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Data Mining Using Fractals and Power Laws [chapter]

Christos Faloutsos
Advances in Data and Web Management  
law) School of Computer Science Carnegie Mellon Even more power laws: library science (Lotka's law of publication count); and citation counts: (citeseer.nj.nec.com 6/2001) • web hit counts [w/ A.  ...  Faloutsos 77 School of Computer Science Carnegie Mellon Fractals & power laws: appear in numerous settings: • medical • geographical / geological • social • computer-system related • <and  ...  More fractals: • cardiovascular system: 3 (!) lungs: ~2.9 C.  ... 
doi:10.1007/978-3-540-72524-4_1 dblp:conf/waim/Faloutsos07 fatcat:kwed44rxqbd23j2rvwyux7gady

Consequences of fractal grade distribution for bulk sorting of a copper porphyry deposit

Peter Coghill, David Miljak, Elizabeth Williams
2015 Geoscience Frontiers  
Fractal distributions, and their associated power laws, have two features highly favourable for segregating ore: a large proportion of low-grade pods and the large scale spatial clustering of grade.  ...  We show the presence of fractal ordering of copper grade in bore core data at short range in the Cadia Ridgeway porphyry deposit and measure its persistence after mining by monitoring the output of the  ...  Acknowledgements The authors wish to thank Newcrest Mining Limited for funding the project and allowing publication of the data, as well as John Huntington for supplying the infrared reflectance data.  ... 
doi:10.1016/j.gsf.2014.09.003 fatcat:vu26mp46sjaujg26ts5fivjsly

Next Generation Data Mining Tools: Power Laws and Self-similarity for Graphs, Streams and Traditional Data [chapter]

Christos Faloutsos
2003 Lecture Notes in Computer Science  
Self-similarity, fractals and power laws are extremely successful in describing real datasets (coast-lines, rivers basins, stock-prices, brainsurfaces, communication-line noise, to name a few).  ...  We show some old and new successes, involving modeling of graph topologies (internet, web and social networks); modeling galaxy and video data; dimensionality reduction; and more.  ...  Conclusions Self-similarity and power laws can solve data mining problems that traditional methods can not.  ... 
doi:10.1007/978-3-540-39857-8_3 fatcat:oxs62jcyp5huzjzbikx2szn2ki

Next Generation Data Mining Tools: Power Laws and Self-similarity for Graphs, Streams and Traditional Data [chapter]

Christos Faloutsos
2003 Lecture Notes in Computer Science  
Self-similarity, fractals and power laws are extremely successful in describing real datasets (coast-lines, rivers basins, stock-prices, brainsurfaces, communication-line noise, to name a few).  ...  We show some old and new successes, involving modeling of graph topologies (internet, web and social networks); modeling galaxy and video data; dimensionality reduction; and more.  ...  Conclusions Self-similarity and power laws can solve data mining problems that traditional methods can not.  ... 
doi:10.1007/978-3-540-39804-2_3 fatcat:vigmo3kq3faivmsu4vebpex7pa

Evaluating Hurst Parameters and Fractal Dimensions of Surveyed Dataset of Tailings Dam Embankment

I. Yakubu, Y. Y. Ziggah, C. Yeboah
2019 Zenodo  
In the mining environment, tailings dam embankment is among the hazards and risk areas. The tailings dam embankment could fail and result to damages to facilities, human injuries or even fatalities.  ...  In this paper, the fractal dimension (D) was determined using D = 2-H.  ...  In this case, the fractal formalism indicates ɱ f(α) behaving as a power law with respect to the analysis scale α, and that the regularity strength has a relationship to the power law exponent. points;  ... 
doi:10.5281/zenodo.2643906 fatcat:rikkqqfdsrdapookcusmpahk6q

A Simple Strategy to Start Domain Ontology from Scratch

Ivo Wolff, Nelson F.
2014 International Journal of Advanced Computer Science and Applications  
Text Mining, Link Analysis and Graph Analysis create an abstract rough sketch of interactions between terms.  ...  Aiming the usage of Domain Ontology as an educational tool for neophyte students and focusing in a fast and easy way to start Domain Ontology from scratch, the semantics are set aside to identify contexts  ...  ACKNOWLEDGMENT We would like to give special thanks to Emeritus Professor Luiz Bevilacqua (COPPE/Federal University of Rio de Janeiro), who helped us through his notable knowledge of fractals.  ... 
doi:10.14569/specialissue.2014.040107 fatcat:4ndht7soszh35nyqav5kltkdd4

Fractals in petrology

Donald L Turcotte
2002 Lithos  
Rayleigh distillation and chromatographic models can explain power-law (fractal) distributions for the extreme values of trace element concentrations.  ...  A fractal (power-law) distribution is the only statistical distribution applicable to a scale-invariant process.  ...  Acknowledgements The author would like to thank Eric Lewin for a very constructive and helpful review.  ... 
doi:10.1016/s0024-4937(02)00194-9 fatcat:dxmat5dctrfhnjktivfwptx324

Fractal Location and Anomalous Diffusion Dynamics for Oil Wells from the KY Geological Survey [article]

