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Ek, Christoffer. "Singular Value Decomposition." Thesis, Linnéuniversitetet, Institutionen för datavetenskap, fysik och matematik, DFM, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-21481.
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Digital information och kommunikation genom digitala medier är ett växande område. E-post och andra kommunikationsmedel används dagligen över hela världen. Parallellt med att området växer så växer även intresset av att hålla informationen säker. Transmission via antenner är inom signalbehandling ett välkänt område. Transmission från en sändare till en mottagare genom fri rymd är ett vanligt exempel. I en tuff miljö som till exempel ett rum med reflektioner och oberoende elektriska apparater kommer det att finnas en hel del distorsion i systemet och signalen som överförs kan, på grund av systemets egenskaper och buller förvrängas.Systemidentifiering är ett annat välkänt begrepp inom signalbehandling. Denna avhandling fokuserar på systemidentifiering i en tuff miljö med okända system. En presentation ges av matematiska verktyg från den linjära algebran samt en tillämpning inom signalbehandling. Denna avhandling grundar sig främst på en matrisfaktorisering känd som Singular Value Decomposition (SVD). SVD’n används här för att lösa komplicerade matrisinverser och identifiera system.Denna avhandling utförs i samarbete med Combitech AB. Deras expertis inom signalbehandling var till stor hjälp när teorin praktiserades. Med hjälp av ett välkänt programmeringsspråk känt som LabView praktiserades de matematiska verktygen och kunde synkroniseras med diverse instrument som användes för att generera signaler och system.Digital information transmission is a growing field. Emails, videos and so on are transmitting around the world on a daily basis. Along the growth of using digital devises there is in some cases a great interest of keeping this information secure. In the field of signal processing a general concept is antenna transmission. Free space between an antenna transmitter and a receiver is an example of a system. In a rough environment such as a room with reflections and independent electrical devices there will be a lot of distortion in the system and the signal that is transmitted might, due to the system characteristics and noise be distorted. System identification is another well-known concept in signal processing. This thesis will focus on system identification in a rough environment and unknown systems. It will introduce mathematical tools from the field of linear algebra and applying them in signal processing. Mainly this thesis focus on a specific matrix factorization called Singular Value Decomposition (SVD). This is used to solve complicated inverses and identifying systems. This thesis is formed and accomplished in collaboration with Combitech AB. Their expertise in the field of signal processing was of great help when putting the algorithm in practice. Using a well-known programming script called LabView the mathematical tools were synchronized with the instruments that were used to generate the systems and signals.
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Kwizera, Petero. "Matrix Singular Value Decomposition." UNF Digital Commons, 2010. http://digitalcommons.unf.edu/etd/381.
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This thesis starts with the fundamentals of matrix theory and ends with applications of the matrix singular value decomposition (SVD). The background matrix theory coverage includes unitary and Hermitian matrices, and matrix norms and how they relate to matrix SVD. The matrix condition number is discussed in relationship to the solution of linear equations. Some inequalities based on the trace of a matrix, polar matrix decomposition, unitaries and partial isometies are discussed. Among the SVD applications discussed are the method of least squares and image compression. Expansion of a matrix as a linear combination of rank one partial isometries is applied to image compression by using reduced rank matrix approximations to represent greyscale images. MATLAB results for approximations of JPEG and .bmp images are presented. The results indicate that images can be represented with reasonable resolution using low rank matrix SVD approximations.
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Samuelsson, Saga. "The Singular Value Decomposition Theorem." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-150917.
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This essay will present a self-contained exposition of the singular value decomposition theorem for linear transformations. An immediate consequence is the singular value decomposition for complex matrices.Denna uppsats kommer presentera en självständig exposition av singulärvärdesuppdelningssatsen för linjära transformationer. En direkt följd är singulärvärdesuppdelning för komplexa matriser.
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Jolly, Vineet Kumar. "Activity Recognition using Singular Value Decomposition." Thesis, Virginia Tech, 2006. http://hdl.handle.net/10919/35219.
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A wearable device that accurately records a user's daily activities is of substantial value. It can be used to enhance medical monitoring by maintaining a diary that lists what a person was doing and for how long. The design of a wearable system to record context such as activity recognition is influenced by a combination of variables. A flexible yet systematic approach for building a software classification environment according to a set of variables is described. The integral part of the software design is the use of a unique robust classifier that uses principal component analysis (PCA) through singular value decomposition (SVD) to perform real-time activity recognition. The thesis describes the different facets of the SVD-based approach and how the classifier inputs can be modified to better differentiate between activities. This thesis presents the design and implementation of a classification environment used to perform activity detection for a wearable e-textile system.Master of Science
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Khatavkar, Rohan. "Sparse and orthogonal singular value decomposition." Kansas State University, 2013. http://hdl.handle.net/2097/15992.
