. Linear discriminant analysis and existing geological information indicate that the groups obtained are statistically and geologically valid.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02312721
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  • 12
    Electronic Resource
    Electronic Resource
    A method of analyzing polymodal distributions in orientation data (1975)
    Springer
    Mathematical geology 7 (1975), S. 285-293 
    Details
    ISSN: 1573-8868
    Keywords: cluster analysis ; data processing ; orientation data ; statistics ; structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A method of cluster analysis for orientation data is described. The method enables vector statistics to be applied to polymodal distributions. Similar results to those found by modal analysis are obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02081702
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  • 13
    Electronic Resource
    Electronic Resource
    Comparison of automatic classification methods applied to lake geochemical samples (1975)
    Springer
    Mathematical geology 7 (1975), S. 237-266 
    Details
    ISSN: 1573-8868
    Keywords: R- and Q-mode analysis ; cluster analysis ; lake geochemistry
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Geochemical samples from part of Lake Geneva were analyzed for 29oxides and trace elements. The variables and samples were subjected to R- and Q-mode analyses. The following techniques were applied in sequence: data transformation (normalization and standardization), data reduction (principal component and factor analysis), and automatic classification (dendrograph). The data were treated using various combinations of these techniques, and the resulting classifications evaluated by means of several criteria. The best classification of the samples is given by a cluster analysis performed on four principal components computed from standardized variables. The discriminatory power of the variables also was measured and determined to depend on their degree of intercorrelation. As a final result, the 29original variables were reduced to four components and the sediment samples classified into four facies, leading to easily interpretable geochemical maps.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02312723
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