Fuzzy C-means Cluster Analysis Research Articles

Cyclostratigraphy and rock-magnetic investigation of the NRM signal in late Miocene palustrine-alluvial deposits of the Librilla section (SE Spain)

[1] We constructed a high-resolution time frame for the cyclic continental palustrine-alluvial section of Librilla (SE Spain) which covers the onset of the Messinian salinity crisis in the marine realm. The section was dated earlier by Garces et al. [1998], using magnetostratigraphy. We resampled part of the section that contained a reversed overprint in detail to refine the magnetostratigraphy and to investigate the behavior of the natural remanent magnetization (NRM) signal. The detailed sampling yielded a better constrained position of the upper reversal of Chron C3An.1n. By counting the number of cycles in C3An.1n and taking into account the duration of this Chron, we were able to show that the basic sedimentary cycles in Librilla reflect climatic precession. Subsequently, the sedimentary pattern was tuned to the summer insolation curve, providing a high-resolution time. Two intervals of complex NRM behavior were identified, showing normal and reversed overprints. The reversed overprints seemed to be restricted mainly to gray palustrine layers. The analysis of coercivity components revealed no difference between samples with overprints or real NRM directions. We performed fuzzy c-means cluster analysis on a geochemical data set to link magnetic behavior to geochemical proxies, resulting in a three-cluster model that roughly describes lithology. Remarkably, all the samples with a normal overprint belong to one particular cluster. The reversed overprints, however, do not show any relation to the cluster partition. We favor the explanation of Garces et al. [1998] that the reversed overprint would be related to the Messinian salinity crisis.

Identification of tumor tissue by FTIR spectroscopy in combination with positron emission tomography

A method is described for identifying tumor tissue by means of FTIR microspectroscopy and positron emission tomography (PET). Thin tissue sections of human squamous carcinoma from hypopharynx (FaDu) and human colon adenocarcinoma (HT-29) grown in nude mice were investigated. FTIR spectroscopic maps of the thin tissue sections were generated and evaluated by Fuzzy C-Means (FCM) clustering and principal component analysis (PCA). The processed data were reassembled into images and compared to stained tissue samples and to PET. Tumor tissue could successfully be identified by this FTIR microspectroscopic method, while it was not possible to accomplish this with PET alone. On the other hand, PET permitted the non-invasive screening for suspicious tissue inside the body, which could not be achieved by FTIR.

The application of fuzzy C-means cluster analysis and non-linear mapping to a soil data set for the detection of polluted sites

It is important to map the distribution of pollutants and to trace their sources to assess potential environmental hazard. The present work concerns the application of multivariate statistical methods to a soil data base from the province of Styria (Austria) to delineate polluted areas and to distinguish between different types of pollution. The soil data base comprised pedological, geochemical and geological data and was extended by magnetic susceptibility measurements to further test the suitability of magnetic susceptibility as a tracer for pollution. Topsoil data from 521 locations were analysed by fuzzy c-means cluster analysis and non-linear mapping. Robust cluster solutions grouped the database according to the geological background and the land use at the sampling sites. The extraction of information on heavy metal pollution appeared to be possible by analysing the geological units separately and reducing the variables to those indicative for the pollution. The link between magnetic susceptibility and the heavy metal content, which was too complex to be described by bivariate statistics, was revealed by the multivariate methods.

Roman bricks from the Lagoon of Venice: a chemical characterization with methods of multivariate analysis

From 18 archaeological sites of the Lagoon of Venice 75 bricks belonging to Roman and medieval building levels have been analysed. Chemical composition and geometric measures allow the characterization of a group of 24 Roman bricks of Imperial age. The group formed by means of fuzzy c-means cluster analysis applied on chemical data have been tested by principal component analysis and finally subjected to discriminant analysis to estimate the relative weights of original variables and classify new elements. Correlations among the data of the major chemical elements confirm the reliability of the complex of chemical data. The aim of this research was to obtain a chemical characterization of Roman bricks (and later, of the medieval ones) coming from the lagoon of Venice thus making it possible: 1) to recognize the age of a brick by means of its chemical analysis; 2) to date the layers of archaeological excavations or the ground where there are medieval building foundations by means of membership bricks; 3) to calculate the rate of local ground lowering in the elapsed years by the difference in level from one layer to another; 4) to estimate local rates of land subsidence by comparison with mean values already known.