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Master of ScienceDepartment of Statistics
Kun Chen
The singular value decomposition (SVD) is a commonly used matrix factorization technique in statistics, and it is very e ective in revealing many low-dimensional structures in a noisy data matrix or a coe cient matrix of a statistical model. In particular, it is often desirable to obtain a sparse SVD, i.e., only a few singular values are nonzero and their corresponding left and right singular vectors are also sparse. However, in several existing methods for sparse SVD estimation, the exact orthogonality among the singular vectors are often sacri ced due to the di culty in incorporating the non-convex orthogonality constraint in sparse estimation. Imposing orthogonality in addition to sparsity, albeit di cult, can be critical in restricting and guiding the search of the sparsity pattern and facilitating model interpretation. Combining the ideas of penalized regression and Bregman iterative methods, we propose two methods that strive to achieve the dual goal of sparse and orthogonal SVD estimation, in the general framework of high dimensional multivariate regression. We set up simulation studies to demonstrate the e cacy of the proposed methods.
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Kardamis, Joseph R. "Audio watermarking techniques using singular value decomposition /." Online version of thesis, 2007. http://hdl.handle.net/1850/4493.
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Montagnon, Chris. "Singular value decomposition and time series forecasting." Thesis, Imperial College London, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.535012.
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Rajamanickam, Sivasankaran. "Efficient algorithms for sparse singular value decomposition." [Gainesville, Fla.] : University of Florida, 2009. http://purl.fcla.edu/fcla/etd/UFE0041153.
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Deng, Cheng. "Time Series Decomposition Using Singular Spectrum Analysis." Digital Commons @ East Tennessee State University, 2014. https://dc.etsu.edu/etd/2352.
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Singular Spectrum Analysis (SSA) is a method for decomposing and forecasting time series that recently has had major developments but it is not yet routinely included in introductory time series courses. An international conference on the topic was held in Beijing in 2012. The basic SSA method decomposes a time series into trend, seasonal component and noise. However there are other more advanced extensions and applications of the method such as change-point detection or the treatment of multivariate time series. The purpose of this work is to understand the basic SSA method through its application to the monthly average sea temperature in a point of the coast of South America, near where “EI Ni˜no” phenomenon originates, and to artificial time series simulated using harmonic functions. The output of the basic SSA method is then compared with that of other decomposition methods such as classic seasonal decomposition, X-11 decomposition using moving averages and seasonal decomposition by Loess (STL) that are included in some time series courses.
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Ho, Anna. "Cross sentence alignment based on singular value decomposition." Thesis, University of Macau, 2008. http://umaclib3.umac.mo/record=b1942865.
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Osmanli, Osman Nuri. "A Singular Value Decomposition Approach For Recommendation Systems." Master's thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612129/index.pdf.
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Data analysis has become a very important area for both companies and researchers as a consequence of the technological developments in recent years. Companies are trying to increase their profit by analyzing the existing data about their customers and making decisions for the future according to the results of these analyses. Parallel to the need of companies, researchers are investigating different methodologies to analyze data more accurately with high performance.
Recommender systems are one of the most popular and widespread data analysis tools. A recommender system applies knowledge discovery techniques to the existing data and makes personalized product recommendations during live customer interaction. However, the huge growth of customers and products especially on the internet, poses some challenges for recommender systems, producing high quality recommendations and performing millions of recommendations per second.
In order to improve the performance of recommender systems, researchers have proposed many different methods. Singular Value Decomposition (SVD) technique based on dimension reduction is one of these methods which produces high quality recommendations, but has to undergo very expensive matrix calculations. In this thesis, we propose and experimentally validate some contributions to SVD technique which are based on the user and the item categorization. Besides, we adopt tags to classical 2D (User-Item) SVD technique and report the results of experiments. Results are promising to make more accurate and scalable recommender systems.
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Wengerhoff, Daniel. "Using the singular value decomposition for image steganography." [Ames, Iowa : Iowa State University], 2006.
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Xiao, Xiaolin. "Complex networks and the generalized singular value decomposition." Thesis, University of Strathclyde, 2011. http://oleg.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=15336.
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Xu, Wei Qiao Sanzheng. "Symmetric singular value decomposition of complex symmetric matrices." *McMaster only, 2006.
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Araki, Sho. "Orthogonal transformation based algorithms for singular value decomposition." Doctoral thesis, Kyoto University, 2021. http://hdl.handle.net/2433/263784.
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Workalemahu, Tsegaselassie. "Singular Value Decomposition in Image Noise Filtering and Reconstruction." Digital Archive @ GSU, 2008. http://digitalarchive.gsu.edu/math_theses/52.
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The Singular Value Decomposition (SVD) has many applications in image processing. The SVD can be used to restore a corrupted image by separating significant information from the noise in the image data set. This thesis outlines broad applications that address current problems in digital image processing. In conjunction with SVD filtering, image compression using the SVD is discussed, including the process of reconstructing or estimating a rank reduced matrix representing the compressed image. Numerical plots and error measurement calculations are used to compare results of the two SVD image restoration techniques, as well as SVD image compression. The filtering methods assume that the images have been degraded by the application of a blurring function and the addition of noise. Finally, we present numerical experiments for the SVD restoration and compression to evaluate our computation.
