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Relevant bibliographies by topics / Independent component analysis

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Academic literature on the topic 'Independent component analysis'

Author: Grafiati

Published: 4 June 2021

Last updated: 9 June 2025

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Journal articles on the topic "Independent component analysis"

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Unnisa, Yaseen, Danh Tran, and Fu Chun Huang. "Statistical Independence and Independent Component Analysis." Applied Mechanics and Materials 553 (May 2014): 564–69. http://dx.doi.org/10.4028/www.scientific.net/amm.553.564.

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Independent Component Analysis (ICA) is a recent method of blind source separation, it has been employed in medical image processing and structural damge detection. It can extract source signals and the unmixing matrix of the system using mixture signals only. This novel method relies on the assumption that source signals are statistically independent. This paper looks at various measures of statistical independence (SI) employed in ICA, the measures proposed by Bakirov and his associates, and the effects of levels of SI of source signals on the output of ICA. Firstly, two statistical independent signals in the form of uniform random signals and a mixing matrix were used to simulate mixture signals to be anlysed byfastICApackage, secondly noise was added onto the signals to investigate effects of levels of SI on the output of ICA in the form of soure signals, the mixing and unmixing matrix. It was found that for p-value given by Bakirov’s SI statistical testing of the null hypothesis H0is a good indication of the SI between two variables and that for p-value larger than 0.05, fastICA performs satisfactorily.

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Kemp, Freda. "Independent Component Analysis Independent Component Analysis: Principles and Practice." Journal of the Royal Statistical Society: Series D (The Statistician) 52, no. 3 (October 2003): 412. http://dx.doi.org/10.1111/1467-9884.00369_14.

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KAWAMOTO, Mitsuru. "Independent Component Analysis." Journal of Japan Society for Fuzzy Theory and Systems 11, no. 5 (1999): 759–62. http://dx.doi.org/10.3156/jfuzzy.11.5_55.

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Sztemberg-Lewandowska, Mirosława. "INDEPENDENT COMPONENT ANALYSIS." Prace Naukowe Uniwersytetu Ekonomicznego we Wrocławiu, no. 468 (2017): 222–29. http://dx.doi.org/10.15611/pn.2017.468.23.

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Fearn, Tom. "Independent Component Analysis." NIR news 19, no. 3 (May 2008): 13–14. http://dx.doi.org/10.1255/nirn.1073.

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Hong, Sung Ee. "Exploring Independent Component Analysis Based on Ball Covariance." Korean Data Analysis Society 21, no. 6 (December 31, 2019): 2721–35. http://dx.doi.org/10.37727/jkdas.2019.21.6.2721.

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Nordhausen, Joni Oja. "UNRAVELING INDEPENDENT COMPONENT ANALYSIS FOR TENSOR-VALUED DATA." Global Multidisciplinary Journal 02, no. 03 (March 2, 2023): 01–07. http://dx.doi.org/10.55640/gmj-abc114.

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In the realm of data analysis, the exploration of independent component analysis (ICA) for tensor-valued data represents a burgeoning area of research. Unlike traditional scalar or vector data, tensor-valued data capture complex relationships and structures across multiple dimensions. Independent component analysis offers a powerful framework for decomposing tensor-valued data into statistically independent components, revealing underlying patterns and dependencies that may remain obscured in raw data representations. This paper delves into the application of ICA techniques specifically tailored for tensor-valued data, exploring theoretical foundations, algorithmic implementations, and practical considerations. Through a comprehensive review and analysis, we elucidate the potential of ICA in uncovering hidden structures and sources of variability within tensor-valued datasets across diverse domains.

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Liu, Thomas T., Karla L. Miller, Eric C. Wong, Lawrence R. Frank, and Richard B. Buxton. "Identifying meaningful components in independent component analysis." NeuroImage 11, no. 5 (May 2000): S652. http://dx.doi.org/10.1016/s1053-8119(00)91582-9.

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Hyvärinen, Aapo, Patrik O. Hoyer, and Mika Inki. "Topographic Independent Component Analysis." Neural Computation 13, no. 7 (July 1, 2001): 1527–58. http://dx.doi.org/10.1162/089976601750264992.