Alkyldibenzofurans in terrestrial rocks: influence of organic facies and maturation

Dibenzofuran (DBF), dibenzothiophene (DBT), and phenanthrene (PHE) have been determined along with their methyl derivatives (MDBFs, MDBTs, MPs) in coals, carbonaceous shales, and mudstones of Lower Cretaceous to Upper Carboniferous ages from the Elmworth gas field (Canada) and from the Sakoa (Madagascar) and Ruhr coal (Germany) basins. The samples contained mainly terrestrial organic matter with thermal maturities in the 0.7–1.9% mean vitrinite reflectance (R r) range. The pronounced predominance of MDBFs over MDBTs in the Sakoa samples is typical of plant debris deposited in lacustrine swamp environments. Onset of intense MDBF generation occurs at fairly low rank (0.77% R r) as indicated by elevated concentrations of 50–120 μg MDBFs/g total organic carbon (TOC). Influences of lithology, organic matter type, and maturity on distributions of the target compounds were extracted from the molecular concentration data by multivariate statistical methods, such as Principal Components Analysis (PCA) and fuzzy c-means cluster analysis with nonlinear mapping (NLM). A specific source effect on 1-MDBT concentrations suggests that lichens contributed to the senescent coal-forming forest in the Sakoa coal basin. Alkyldibenzofurans hence are potential lichen biomarkers. MDBFs can be used as maturity indicators only beyond 1.0% R r where Ruhr coals displayed a distinct increase in the 1−/4−MDBF ratio.

A pseudo-Thellier relative palaeointensity record, and rock magnetic and geochemical parameters in relation to climate during the last 276 kyr in the Azores region

SUMMARY In the pseudo-Thellier method for relative palaeointensity determinations (Tauxe et al. 1995) the slope of the NRM intensity left after AF demagnetization versus ARM intensity gained at the same peak field is used as a palaeointensity measure. We tested this method on a marine core from the Azores, spanning the last 276 kyr. We compared the pseudo-Thellier palaeointensity record with the conventional record obtained earlier by Lehman et al. (1996), who normalized NRM by SIRM. The two records show similar features: intensity lows with deviating palaeomagnetic directions at 40‐45 ka and at 180‐190 ka. The first interval is associated with the Laschamps excursion, while the 180‐190 ka low represents the Iceland Basin excursion (Channell et al. 1997). The pseudo-Thellier method, in combination with a jackknife resampling scheme, provides error estimates on the palaeointensity. Spectral analysis of the rock magnetic parameters and the palaeointensity estimates shows orbitally forced periods, particularly 23 kyr for climatic precession. This suggests that palaeointensity is still slightly contaminated by climate. Fuzzy c-means cluster analysis of rock magnetic and geochemical parameters yields a seven-cluster model of predominantly calcareous clusters and detrital clusters. The clusters show a strong correlation with climate, for example samples from detrital clusters predominantly appear during rapid warming. Although both the pseudo-Thellier palaeointensity m a and fuzzy clusters show climatic influences, we have not been able to find an unambiguous connection between the clusters and m a .

Analysis and interpretation of infrared microscopic maps: Visualization and classification of skin components by digital staining and multivariate analysis

Four analytical methods have been applied to infrared microscopic maps of human skin which contained basal cell carcinoma tumors—namely, point spectroscopy, grayscale functional group mapping, digital staining, and fuzzy C-means (FCM) cluster analysis. Spectroscopic interpretation using point spectroscopy allowed discrimination between normal and tumor-bearing skin components. Functional group mapping provided information on the distribution of lipids, proteins, nucleic acids, and collagen within skin sections. While functional group mapping only allowed examination of one material (or a ratio of two materials) at a time, a new approach termed digital staining allowed visualization of the distribution of up to three materials at one time. Digital staining thus gave a more detailed understanding of the tissue section. Finally, application of FCM cluster analysis, a nonsubjective, unsupervised classification methodology, allowed us to group spectra into five distinct clusters, which correlated to distinct tissue components in skin. Tumor-bearing skin was clearly separated from normal skin. When different analytical methods are used in conjunction, a unique understanding of tissues can be obtained. Our results demonstrate that infrared microscopy has potential for the pathological diagnosis of skin tumors. © 1999 John Wiley & Sons, Inc. Biospectroscopy 5: 265–275, 1999

Distribution of Recent Benthic Foraminifera in the Southern Basin of the Venice Lagoon (Italy): Statistical Evaluation of Taxa Significance

The total benthic foraminiferal assemblage (living and dead) is analyzed for 95 samples collected in the southern basin of the Venice Lagoon [Chioggia Basin, Italy]. Quantitative results of the identified 48 species are statistically treated by correspondence analysis and Fuzzy c-means cluster analysis to define both the zonal environmental similarities (biotopes) and the faunal similarities (biofacies). In this lagoon basin, the biotopes delineate the area of marine influence, areas of mixed sea/lagoon, and zones of greater human impact that seem less heavily polluted with respect to the other two lagoon basins. The faunal similarities identified distinguish present sea and lagoon influences from the salt marsh assemblage, which are linked to the paleoenvironment. We show through statistical analyses that abundance is not the only factor governing the importance of the different taxa in defining biotopes. The important factor we found out is significance assumed as the ratio between abundance and distribution for both abundant and rare species. Results complete the knowledge on the present environmental condition of the Venice Lagoon and suggest limits of feasible simplifications to better define biotopes. These limits are given by the significant value of each taxon, which is greater, the smaller the equidistribution of the taxon itself.