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Zhang, Lingsong Marron James Stephen Zhu Zhengyuan Shen Haipeng. "Functional singular value decomposition and multi-resolution anomaly detection." Chapel Hill, N.C. : University of North Carolina at Chapel Hill, 2007. http://dc.lib.unc.edu/u?/etd,1166.
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Thesis (Ph. D.)--University of North Carolina at Chapel Hill, 2007.Title from electronic title page (viewed Mar. 27, 2008). "... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Statistics and Operations Research." Discipline: Statistics and Operations Research; Department/School: Statistics and Operations Research.
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Nagata, Munehiro. "Studies on Accurate Singular Value Decomposition for Bidiagonal Matrices." 京都大学 (Kyoto University), 2016. http://hdl.handle.net/2433/215686.
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原著論文リスト[A1]: “The final publication is available at Springer via http://dx.doi.org/10.1007/s11075-012-9607-5.”. [A2]: “The final publication is available at Springer via http://dx.doi.org/10.1007/s10092-013-0085-5.”, [A3]: DOI“10.1016/j.camwa.2015.11.022”Kyoto University (京都大学)
0048
新制・課程博士
博士(情報学)
甲第19859号
情博第610号
新制||情||106(附属図書館)
32895
京都大学大学院情報学研究科数理工学専攻
(主査)教授 中村 佳正, 教授 矢ｹ崎 一幸, 教授 山下 信雄
学位規則第4条第1項該当
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Krishnamurthy, Jayant (Jayant S. ). "Finding analogies in semantic networks using the singular value decomposition." Thesis, Massachusetts Institute of Technology, 2009. http://hdl.handle.net/1721.1/53131.
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Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2009.Includes bibliographical references (p. 59-61).
We present CROSSBRIDGE, an algorithm for finding analogies in large, sparse semantic networks. We treat analogies as comparisons between domains of knowledge. A domain is a small semantic network, i.e., a set of concepts and binary relations between concepts. We treat our knowledge base (the large semantic network) as if it contained many domains of knowledge, then apply dimensionality reduction to find the most salient relation structures among the domains. Relation structures are systems of relations similar to the structures mapped between domains in structure mapping[6]. These structures are effectively n-ary relations formed by combining multiple pairwise relations. The most salient relation structures form the basis of domain space, a space containing all domains of knowledge from the large semantic network. The construction of domain space places analogous domains near each other in domain space. CROSSBRIDGE finds analogies using similarity information from domain space and a heuristic search process. We evaluate our method on ConceptNet[10], a large semantic network of common sense knowledge. We compare our approach with an implementation of structure mapping and show that our algorithm is more efficient and has superior analogy recall.
by Jayant Krishnamurthy.
M.Eng.
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Niessen, Christopher Charles. "A VLSI systolic array processor for complex singular value decomposition." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/34099.
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Thesis (B.S. and M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1994.Includes bibliographical references (leaves 219-221).
The singular value decomposition is one example of a variety of more complex routines that are finding use in modern high performance signal processing systems. In the interest of achieving the maximum possible performance, a systolic array processor for computing the singular value decomposition of an arbitrary complex matrix was designed using a silicon compiler system. This system allows for ease of design by specification of the processor architecture in a high level language, utilizing parts from a variety of cell libraries, while still benefiting from the power of custom VLSI. The level of abstraction provided by this system allowed more complex functional units to be built up from existing simple library parts. A novel fast interpolation cell for computation of square roots and inverse square roots was designed, allowing for a new algebraic approach to the singular value decomposition problem. The processors connect together in a systolic array to maximize computational efficiency while minimizing overhead due to high communication requirements.
by Christopher Charles Niessen.
B.S.and M.S.
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Iwasaki, Masashi. "Studies of Singular Value Decomposition in Terms of Integrable Systems." 京都大学 (Kyoto University), 2004. http://hdl.handle.net/2433/68903.
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Konda, Taro. "Studies on a Parallel Algorithm for Bidiagonal Singular Value Decomposition." 京都大学 (Kyoto University), 2009. http://hdl.handle.net/2433/123850.
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Haque, S. M. Rafizul. "Singular Value Decomposition and Discrete Cosine Transform based Image Watermarking." Thesis, Blekinge Tekniska Högskola, Avdelningen för för interaktion och systemdesign, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-5269.