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In ordinary independent component analysis, the components are assumed to be completely independent, and they do not necessarily have any meaningful order relationships. In practice, however, the estimated “independent” components are often not at all independent. We propose that this residual dependence structure could be used to define a topo-graphic order for the components. In particular, a distance between two components could be defined using their higher-order correlations, and this distance could be used to create a topographic representation. Thus, we obtain a linear decomposition into approximately independent components, where the dependence of two components is approximated by the proximity of the components in the topographic representation.

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Miettinen, Jari, Markus Matilainen, Klaus Nordhausen, and Sara Taskinen. "Extracting Conditionally Heteroskedastic Components using Independent Component Analysis." Journal of Time Series Analysis 41, no. 2 (September 8, 2019): 293–311. http://dx.doi.org/10.1111/jtsa.12505.

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Dissertations / Theses on the topic "Independent component analysis"

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Gao, Pei. "Nonlinear independent component analysis." Thesis, University of Newcastle Upon Tyne, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.437979.

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Harmeling, Stefan. "Independent component analysis and beyond." Phd thesis, [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=973631805.

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Blaschke, Tobias. "Independent component analysis and slow feature analysis." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2005. http://dx.doi.org/10.18452/15270.

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Der Fokus dieser Dissertation liegt auf den Verbindungen zwischen ICA (Independent Component Analysis - Unabhängige Komponenten Analyse) und SFA (Slow Feature Analysis - Langsame Eigenschaften Analyse). Um einen Vergleich zwischen beiden Methoden zu ermöglichen wird CuBICA2, ein ICA Algorithmus basierend nur auf Statistik zweiter Ordnung, d.h. Kreuzkorrelationen, vorgestellt. Dieses Verfahren minimiert zeitverzögerte Korrelationen zwischen Signalkomponenten, um die statistische Abhängigkeit zwischen denselben zu reduzieren. Zusätzlich wird eine alternative SFA-Formulierung vorgestellt, die mit CuBICA2 verglichen werden kann. Im Falle linearer Gemische sind beide Methoden äquivalent falls nur eine einzige Zeitverzögerung berücksichtigt wird. Dieser Vergleich kann allerdings nicht auf mehrere Zeitverzögerungen erweitert werden. Für ICA lässt sich zwar eine einfache Erweiterung herleiten, aber ein ähnliche SFA-Erweiterung kann nicht im originären SFA-Sinne (SFA extrahiert die am langsamsten variierenden Signalkomponenten aus einem gegebenen Eingangssignal) interpretiert werden. Allerdings kann eine im SFA-Sinne sinnvolle Erweiterung hergeleitet werden, welche die enge Verbindung zwischen der Langsamkeit eines Signales (SFA) und der zeitlichen Vorhersehbarkeit desselben verdeutlich. Im Weiteren wird CuBICA2 und SFA kombiniert. Das Resultat kann aus zwei Perspektiven interpretiert werden. Vom ICA-Standpunkt aus führt die Kombination von CuBICA2 und SFA zu einem Algorithmus, der das Problem der nichtlinearen blinden Signalquellentrennung löst. Vom SFA-Standpunkt aus ist die Kombination eine Erweiterung der standard SFA. Die standard SFA extrahiert langsam variierende Signalkomponenten die untereinander unkorreliert sind, dass heißt statistisch unabhängig bis zur zweiten Ordnung. Die Integration von ICA führt nun zu Signalkomponenten die mehr oder weniger statistisch unabhängig sind.<br>Within this thesis, we focus on the relation between independent component analysis (ICA) and slow feature analysis (SFA). To allow a comparison between both methods we introduce CuBICA2, an ICA algorithm based on second-order statistics only, i.e.\ cross-correlations. In contrast to algorithms based on higher-order statistics not only instantaneous cross-correlations but also time-delayed cross correlations are considered for minimization. CuBICA2 requires signal components with auto-correlation like in SFA, and has the ability to separate source signal components that have a Gaussian distribution. Furthermore, we derive an alternative formulation of the SFA objective function and compare it with that of CuBICA2. In the case of a linear mixture the two methods are equivalent if a single time delay is taken into account. The comparison can not be extended to the case of several time delays. For ICA a straightforward extension can be derived, but a similar extension to SFA yields an objective function that can not be interpreted in the sense of SFA. However, a useful extension in the sense of SFA to more than one time delay can be derived. This extended SFA reveals the close connection between the slowness objective of SFA and temporal predictability. Furthermore, we combine CuBICA2 and SFA. The result can be interpreted from two perspectives. From the ICA point of view the combination leads to an algorithm that solves the nonlinear blind source separation problem. From the SFA point of view the combination of ICA and SFA is an extension to SFA in terms of statistical independence. Standard SFA extracts slowly varying signal components that are uncorrelated meaning they are statistically independent up to second-order. The integration of ICA leads to signal components that are more or less statistically independent.