Fuzzy C-means clustering and principal component analysis of time series from near-infrared imaging of forearm ischemia

Fuzzy C-means clustering and principal components analysis were used to analyze a temporal series of near-IR images taken of a human forearm during periods of venous outflow restriction and complete forearm ischemia. The principal component eigen-time course analysis provided no useful information and the principal component eigen-image analysis gave results that correlated poorly with anatomical features. The fuzzy C-means clustering analysis, on the other hand, showed distinct regional differences in the hemodynamic response and scattering properties of the tissue, which correlated well with the anatomical features of the forearm.

Analysis of Spectroscopic Imaging Data by Fuzzy C-Means Clustering

A novel method of analyzing spectroscopic imaging data is presented. A fuzzy C-means clustering algorithm has been applied to the analysis of near-infrared spectroscopic imaging data acquired with the combination of a CCD camera and a liquid crystal tunable filter. The use of fuzzy C-means clustering dramatically increased the information obtained from near-IR spectroscopic images and allowed for the detection of small subregions of the image that contained novel and unanticipated spectral features, without the need for a priori knowledge of the chemical composition of the sample. Two illustrative samples were analyzed, one comprised of four different inks printed on label paper and the other containing indocyanine green and human blood patches. The regions containing the different constituents were clearly demarcated and their mean spectra determined. The mean spectra of the second sample were shown to match those obtained using a scanning near-IR spectrometer. In addition to probing the spatial and spectral characteristics of the samples, the fuzzy C-means clustering analysis also helped improve the signal-to-noise ratio of the spectra.

Fuzzy c-means cluster analysis of early diagenetic effects on natural remanent magnetisation acquisition in a 1.1 Myr piston core from the Central Mediterranean

The influence of early diagenesis on the natural remanent magnetisation (NRM) in sediments from the Calabrian ridge (Central Mediterranean) is analysed with the help of fuzzy c-means (FCM) cluster analysis and non-linear mapping (NLM). The sediments are variably coloured: white, beige, purplish, greenish and grey layers occur with occasionally intercalated sapropels. The NRM acquired depends on both depositional conditions and diagenetic processes. To describe these, FCM was performed with χ in , ARM, CaCO 3, Ba, Mn and S as variables. An eight-cluster model was derived with the clusters belonging to two categories: one expressing mainly diagenetic processes, i.e. dissolution and precipitation, and the other expressing mainly depositional conditions. The impact of diagenesis on NRM acquisition is profound and not restricted to the close vicinity of the anoxic sapropelitic layers. As a consequence, the influence of diagenetic processes on the NRM should be thoroughly assessed when selecting samples, e.g. for the determination of the relative palaeointensity of the geomagnetic field. Application of multivariate classification techniques appears to be useful because it links rock magnetic parameters to the geochemical environment. In the present piston core, three short reversed geomagnetic events in the Brunhes chron are preserved and, indeed, occur in clusters expressing no or minor diagenesis. The recording of the Blake event, however, has been prevented by later precipitation of magnetite in the corresponding interval.

A comparison of several vector quantization codebook generation approaches

A review and a performance comparison of several often-used vector quantization (VQ) codebook generation algorithms are presented. The codebook generation algorithms discussed include the Linde-Buzo-Gray (LBG) binary-splitting algorithm, the pairwise nearest-neighbor algorithm, the simulated annealing algorithm, and the fuzzy c-means clustering analysis algorithm. A new directed-search binary-splitting method which reduces the complexity of the LBG algorithm, is presented. Also, a new initial codebook selection method which can obtain a good initial codebook is presented. By using this initial codebook selection algorithm, the overall LBG codebook generation time can be reduced by a factor of 1.5-2.