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Rapid evolution of digital technology has improved the ease of access to digital information enabling reliable, faster and efficient storage, transfer and processing of digital data. It also leads to the consequence of making the illegal production and redistribution of digital media easy and undetectable. Hence, the risk of copyright violation of multimedia data has increased due to the enormous growth of computer networks that provides fast and error free transmission of any unauthorized duplicate and possibly manipulated copy of multimedia information. One possible solution may be to embed a secondary signal or pattern into the image that is not perceivable and is mixed so well with the original digital data that it is inseparable and remains unaffected against any kind of multimedia signal processing. This embedded secondary information is digital watermark which is, in general, a visible or invisible identification code that may contain some information about the intended recipient, the lawful owner or author of the original data, its copyright etc. in the form of textual data or image. In order to be effective for copyright protection, digital watermark must be robust which are difficult to remove from the object in which they are embedded despite a variety of possible attacks. Several types of watermarking algorithms have been developed so far each of which has its own advantages and limitations. Among these, recently Singular Value Decomposition (SVD) based watermarking algorithms have attracted researchers due to its simplicity and some attractive mathematical properties of SVD. Here a number of pure and hybrid SVD based watermarking schemes have been investigated and finally a RST invariant modified SVD and Discrete Cosine Transform (DCT) based algorithm has been developed. A preprocessing step before the watermark extraction has been proposed which makes the algorithm resilient to geometric attack i.e. RST attack. Performance of this watermarking scheme has been analyzed by evaluating the robustness of the algorithm against geometric attack including rotation, scaling, translation (RST) and some other attacks. Experimental results have been compared with existing algorithm which seems to be promising.Phone number: +88041730212
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Marshall, Patrick M. "Least squares solutions in statistical orbit determination using singular value decomposition." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 1999. http://handle.dtic.mil/100.2/ADA368336.
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Thesis (M.S. in Applied Physics) Naval Postgraduate School, June 1999."June 1999". Thesis advisor(s): D.A. Danielson, David Canright. Includes bibliographical references (p. 49). Also available online.
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Sen, Sujit. "Innovations and singular value decomposition for blind sequence detection in wireless channels." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape8/PQDD_0020/MQ45997.pdf.
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Love, Andrew R. "Automatically Locating Sensor Position on an E-textile Garment Via Pattern Recognition." Thesis, Virginia Tech, 2009. http://hdl.handle.net/10919/35374.
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Electronic textiles are a sound platform for wearable computing. Many applications have been devised that use sensors placed on these textiles for fields such as medical monitoring and military use or for display purposes. Most of these applications require that the sensors have known locations for accurate results. Activity recognition is one application that is highly dependent on knowledge of the sensor position. Therefore, this thesis presents the design and implementation of a method whereby the location of the sensors on the electronic textile garments can be automatically identified when the user is performing an appropriate activity. The software design incorporates principle component analysis using singular value decomposition to identify the location of the sensors. This thesis presents a method to overcome the problem of bilateral symmetry through sensor connector design and sensor orientation detection. The scalability of the solution is maintained through the use of culling techniques. This thesis presents a flexible solution that allows for the fine-tuning of the accuracy of the results versus the number of valid queries, depending on the constraints of the application. The resulting algorithm is successfully tested on both motion capture and sensor data from an electronic textile garment.Master of Science
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Yi, Dingrong 1969. "Singular value decomposition of Arctic Sea ice cover and overlying atmospheric circulation fluctuations." Thesis, McGill University, 1998. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=20610.
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The relationship between the Arctic and sub-Arctic sea-ice concentration (SIC) anomalies, particularly those associated with the Greenland and Labrador Seas' "Ice and Salinity Anomalies (ISAs)" occurring during the 1960s/1970s, 1970s/1980s, and 1980s/1990s, and the overlying atmospheric circulation (SLP) fluctuations is investigated using the Empirical Orthogonal Function (EOF) and Singular Value Decomposition (SVD) analysis methods. The data used are monthly SIC and SLP anomalies, which cover the Northern Hemisphere north of 450 and extend over the 38-year period 1954--1991.One goal of the thesis is to describe the spatial and temporal variability of SIC and atmospheric circulation on interannual and decadal timescales. Another goal is to investigate the nature and strength of the air-ice interactions. The air-ice interactions are investigated in detail in the first SVD mode of the coupled variability, which is characterized by decadal-to-interdecadal timescales. Subsequently, the nature and strength of the air-ice interactions are studied in the second SVD mode, which shows a long-term trend. The interactions in the third SVD mode which has an interannual timescale are briefly mentioned. (Abstract shortened by UMI.)
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Vennebusch, Markus. "Singular value decomposition and cluster analysis as regression diagnostics tools in geodetic VLBI." [S.l.] : [s.n.], 2007. http://deposit.ddb.de/cgi-bin/dokserv?idn=984912878.
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Kaufman, Jason R. "Digital video watermarking using singular value decomposition and two-dimensional principal component analysis." Ohio : Ohio University, 2006. http://www.ohiolink.edu/etd/view.cgi?ohiou1141855950.
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Yi, Dingrong. "Singular value decomposition of Arctic sea ice cover and overlying atmospheric circulation fluctuations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0005/MQ44321.pdf.
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Toyokawa, Hiroki. "Studies on Algorithms and Their Implementations for Fast and Accurate Singular Value Decomposition." 京都大学 (Kyoto University), 2013. http://hdl.handle.net/2433/174845.
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Qamar, Aamir, Islamud Din, and Muhammad Abbas Khan. "Analysis of Spherical Harmonics and Singular Value Decomposition as Compression Tools in Image Processing." Thesis, Linnéuniversitetet, Institutionen för datavetenskap, fysik och matematik, DFM, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-18608.