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Brock, James L. "Acoustic classification using independent component analysis /." Link to online version, 2006. https://ritdml.rit.edu/dspace/handle/1850/2067.

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Papathanassiou, Christos. "Independent component analysis of magnetoencephalographic signals." Thesis, University of Surrey, 2003. http://epubs.surrey.ac.uk/771941/.

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Magnetoencephalography (MEG) is a non-invasive brain imaging technique which allows instant tracking of changes in brain activity. However, it is affected by strong artefact signals generated by the heart or the eye blinking. The blind source separation problem is typically encountered in MEG studies when a set of unknown signals, originating from different sources inside or outside the brain, is mixed with an also unknown mixing matrix during their recording. Independent component analysis (ICA) is a recently developed technique which aims to estimate the original sources given only the observed mixtures. ICA can decompose the observed data into the original biological sources. However, ICA suffers from a major intrinsic ambiguity. In particular, it cannot determine the order of extraction of the source signals. Thus, if there are numerous source signals hidden in lengthy MEG recordings, the extraction of the biological signal of interest can be an extremely prolonged procedure. In this thesis, a modification of the ordinary ICA is introduced in order to cope with this ambiguity. In case there is prior knowledge concerning one of the original signals, this information is exploited by adding a penalty/constraint term to the standard ICA quality function in order to favour the extraction of that particular signal. Our approach requires no reference signal, but the knowledge of some statistical property of one of the original sources, namely its autocorrelation function. Our algorithm is validated with simulated data for which the mixing matrix is known, and is also applied to real MEG data to remove artefact signals. Finally, it is demonstrated how ICA can simplify the ill-posed problem of localising the sources/dipoles in the cortex (inverse problem). The advantage of ICA lies in using nonaveraged trials. In addition, there is no need to know in advance the number of dipoles.

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Miskin, James William. "Ensemble learning for independent component analysis." Thesis, University of Cambridge, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.621116.

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Garvey, Jennie Hill. "Independent component analysis by entropy maximization (infomax)." Thesis, Monterey, Calif. : Naval Postgraduate School, 2007. http://bosun.nps.edu/uhtbin/hyperion-image.exe/07Jun%5FGarvey.pdf.

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Thesis (M.S. in Electrical Engineering)--Naval Postgraduate School, June 2007.<br>Thesis Advisor(s): Frank E. Kragh. "June 2007." Includes bibliographical references (p. 103). Also available in print.

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Mitianoudis, Nikolaos. "Audio source separation using independent component analysis." Thesis, Queen Mary, University of London, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.406171.

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Choudrey, Rizwan A. "Variational methods for Bayesian independent component analysis." Thesis, University of Oxford, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.275566.

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Kalkan, Olcay Altınkaya Mustafa Aziz. "Independent component analysis applications in CDMA systems/." [s.l.]: [s.n.], 2004. http://library.iyte.edu.tr/tezler/master/elektronikvehaberlesme/T000473.rar.

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Books on the topic "Independent component analysis"

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Hyvarinen, Aapo. Independent component analysis. New York: J. Wiley, 2001.