Clustering of 29Si NMR data of aluminosilicate glasses using, k-means and fuzzy c-means — a comparison

Abstract Ehrentreich, F., Nofz, M. and Bartel, H.-G., 1992. Clustering of 29 Si NMR data of aluminosilicate glasses using k -means and fuzzy c -means. Chemometrics and Intelligent Laboratory Systems , 15: 61–73. The results of applying k -means (KM) and fuzzy c -means (FCM) methods of cluster analysis to a set of 29 Si NMR data of calcium aluminosilicate glasses are compared. Hard partitions are obtained as a result of KM cluster analysis, i.e. each object belongs to only one definite cluster. The FCM algorithm optimizes the degree of membership of objects in all the clusters — each object may thus belong to more than one cluster. The results of FCM are influenced by a parameter which controls the ‘degree of fuzziness’. This influence is studied and a method is suggested which makes the manifold of data obtained by FCM convenient and clear. The discussion of the partitions obtained shows that the FCM analysis yields valuable additional information on outliers and hybrids, i.e. less typical members of the clusters. The results of KM and FCM cluster analysis support the interpretation of the 29 Si NMR data on the basis of a structural model for the calcium aluminosilicate glasses.

Multivariate Statistical Analysis of the Wfarddc North American Fly Ash Database

ABSTRACTThe database of chemical, mineralogical and physical characteristics of North American Fly ashes, assembled by the WFARDDC in North Dakota, was analyzed using multivariate statistics. Prior to the multivariate analysis, the data were rearranged in subgroups containing information on bulk-chemistry, glass chemistry, mineralogy and ASTM physical test results. These groups were analyzed individually. The multivariate technique used was Fuzzy C-Means Cluster Analysis, combined with Non-Linear Mapping. Analysis of the data-set indicates a relation between glass network former and network modifier content. The database shows that a subdivision on the basis of bulk CaO (< 11%; 11–20%; >20%) correlates well with the ASTM C618 Σ(SiO2 +Al2O3 +Fe2O3) and/or specific gravity. Mineralogical data indicate a subdivision into clusters containing varying amounts of mullite, quartz and/or ferrite spinel and a variety of Ca-containing minerals; high CaO ashes usually have high Ca-mineral contents. Of the CaO containing minerals, only portlandite contributed slightly to the compressive strength as defined by ASTM C618. Analysis of glass chemistry reveals smaller differences in absolute amounts of major oxides than would be expected on the basis of bulk chemistry alone. Surprisingly, the total glass content does not contribute significantly to 28 day compressive strength; multiple regression analysis only indicates a significant relation of particle size and specific gravity with the ASTM Pozzolanic Activity Index (portland cement). The Pozzolanic Activity Index with lime seems to be of limited importance in evaluating the performance of fly ashes as mineral admixtures in concrete. On the basis of the statistical analysis, suggestions for selection of important classifying variables are made.

Microprobe Study of Chemical Inter-Grain Variation In Class-F Fly Ash: Application of Fuzzy C-Means Cluster Analysis and Non-Linear Mapping

AbstractThe chemistry of individual grains of several Class F fly ashes has been investigated by electron microprobe analysis. To interpret the analytical data-set, a combination of two multivariate statistical procedures was applied. The method involves the use of both fuzzy c-means cluster analysis (FCM) and non-linear mapping (NLM). It allows for a quick visual interpretation of the fly ash analysis and provides information which is not obtained through the use of the commonly used classical two-or three dimensional data representation plots alone. The method provides information on the occurrence of “outlying” samples, such as quartz grains, lime, calcium-sulfate or iron-containing particles. When the data-set is truncated for these outlying particles, cluster analysis of all ash data indicates that a model of 4–5 clusters can best explain chemical differences between the bulk of the particles of several class-F fly ashes. These clusters are related to each other by an inverse relation between the SiO2 and the A12O3 content, and some clusters display marked differences of either the oxides of Ti, Fe, Ca, Mg, K and/or K and Na. Inter-grain variation of one separate fly ash indicates that similar variations occur within individual fly ashes, only the absolute differences being smaller. The results are interpreted to represent either the coalescence or fusion of chemically different particles or small chemical differences in precursor clay minerals. The method of data-reduction presented here provides quick information on chemical relationships and is particularly suited to evaluate small data-sets. The method has potential to be combined with other input parameters, such as pozzolanic activity, glass content, particle size distribution and others.

Approximate fuzzy C-means (AFCM) cluster analysis of medical Magnetic Resonance Image (MRI) data

Approximate fuzzy C-means (AFCM) cluster analysis of medical Magnetic Resonance Image (MRI) data

The application of fuzzy c-means cluster analysis and non-linear mapping to geochemical datasets: examples from Portugal

In the interpretation of relatively small multivariate datasets, deviations from homogeneity may cause severe problems. In these cases fuzzy c-means cluster analysis (FCM) and non-linear mapping (NLM) are conceptionally suited to discern structure in the datasets. Particularly, the combined use of FCM and NLM furnishes a powerful method to find meaningful data groupings within a dataset. This is illustrated with two case studies, for water and combined water and stream sediment analyses, respectively, where FCM and NLM were applied. The results are easily related to geology, mineral occurrences and environmental factors.