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Spherical Harmonics (SPHARM) and Singular Value Decomposition (SVD) utilize the orthogonal relations of its parameters to represent and process images. The process involve mapping of the image from its original parameter domain to a new domain where the processing is performed. This process induces distortion and smoothing is required. The image now mapped to the new parameter domain is descripted using SPHARM and SVD using one at a time. The least significant values for the SPHARM coefficients and singular values of SVD are truncated which induces compression in the reconstructed image keeping the memory allocation in view. In this thesis, we have applied SPHARM and SVD tools to represent and reconstruct an image. The image is first mapped to the unit sphere (a sphere with unit radius). The image gets distorted that is maximum at the north and south poles, for which smoothing is approached by leaving 0.15*π space blank at each pole where no mapping is done. Sampling is performed for the θ and φ parameters and the image is represented using spherical harmonics and its coefficients are calculated. The same is then repeated for the SVD and singular values are computed. Reconstruction is performed using the calculated parameters, but defined over some finite domain, which is done by truncating the SPHARM coefficients and the singular values inducing image compression. Results are formulated for the various truncation choices and analyzed and finally it is concluded that SPHARM is better as compared with SVD as compression tool as there is not much difference in the quality of the reconstructed image with both tools, though SVD seem better quality wise, but with much higher memory allocation than SPHARM.
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Winck, Ryder Christian. "Simultaneous control of coupled actuators using singular value decomposition and semi-nonnegative matrix factorization." Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/45907.
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This thesis considers the application of singular value decomposition (SVD) and semi-nonnegative matrix factorization (SNMF) within feedback control systems, called the SVD System and SNMF System, to control numerous subsystems with a reduced number of control inputs. The subsystems are coupled using a row-column structure to allow mn subsystems to be controlled using m+n inputs. Past techniques for controlling systems in this row-column structure have focused on scheduling procedures that offer limited performance. The SVD and SNMF Systems permit simultaneous control of every subsystem, which increases the convergence rate by an order of magnitude compared with previous methods. In addition to closed loop control, open loop procedures using the SVD and SNMF are compared with previous scheduling procedures, demonstrating significant performance improvements. This thesis presents theoretical results for the controllability of systems using the row-column structure and for the stability and performance of the SVD and SNMF Systems. Practical challenges to the implementation of the SVD and SNMF Systems are also examined. Numerous simulation examples are provided, in particular, a dynamic simulation of a pin array device, called Digital Clay, and two physical demonstrations are used to assess the feasibility of the SVD and SNMF Systems for specific applications.
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Liu, Chang. "Singular Value Decomposition Applied to Damage Diagnosis for Ultrasonic Guided Wave Structural Health Monitoring." Research Showcase @ CMU, 2014. http://repository.cmu.edu/dissertations/402.
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A structural health monitoring (SHM) system takes frequent monitoring records from permanently installed transducers on structures, and uses the information to identify potential structural degradation and to proactively maintain the structures. Guided wave testing is an attractive technique for structural health monitoring of large structures, because guided waves can propagate long distance and are sensitive to subtle and hidden damage. In guided wave SHM systems, ultrasonic records are often affected by environmental and operational variations, which produce undesired changes and cause false results. Moreover, although continuous monitoring produces sufficient information regarding structural integrity, we lack a data processing tool to extract, store, and utilize the damage-sensitive information to leverage the accuracy and robustness of damage detection and localization. In this dissertation, we develop a data-driven framework based on singular value decomposition that processes guided wave monitoring records to separate damage-related information from effects of environmental and operational variations. The method decomposes sequential monitoring records to reveal trends of different variations, and identifies the singular vector associated with damage development. Combined with delay-and-sum localization method, we can robustly localize the damage using the right singular vectors, which resemble the scatter signal and are robust to environmental and operational variations. The SVD framework is then refined, by adaptively updating the singular vectors with each arriving ultrasonic record , to achieve online damage detection and localization. The SVD damage diagnosis methodology is applied experimentally to detect and localize damage in plate and pipe structures, both in laboratory tests and in field tests.
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Qi, Weibin. "Image denoising with spline interpolation based on singular value decomposition and other evaluation methods." Thesis, University of Ottawa (Canada), 2005. http://hdl.handle.net/10393/27014.
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In this thesis, we construct two new algorithms for image denoising, namely, spline and spline-wavelet, which combine spline interpolation and wavelets together with nonlinear filtering based on block singular value decomposition. Those two approaches are compared with other existing methods, which involve BlockSvd filter, wavelet (global thresholding) filter, median filter, average filter, and adaptive filter. The performance of these approaches differs little from each other. Generally speaking, median filter is very suitable for processing images to reduce "salt and pepper" noise. But for zero-mean Gaussian and speckle noises, an adaptive filter and spline-wavelet methods are more stable and slightly superior to other filters in most conditions and for most images. The proposed algorithms were tested under different types of images and a wide range of signal to noise ratios (SNR). The numerical results demonstrate that these methods can be used in different and useful ways for reducing image noise.