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Juha, Karhunen, and Oja Erkki, eds. Independent component analysis. New York: J. Wiley, 2001.

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Lee, Te-Won. Independent Component Analysis. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4757-2851-4.

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Girolami, Mark, ed. Advances in Independent Component Analysis. London: Springer London, 2000. http://dx.doi.org/10.1007/978-1-4471-0443-8.

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Girolami, Mark. Advances in Independent Component Analysis. London: Springer London, 2000.

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Lee, Te-Won. Independent Component Analysis: Theory and Applications. Boston, MA: Springer US, 1998.

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Davies, Mike E., Christopher J. James, Samer A. Abdallah, and Mark D. Plumbley, eds. Independent Component Analysis and Signal Separation. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-74494-8.

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Adali, Tülay, Christian Jutten, João Marcos Travassos Romano, and Allan Kardec Barros, eds. Independent Component Analysis and Signal Separation. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-00599-2.

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1965-, Roberts Stephen, and Everson Richard 1961-, eds. Independent component analysis: Principles and practice. Cambridge: Cambridge University Press, 2001.

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Lee, Te-Won. Independent component analysis: Theory and applications. Boston: Kluwer Academic Publishers, 1998.

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Book chapters on the topic "Independent component analysis"

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Lee, Te-Won. "Independent Component Analysis." In Independent Component Analysis, 27–66. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4757-2851-4_2.

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Robila, Stefan A. "Independent Component Analysis." In Advanced Image Processing Techniques for Remotely Sensed Hyperspectral Data, 109–32. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-05605-9_5.

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Du, Ke-Lin, and M. N. S. Swamy. "Independent Component Analysis." In Neural Networks and Statistical Learning, 419–50. London: Springer London, 2013. http://dx.doi.org/10.1007/978-1-4471-5571-3_14.

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Du, Ke-Lin, and M. N. S. Swamy. "Independent Component Analysis." In Neural Networks and Statistical Learning, 447–82. London: Springer London, 2019. http://dx.doi.org/10.1007/978-1-4471-7452-3_15.

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Choi, Seungjin. "Independent Component Analysis." In Handbook of Natural Computing, 435–59. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-540-92910-9_13.

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Back, Andrew D. "Independent Component Analysis." In Studies in Fuzziness and Soft Computing, 59–95. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-39972-8_3.

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Efimov, Dmitry. "Independent Component Analysis." In Encyclopedia of Social Network Analysis and Mining, 1–5. New York, NY: Springer New York, 2016. http://dx.doi.org/10.1007/978-1-4614-7163-9_147-1.

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Shi, Xizhi. "Independent Component Analysis." In Blind Signal Processing, 60–83. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-11347-5_3.

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Hyvärinen, Aapo, Jarmo Hurri, and Patrik O. Hoyer. "Independent Component Analysis." In Computational Imaging and Vision, 151–75. London: Springer London, 2009. http://dx.doi.org/10.1007/978-1-84882-491-1_7.

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Sreevalsan-Nair, Jaya. "Independent Component Analysis." In Encyclopedia of Mathematical Geosciences, 642–44. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-030-85040-1_158.

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Conference papers on the topic "Independent component analysis"

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Asaba, Kai, Shota Saito, Shunsuke Horii, and Toshiyasu Matsushima. "Bayesian Independent Component Analysis under Hierarchical Model on Independent Components." In 2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference (APSIPA ASC). IEEE, 2018. http://dx.doi.org/10.23919/apsipa.2018.8659578.

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Sheehan, Michael P., Madeleine S. Kotzagiannidis, and Mike E. Davies. "Compressive Independent Component Analysis." In 2019 27th European Signal Processing Conference (EUSIPCO). IEEE, 2019. http://dx.doi.org/10.23919/eusipco.2019.8903095.

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Sela, Matan, and Ron Kimmel. "Randomized independent component analysis." In 2016 IEEE International Conference on the Science of Electrical Engineering (ICSEE). IEEE, 2016. http://dx.doi.org/10.1109/icsee.2016.7806178.

