On Distance Measures for the Fuzzy K-means Algorithm for Joint Data

Hammah, R.E.; Curran, J.H.

doi:10.1007/s006030050041

Cited by 74 publications

(32 citation statements)

References 14 publications

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“…Cluster analysis of fracture orientation provides a transparent means of separating fracture orientation data into sets, as proposed by Shanley and Mahtab []. Agglomerative, K ‐means, and fuzzy K ‐means clustering have been used to analyze orientation data derived from scanline measurements, predominantly for engineering purposes [e.g., Hammah and Curran , , ; Zhou and Maerz , ; Tokhmechi et al , ; Li et al , ] but rarely for reservoir borehole data interpretation.…”

Section: Introductionmentioning

confidence: 99%

Statistical methods of fracture characterization using acoustic borehole televiewer log interpretation

et al. 2017

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Acoustic borehole televiewer (BHTV) logs provide measurements of fracture attributes (orientations, thickness, and spacing) at depth. Orientation, censoring, and truncation sampling biases similar to those described for one‐dimensional outcrop scanlines, and other logging or drilling artifacts specific to BHTV logs, can affect the interpretation of fracture attributes from BHTV logs. K‐means, fuzzy K‐means, and agglomerative clustering methods provide transparent means of separating fracture groups on the basis of their orientation. Fracture spacing is calculated for each of these fracture sets. Maximum likelihood estimation using truncated distributions permits the fitting of several probability distributions to the fracture attribute data sets within truncation limits, which can then be extrapolated over the entire range where they naturally occur. Akaike Information Criterion (AIC) and Schwartz Bayesian Criterion (SBC) statistical information criteria rank the distributions by how well they fit the data. We demonstrate these attribute analysis methods with a data set derived from three BHTV logs acquired from the high‐temperature Rotokawa geothermal field, New Zealand. Varying BHTV log quality reduces the number of input data points, but careful selection of the quality levels where fractures are deemed fully sampled increases the reliability of the analysis. Spacing data analysis comprising up to 300 data points and spanning three orders of magnitude can be approximated similarly well (similar AIC rankings) with several distributions. Several clustering configurations and probability distributions can often characterize the data at similar levels of statistical criteria. Thus, several scenarios should be considered when using BHTV log data to constrain numerical fracture models.

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Section: Introductionmentioning

confidence: 99%

Statistical methods of fracture characterization using acoustic borehole televiewer log interpretation

et al. 2017

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“…For example in [11] a clustering problem using FCM algorithm based on the scaled distance is evaluated and its advantages are demonstrated. But in our work we use the classical distance given in the formula (2.1).…”

Section: Basic Definitions and Propertiesmentioning

confidence: 99%

A new unsupervised approach for fuzzy clustering

Nasıbov

Ulutagay

2007

Fuzzy Sets and Systems

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“…Usually these algorithms are very sensitive to the choice of the dissimilarity function [1], [17]. The dissimilarity function must have the good properties of non-negativity and symmetry and satisfy the triangle inequality.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy partition-based distance practical use and implementation

Guillaume¹,

Charnomordic²

2013

2013 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

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This work discusses the implementation of a semidistance based on fuzzy partitions, that allows to introduce expert knowledge into distance computations done on numerical data. It can be used in various kinds of statistical clustering or other applications. The semi-distance univariate behaviour is first studied, then a multivariate clustering case study is presented, that includes an optimization procedure. All calculations are done using open source softwares: FisPro for fuzzy modelling and R for clustering. Emphasis is given to a number of software functionalities, which are targeted at the practical use of the semi-distance.

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On Distance Measures for the Fuzzy K-means Algorithm for Joint Data

Cited by 74 publications

References 14 publications

Statistical methods of fracture characterization using acoustic borehole televiewer log interpretation

Statistical methods of fracture characterization using acoustic borehole televiewer log interpretation

A new unsupervised approach for fuzzy clustering

Fuzzy partition-based distance practical use and implementation

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