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Liang, Qiao. "Singular Value Computation and Subspace Clustering." UKnowledge, 2015. http://uknowledge.uky.edu/math_etds/30.
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In this dissertation we discuss two problems. In the first part, we consider the problem of computing a few extreme eigenvalues of a symmetric definite generalized eigenvalue problem or a few extreme singular values of a large and sparse matrix. The standard method of choice of computing a few extreme eigenvalues of a large symmetric matrix is the Lanczos or the implicitly restarted Lanczos method. These methods usually employ a shift-and-invert transformation to accelerate the speed of convergence, which is not practical for truly large problems. With this in mind, Golub and Ye proposes an inverse-free preconditioned Krylov subspace method, which uses preconditioning instead of shift-and-invert to accelerate the convergence. To compute several eigenvalues, Wielandt is used in a straightforward manner. However, the Wielandt deflation alters the structure of the problem and may cause some difficulties in certain applications such as the singular value computations. So we first propose to consider a deflation by restriction method for the inverse-free Krylov subspace method. We generalize the original convergence theory for the inverse-free preconditioned Krylov subspace method to justify this deflation scheme. We next extend the inverse-free Krylov subspace method with deflation by restriction to the singular value problem. We consider preconditioning based on robust incomplete factorization to accelerate the convergence. Numerical examples are provided to demonstrate efficiency and robustness of the new algorithm.
In the second part of this thesis, we consider the so-called subspace clustering problem, which aims for extracting a multi-subspace structure from a collection of points lying in a high-dimensional space. Recently, methods based on self expressiveness property (SEP) such as Sparse Subspace Clustering and Low Rank Representations have been shown to enjoy superior performances than other methods. However, methods with SEP may result in representations that are not amenable to clustering through graph partitioning. We propose a method where the points are expressed in terms of an orthonormal basis. The orthonormal basis is optimally chosen in the sense that the representation of all points is sparsest. Numerical results are given to illustrate the effectiveness and efficiency of this method.
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Renkjumnong, Wasuta. "SVD and PCA in Image Processing." Digital Archive @ GSU, 2007. http://digitalarchive.gsu.edu/math_theses/31.
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The Singular Value Decomposition is one of the most useful matrix factorizations in applied linear algebra, the Principal Component Analysis has been called one of the most valuable results of applied linear algebra. How and why principal component analysis is intimately related to the technique of singular value decomposition is shown. Their properties and applications are described. Assumptions behind this techniques as well as possible extensions to overcome these limitations are considered. This understanding leads to the real world applications, in particular, image processing of neurons. Noise reduction, and edge detection of neuron images are investigated.
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Chong, Justin Brandon. "Activity Recognition Processing in a Self-Contained Wearable System." Thesis, Virginia Tech, 2008. http://hdl.handle.net/10919/35141.
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Electronic textiles provide an eective platform to contain wearable computing elements, espe-
cially components geared towards the application of activity recognition. An activity recogni-
tion system built into a wearable textile substrate can be utilized in a variety of areas including
health monitoring, military applications, entertainment, and fashion. Many of the activity
recognition and motion capture systems previously developed have several drawbacks and lim-
itations with regard to their respective designs and implementations. Some such systems are
often times expensive, not conducive to mass production, and may be dicult to calibrate.
An eective system must also be scalable and should be deployable in a variety of environ-
ments and contexts. This thesis presents the design and implementation of a self-contained
motion sensing wearable electronic textile system with an emphasis toward the application of
activity recognition. The system is developed with scalability and deployability in mind, and
as such, utilizes a two-tier hierarchical model combined with a network infrastructure and
wireless connectivity. An example prototype system, in the form of a jumpsuit garment, is
presented and is constructed from relatively inexpensive components and materials.Master of Science
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Ifrah, Philip. "Tree search and singular value decomposition : a comparison of two strategies for point-pattern matching." Thesis, McGill University, 1996. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=27229.
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Two approaches for solving point-pattern matching problems are compared; namely, a graph-matching algorithm (1) and an SVD-based procedure (2). In both cases, the features that are used in the matching process are point coordinates in Euclidean n-space, ${ rm I !E} sp{n}.$ The patterns being matched are assumed to be related by a combination of two transformations: (1) a permutation of the feature points which establishes the correspondence between the feature points of the different patterns and (2) a global geometric transformation based on rigid motions which aligns the patterns once the point correspondences are known. The problem of finding the first transformation, known as the point correspondence problem, is the most demanding part of the matching process in terms of computational requirements; accordingly, the focus is placed on the algorithms' ability to establish point correspondences. Computer simulations are used to evaluate the performance of the algorithms' respective search strategies in terms of both the accuracy of the final solution and the speed with which the solution is obtained. In all of the experiments, the performance of the graph matching algorithm is clearly superior to that of the SVD-based method in terms of both speed and accuracy; however, it is shown that the computational requirements of the tree search procedure used by the graph matching algorithm are strongly dependent on factors such as the magnitude of the noises that are contained in the patterns and on the mutual distances between the feature points. The major weakness of the SVD-based algorithm is its inconsistency in converging to the expected solution, especially when extra or occluded points are present in one or more of the patterns to be matched.