Keith Andrew (Department of Physics and Astronomy, Western Kentucky University), Karla M. Andrew (Center for Water Resource Studies, Western Kentucky University), Kevin A. Andrew (Carol Martin Gatton Academy of Math and Science, Western Kentucky University)
2009 arXiv   pre-print
Following the porosity and diffusivity studies of Tarafdar and Roy1 we extract fractal dimensions of the fossil fuel mining locations and search for evidence of scaling laws for the set of deposits.  ...  This data was then exported into a spreadsheet showing latitude and longitude for each point to be used for modeling at different scales to determine the fractal dimension of the set.  ...  Acknowledgements: This work has been generously supported by a KY NASA Space Grant Consortium grant, the WKU Institute for Astrophysics and Space Science and the WKU Center for Water Resource Studies.  ... 
arXiv:0912.2540v1 fatcat:3tomtf2yg5anhd5gqbt6szykza

A Field Study on the Law of Spatiotemporal Development of Rock Movement of Under-Sea Mining, Shandong, China

Jia Liu, Fengshan Ma, Jie Guo, Guang Li, Yewei Song, Yang Wan
2022 Sustainability  
The findings are of great theoretical value for the further study of mining settlements to better understand the physical mechanisms of internal movement and rock mass failures through the fractal law  ...  In order to ensure the safety of under-sea mining, it is necessary to study the rock movement laws and the mechanisms.  ...  The power-law and fractal theory are closely linked and complement each other.  ... 
doi:10.3390/su14105864 fatcat:iczqn5y4uremvomdo2rk7jjw2e

Multi-Fractal Model of Coal Resources Distribution and Its Application in Spatial Distribution Law of Coal thickness

Liu Xing, Hu Baolin, Jiang Songmei
2017 International Journal of Signal Processing, Image Processing and Pattern Recognition  
data to reveal the law of coal thickness distribution effectively.  ...  the coal thickness distribution follows the multi-fractal model and the S-A method is effective for those geological data processing. .So the processing and analysis of geological data is favor of multi-fractal  ...  Acknowledgments I would like to express my gratitude to all those who helped me during the writing and publishing of this thesis and this thesis is sponsored by NSFC (NO.: 41372368), NSFC of Anhui(NO.:  ... 
doi:10.14257/ijsip.2017.10.4.08 fatcat:6f36zalofre73a7fa4vdl3idba

Derivation of infinite-slit-smeared small-angle scattering from porous surface and porous mass fractals

P. J. McMahon, S. D. Moss
1999 Journal of Applied Crystallography  
Small-angle X-ray scattering (SAXS) is often used to study porous and aggregated fractal materials.  ...  An equation is derived that allows analysis of normalization from deconvolution routines applied to porous-fractal data. This model is tested using simulated and experimental SAXS data.  ...  surface measure or volume measure from the power-law ®t to the slit-smeared data.  ... 
doi:10.1107/s0021889899008559 fatcat:utphygmqzvdbxp5poeumnyzsoy

Density/area power-law models for separating multi-scale anomalies of ore and toxic elements in stream sediments in Gejiu mineral district, Yunnan Province, China

Q. Cheng, Q. Xia, W. Li, S. Zhang, Z. Chen, R. Zuo, W. Wang
2010 Biogeosciences  
density (S) and the area (A) enclosed by the above-threshold spectrum energy density can be fitted by power-law models.  ...  This contribution introduces a fractal filtering technique newly developed on the basis of a spectral energy density vs. area power-law model in the context of multifractal theory.  ...  Fractal filtering technique The fractal filtering technique was developed on the basis of the S-A power-law model by Cheng, Xu and Grunsky (1999) for decomposing mixing patterns into components according  ... 
doi:10.5194/bg-7-3019-2010 fatcat:nc2iflvvozd65k3z6yz2qwf2ea

Density/area power-law models for separating multi-scale anomalies of ore and toxic elements in stream sediments in Gejiu mineral district, Yunnan Province, China

Q. Cheng, Q. Xia, W. Li, S. Zhang, Z. Chen, R. Zuo, W. Wang
2010 Biogeosciences Discussions  
density (S) and the area (A) enclosed by the above-threshold spectrum energy density can be fitted by power-law models.  ...  This contribution introduces a fractal filtering technique newly developed on the basis of a spectral energy density vs. area power-law model in the context of multifractal theory.  ...  Fractal filtering technique The fractal filtering technique was developed on the basis of the S-A power-law model by Cheng, Xu and Grunsky (1999) for decomposing mixing patterns into components according  ... 
doi:10.5194/bgd-7-4273-2010 fatcat:vr4vb5cemzhkhpmpoolhygpbr4

Fractals and the Pareto Distribution Applied to Petroleum Accumulation-Size Distributions [chapter]

Robert A. Crovelli, Christopher C. Barton
1995 Fractals in Petroleum Geology and Earth Processes  
The Pareto distribution is a fractal probability distribution that has a power-law form with two important scaling (self-similar) properties: scaling under lower truncation and asymptotic scaling under  ...  Adoption of the Pareto distribution was independent of the study of fractals; however, the Pareto distribution is the probability distribution uniquely characteristic of fractals.  ...  power laws.  ... 
doi:10.1007/978-1-4615-1815-0_4 fatcat:b5ajmubywnftxnxhbxstzjl2xm

Fractal dimension, wavelet shrinkage and anomaly detection for mine hunting

J.D.B. Nelson, N.G. Kingsbury
2012 IET Signal Processing  
We exploit previous work that used dual-tree wavelets and fractal dimension to adaptively suppress sand ripples and a matched filter as an initial detector.  ...  An anomaly detection approach is considered for the mine hunting in sonar imagery problem.  ...  Again, the fractal dimension is (3 − H), and the power law (2) holds in an average power spectrum sense [15] .  ... 
doi:10.1049/iet-spr.2011.0070 fatcat:77kaxotaindc7fbygy6ietkfqm
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