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Baloch, S. H., H. Krim, and M. G. Genton. "Robust independent component analysis." In 2005 Microwave Electronics: Measurements, Identification, Applications. IEEE, 2005. http://dx.doi.org/10.1109/ssp.2005.1628565.

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Wei, Hong, Xinling Shi, Jian Yang, and Yuanyuan Pu. "Speech Independent Component Analysis." In 2010 International Conference on Measuring Technology and Mechatronics Automation (ICMTMA 2010). IEEE, 2010. http://dx.doi.org/10.1109/icmtma.2010.604.

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Yan Chen and G. Leedham. "Independent component analysis segmentation algorithm." In Eighth International Conference on Document Analysis and Recognition (ICDAR'05). IEEE, 2005. http://dx.doi.org/10.1109/icdar.2005.140.

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Duan, Kuaikuai, Vince D. Calhoun, Jingyu Liu, and Rogers F. Silva. "aNy-way Independent Component Analysis." In 2020 42nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC) in conjunction with the 43rd Annual Conference of the Canadian Medical and Biological Engineering Society. IEEE, 2020. http://dx.doi.org/10.1109/embc44109.2020.9175277.

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Theis, F. J. "Mathematics in independent component analysis." In Seventh International Symposium on Signal Processing and Its Applications, 2003. Proceedings. IEEE, 2003. http://dx.doi.org/10.1109/isspa.2003.1224952.

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Zhao, Yongjian, Xiaoming Kong, Haining Jiang, and Meixia Qu. "Constrained independent component analysis techniques." In 2014 IEEE Workshop on Electronics, Computer and Applications (IWECA). IEEE, 2014. http://dx.doi.org/10.1109/iweca.2014.6845646.

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Painsky, Amichai, Saharon Rosset, and Meir Feder. "Generalized binary independent component analysis." In 2014 IEEE International Symposium on Information Theory (ISIT). IEEE, 2014. http://dx.doi.org/10.1109/isit.2014.6875048.

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Reports on the topic "Independent component analysis"

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Schennach, Susanne M., and Florian Gunsilius. Independent nonlinear component analysis. The IFS, September 2019. http://dx.doi.org/10.1920/wp.cem.2019.4619.

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Robin, Jean-Marc, and Stéphane Bonhomme. Consistent noisy independent component analysis. Institute for Fiscal Studies, February 2008. http://dx.doi.org/10.1920/wp.cem.2008.0408.

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Salerno, Marc L. An Independent Component Analysis Blind Beamformer. Fort Belvoir, VA: Defense Technical Information Center, December 2000. http://dx.doi.org/10.21236/ada384795.

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Kolski, Jeffrey S., Robert J. Macek, and Rodney C. McCrady. Application of Independent Component Analysis (ICA) to Long Bunch Beams in the Los Alamos Storage Ring. Office of Scientific and Technical Information (OSTI), January 2011. http://dx.doi.org/10.2172/1008001.

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Qi, Yuan. Learning Algorithms for Audio and Video Processing: Independent Component Analysis and Support Vector Machine Based Approaches. Fort Belvoir, VA: Defense Technical Information Center, August 2000. http://dx.doi.org/10.21236/ada458739.

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Nieto-Castanon, Alfonso. CONN functional connectivity toolbox (RRID:SCR_009550), Version 18. Hilbert Press, 2018. http://dx.doi.org/10.56441/hilbertpress.1818.9585.

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CONN is a Matlab-based cross-platform software for the computation, display, and analysis of functional connectivity in fMRI (fcMRI). Connectivity measures include seed-to-voxel connectivity maps, ROI-to- ROI connectivity matrices, graph properties of connectivity networks, generalized psychophysiological interaction models (gPPI), intrinsic connectivity, local correlation and other voxel-to-voxel measures, independent component analyses (ICA), and dynamic component analyses (dyn-ICA). CONN is available for resting state data (rsfMRI) as well as task-related designs. It covers the entire pipeline from raw fMRI data to hypothesis testing, including spatial coregistration, ART-based scrubbing, aCompCor strategy for control of physiological and movement confounds, first-level connectivity estimation, and second-level random-effect analyses and hypothesis testing.