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Ifrah, Philip Isaac. "Tree search and singular value decomposition, a comparison of two strategies for point-pattern matching." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/mq29602.pdf.
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Vennebusch, Markus [Verfasser]. "Singular Value Decomposition and Cluster Analysis as Regression Diagnostics Tools in Geodetic VLBI / Markus Vennebusch." Bonn : Universitäts- und Landesbibliothek Bonn, 2019. http://d-nb.info/1197798692/34.
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Cai, HanQin. "Accelerating truncated singular-value decomposition: a fast and provable method for robust principal component analysis." Diss., University of Iowa, 2018. https://ir.uiowa.edu/etd/6068.
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Principal component analysis (PCA) is one of the most popular statistical procedures for dimension reduction. A modification of PCA, called robust principal component analysis (RPCA), has been studied to overcome the well-known shortness of PCA: sensitivity to outliers and corrupted data points. Earlier works have proved RPCA can be exactly recovered via semidenite programming. Recently, researchers have provided some provable non-convex solvers for RPCA, based on projected gradient descent or alternating projections, in full or partial observed settings. Yet, we nd the computational complexity of the recent RPCA algorithms can be improved further. We study RPCA in the fully observed setting, which is about separating a low rank matrix L and a sparse matrix S from their given sum D = L + S. In this thesis, a new non-convex algorithm, dubbed accelerated alternating projections, is introduced for solving RPCA rapidly. The proposed new algorithm signicantly improves the computational efficiency of the existing alternating projections based algorithm proposed in [1] when updating the estimate of low rank factor. The acceleration is achieved by rst projecting a matrix onto some low dimensional subspace before obtaining a new estimate of the low rank matrix via truncated singular-value decomposition. Essentially, truncated singular-value decomposition (a.k.a. the best low rank approximation) is replaced by a high-efficiency sub-optimal low rank approximation, while the convergence is retained. Exact recovery guarantee has been established, which shows linear convergence of the proposed algorithm under certain natural assumptions. Empirical performance evaluations establish the advantage of our algorithm over other state-of-the-art algorithms for RPCA. An application experiment on video background subtraction has been also established.
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Brown, Michael J. "SINGULAR VALUE DECOMPOSITION AND 2D PRINCIPAL COMPONENT ANALYSIS OF IRIS-BIOMETRICS FOR AUTOMATIC HUMAN IDENTIFICATION." Ohio University / OhioLINK, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1149187904.
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Yang, Xue. "Neumann problems for second order elliptic operators with singular coefficients." Thesis, University of Manchester, 2012. https://www.research.manchester.ac.uk/portal/en/theses/neumann-problems-for-second-order-elliptic-operators-with-singular-coefficients(2e65b780-df58-4429-89df-6d87777843c8).html.
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In this thesis, we prove the existence and uniqueness of the solution to a Neumann boundary problem for an elliptic differential operator with singular coefficients, and reveal the relationship between the solution to the partial differential equation (PDE in abbreviation) and the solution to a kind of backward stochastic differential equations (BSDE in abbreviation).This study is motivated by the research on the Dirichlet problem for an elliptic operator (\cite{Z}). But it turns out that different methods are needed to deal with the reflecting diffusion on a bounded domain. For example, the integral with respect to the boundary local time, which is a nondecreasing process associated with the reflecting diffusion, needs to be estimated. This leads us to a detailed study of the reflecting diffusion. As a result, two-sided estimates on the heat kernels are established. We introduce a new type of backward differential equations with infinity horizon and prove the existence and uniqueness of both L2 and L1 solutions of the BSDEs. In this thesis, we use the BSDE to solve the semilinear Neumann boundary problem. However, this research on the BSDEs has its independent interest. Under certain conditions on both the "singular" coefficient of the elliptic operator and the "semilinear coefficient" in the deterministic differential equation, we find an explicit probabilistic solution to the Neumann problem, which supplies a L2 solution of a BSDE with infinite horizon. We also show that, less restrictive conditions on the coefficients are needed if the solution to the Neumann boundary problem only provides a L1 solution to the BSDE.
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"Some Topics Concerning the Singular Value Decomposition and Generalized Singular Value Decomposition." Doctoral diss., 2012. http://hdl.handle.net/2286/R.I.15152.
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abstract: This dissertation involves three problems that are all related by the use of the singular value decomposition (SVD) or generalized singular value decomposition (GSVD). The specific problems are (i) derivation of a generalized singular value expansion (GSVE), (ii) analysis of the properties of the chi-squared method for regularization parameter selection in the case of nonnormal data and (iii) formulation of a partial canonical correlation concept for continuous time stochastic processes. The finite dimensional SVD has an infinite dimensional generalization to compact operators. However, the form of the finite dimensional GSVD developed in, e.g., Van Loan does not extend directly to infinite dimensions as a result of a key step in the proof that is specific to the matrix case. Thus, the first problem of interest is to find an infinite dimensional version of the GSVD. One such GSVE for compact operators on separable Hilbert spaces is developed. The second problem concerns regularization parameter estimation. The chi-squared method for nonnormal data is considered. A form of the optimized regularization criterion that pertains to measured data or signals with nonnormal noise is derived. Large sample theory for phi-mixing processes is used to derive a central limit theorem for the chi-squared criterion that holds under certain conditions. Departures from normality are seen to manifest in the need for a possibly different scale factor in normalization rather than what would be used under the assumption of normality. The consequences of our large sample work are illustrated by empirical experiments. For the third problem, a new approach is examined for studying the relationships between a collection of functional random variables. The idea is based on the work of Sunder that provides mappings to connect the elements of algebraic and orthogonal direct sums of subspaces in a Hilbert space. When combined with a key isometry associated with a particular Hilbert space indexed stochastic process, this leads to a useful formulation for situations that involve the study of several second order processes. In particular, using our approach with two processes provides an independent derivation of the functional canonical correlation analysis (CCA) results of Eubank and Hsing. For more than two processes, a rigorous derivation of the functional partial canonical correlation analysis (PCCA) concept that applies to both finite and infinite dimensional settings is obtained.Dissertation/Thesis
Ph.D. Statistics 2012
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Shah, Mili. "A symmetry preserving singular value decomposition." Thesis, 2007. http://hdl.handle.net/1911/20648.
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This thesis concentrates on the development, analysis, implementation, and application of a symmetry preserving singular value decomposition (SPSVD). This new factorization enhances the singular value decomposition (SVD)---a powerful method for calculating a low rank approximation to a large data set---by producing the best symmetric low rank approximation to a matrix with respect to the Frobenius norm and matrix-2 norm.
Calculating an SPSVD is a two-step process. In the first step, a matrix representation for the symmetry of a given data set must be determined. This process is presented as a novel iterative reweighting method: a scheme which is rapidly convergent in practice and seems to be extremely effective in ignoring outliers of the data. In the second step, the best approximation that maintains the symmetry calculated from the first step is computed. This approximation is designated the SPSVD of the data set.
In many situations, the SPSVD needs efficient updating. For instance, if new data is given, then the symmetry of the set may change and an alternative matrix representation has to be formed. A modification in the matrix representation also alters the SPSVD. Therefore, proficient methods to address each of these issues are developed in this thesis.
This thesis applies the SPSVD to molecular dynamic (MD) simulations of proteins and to face analysis. Symmetric motions of a molecule may be lost when the SVD is applied to MD trajectories of proteins. This loss is corrected by implementing the SPSVD to create major modes of motion that best describe the symmetric movements of the protein. Moreover, the SPSVD may reduce the noise that often occurs on the side chains of molecules. In face analysis, the SVD is regularly used for compression. Because faces are nearly symmetric, applying the SPSVD to faces creates a more efficient compression. This efficiency is a result of having to store only half the picture for the SPSVD. Therefore, it is apparent that the SPSVD is an effective method for calculating a symmetric low rank approximation for a set of data.
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Hsieh, Kwen Jenn, and 謝昆. "Singular Value Decomposition for Texture Analysis." Thesis, 1995. http://ndltd.ncl.edu.tw/handle/21687337987753189799.
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"Clustering datasets with singular value decomposition." COLLEGE OF CHARLESTON, 2009. http://pqdtopen.proquest.com/#viewpdf?dispub=1461189.
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LIN, WEN-QIN, and 林文欽. "Singular system decomposition and model reduction." Thesis, 1990. http://ndltd.ncl.edu.tw/handle/33479976865278441278.
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Chen, Allan, and 陳亮瑜. "Universal Singular Value Decomposition for Lighting Compensation." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/49314312423284926867.
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碩士國立高雄應用科技大學
光電與通訊研究所
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Face recognition has been getting pretty good at full frontal faces and well illumination, but as soon as you go towards poor lighting, there have been problems. This thesis presents a new compensation way for variant lighting based on the proposed universal singular value decomposition method. The lighting source is classified as frontal or side lighting based on the observation of B color channel magnitude and the reconstructed image using the first singular value. To reduce the influence of light variation on face recognition, universal singular value decomposition was proposed in each individual color channel of RGB. Using the channel with the greatest mean color value of the distribution as the basis, the weight of the lighting compensation coefficients in the other two channels was proportionally adjusted to adapt the dynamic range of the RGB color channels. We employed 67 frontal images under 45 illumination conditions which were randomly selected from the CMU-PIE database for training and experiment. The results with projection color space transformation revealed that the recognition rate from our proposed approach was 97.62% and higher than those of methods proposed in relevant studies. Keywords: Face recognition, frontal or side lighting, universal singular value decomposition, CMU-PIE database.