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Nieto-Castanon, Alfonso. CONN functional connectivity toolbox (RRID:SCR_009550), Version 20. Hilbert Press, 2020. http://dx.doi.org/10.56441/hilbertpress.2048.3738.

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CONN is a Matlab-based cross-platform software for the computation, display, and analysis of functional connectivity in fMRI (fcMRI). Connectivity measures include seed-to-voxel connectivity maps, ROI-to- ROI connectivity matrices, graph properties of connectivity networks, generalized psychophysiological interaction models (gPPI), intrinsic connectivity, local correlation and other voxel-to-voxel measures, independent component analyses (ICA), and dynamic component analyses (dyn-ICA). CONN is available for resting state data (rsfMRI) as well as task-related designs. It covers the entire pipeline from raw fMRI data to hypothesis testing, including spatial coregistration, ART-based scrubbing, aCompCor strategy for control of physiological and movement confounds, first-level connectivity estimation, and second-level random-effect analyses and hypothesis testing.

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Nieto-Castanon, Alfonso. CONN functional connectivity toolbox (RRID:SCR_009550), Version 19. Hilbert Press, 2019. http://dx.doi.org/10.56441/hilbertpress.1927.9364.

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CONN is a Matlab-based cross-platform software for the computation, display, and analysis of functional connectivity in fMRI (fcMRI). Connectivity measures include seed-to-voxel connectivity maps, ROI-to- ROI connectivity matrices, graph properties of connectivity networks, generalized psychophysiological interaction models (gPPI), intrinsic connectivity, local correlation and other voxel-to-voxel measures, independent component analyses (ICA), and dynamic component analyses (dyn-ICA). CONN is available for resting state data (rsfMRI) as well as task-related designs. It covers the entire pipeline from raw fMRI data to hypothesis testing, including spatial coregistration, ART-based scrubbing, aCompCor strategy for control of physiological and movement confounds, first-level connectivity estimation, and second-level random-effect analyses and hypothesis testing.

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Miller, Erik G., and John W. Fisher III. Independent Components Analysis by Direct Entropy Minimization. Fort Belvoir, VA: Defense Technical Information Center, January 2003. http://dx.doi.org/10.21236/ada603560.

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Hart, James, Nasir Zulfiqar, and Carl Popelar. L52289 Use of Pipeline Geometry Monitoring to Assess Pipeline Condition. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), December 2008. http://dx.doi.org/10.55274/r0010254.

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Describes an algorithm is developed for deducing the longitudinal or axial strain from geometry pig measurements of a laterally displaced pipeline; often caused by geohazards. The development is limited to those lateral displacements of the pipeline that results in a predominantly transverse loading; i.e., the induced transverse component of the loading is much greater than its axial component. The emphasis is upon evaluating inelastic straining that accompanies large lateral displacement of the pipeline. The induced extensional strain is found to vary linearly with the change in curvature of the pipeline. The validity of the approach is established through favorable comparisons of the predictions for the extensional strains with those determined from buried pipeline finite element simulations of various displaced pipe configurations, pipe geometries, and loading amplitudes. Since the algorithm relies only upon measurements of the geometry of the displaced pipeline, it is independent of the pipe's and soil's material properties, pipe-soil interaction, and the loading conditions. Benefit: The efficacy of the algorithm is demonstrated by performing a large matrix of finite element simulations of displaced pipelines of different geometries subjected to block subsidence, landslides intersecting the pipeline at varying angles, fault crossings at different angles and different loading states, and comparing the analytical strains with the strains deduced from digital pig measurements of the curvature of the deformed pipeline. In this regard, the finite element simulations serve the role of surrogate geometry pig measurements. These comparisons are used to establish the resolution of the change in curvature measurement required of a geometry pig to produce a reliable estimate for the longitudinal strain in a displaced pipeline. An error analysis is also performed to establish the relative error as a function of the curvature measurement gage length, a characteristic feature-length, and the abruptness of the displaced shape of the pipeline.

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