Bibliographic Notes
Contents
Bibliographic Notes#
Following is a partial list of books and articles which have been referenced heavily in this work. This list is by no means exhaustive.
General introduction to optimization can be found in [63].
[17] is a standard textbook for convex optimization theory, applications and algorithms.
[58] is a good reference for linear programming.
[16] covers alternating direction method of multipliers (ADMM) algorithms.
[65] provides good coverage on proximal algorithms.
Bibliography#
- 1
Michal Aharon, Michael Elad, and Alfred M Bruckstein. K-svd and its non-negative variant for dictionary design. In Optics & Photonics 2005, 591411–591411. International Society for Optics and Photonics, 2005.
- 2
Charalambos D Aliprantis and Owen Burkinshaw. Principles of real analysis. Gulf Professional Publishing, 1998.
- 3
M. Artin. Algebra. Pearson Modern Classics for Advanced Mathematics Series. Pearson, 2017. ISBN 9780134689609. URL: https://books.google.co.in/books?id=ZfIXMQAACAAJ.
- 4
Afonso S Bandeira, Edgar Dobriban, Dustin G Mixon, and William F Sawin. Certifying the restricted isometry property is hard. IEEE transactions on information theory, 59(6):3448–3450, 2013.
- 5
Ronen Basri and David W Jacobs. Lambertian reflectance and linear subspaces. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 25(2):218–233, 2003.
- 6
Amir Beck. Introduction to nonlinear optimization: Theory, algorithms, and applications with MATLAB. SIAM, 2014.
- 7
Amir Beck. First-order methods in optimization. SIAM, 2017.
- 8
D. Bertsekas and J.N. Tsitsiklis. Introduction to Probability. Athena Scientific optimization and computation series. Athena Scientific, 2008. ISBN 9781886529236. URL: https://books.google.co.in/books?id=-oNZEAAAQBAJ.
- 9
Dimitri Bertsekas, Angelia Nedic, and Asuman Ozdaglar. Convex analysis and optimization. Volume 1. Athena Scientific, 2003.
- 10
P. Billingsley. Probability and Measure. Wiley Series in Probability and Statistics. Wiley, 2012. ISBN 9781118341919. URL: https://books.google.co.in/books?id=a3gavZbxyJcC.
- 11
Christopher M Bishop and Nasser M Nasrabadi. Pattern recognition and machine learning. Volume 4. Springer, 2006.
- 12
Ȧke Björck and Gene H Golub. Numerical methods for computing angles between linear subspaces. Mathematics of computation, 27(123):579–594, 1973.
- 13
Petros T Boufounos and Richard G Baraniuk. 1-bit compressive sensing. In 2008 42nd Annual Conference on Information Sciences and Systems, 16–21. IEEE, 2008.
- 14
Terrance E Boult and Lisa Gottesfeld Brown. Factorization-based segmentation of motions. In Visual Motion, 1991., Proceedings of the IEEE Workshop on, 179–186. IEEE, 1991.
- 15
Stephen Boyd and Almir Mutapcic. Subgradient methods. 2008.
- 16
Stephen Boyd, Neal Parikh, Eric Chu, Borja Peleato, and Jonathan Eckstein. Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends in Machine Learning, 3(1):1–122, 2011.
- 17
Stephen P Boyd and Lieven Vandenberghe. Convex optimization. Cambridge university press, 2004.
- 18
Emmanuel J Candes and Justin Romberg. Practical signal recovery from random projections. Wavelet Applications in Signal and Image Processing XI Proc. SPIE Conf. 5914., 2004.
- 19
Emmanuel J Candes and Terence Tao. Decoding by linear programming. Information Theory, IEEE Transactions on, 51(12):4203–4215, 2005.
- 20
Emmanuel J Candes and Terence Tao. Near-optimal signal recovery from random projections: universal encoding strategies? Information Theory, IEEE Transactions on, 52(12):5406–5425, 2006.
- 21
Emmanuel J Candès. The restricted isometry property and its implications for compressed sensing. Comptes Rendus Mathematique, 346(9):589–592, 2008.
- 22
Jie Chen and Xiaoming Huo. Theoretical results on sparse representations of multiple-measurement vectors. Signal Processing, IEEE Transactions on, 54(12):4634–4643, 2006.
- 23
Scott Shaobing Chen, David L Donoho, and Michael A Saunders. Atomic decomposition by basis pursuit. SIAM journal on scientific computing, 20(1):33–61, 1998.
- 24
João Paulo Costeira and Takeo Kanade. A multibody factorization method for independently moving objects. International Journal of Computer Vision, 29(3):159–179, 1998.
- 25
Mark A Davenport and Michael B Wakin. Analysis of orthogonal matching pursuit using the restricted isometry property. Information Theory, IEEE Transactions on, 56(9):4395–4401, 2010.
- 26
Arthur P Dempster, Nan M Laird, and Donald B Rubin. Maximum likelihood from incomplete data via the em algorithm. Journal of the royal statistical society. Series B (methodological), pages 1–38, 1977.
- 27
Harm Derksen. Hilbert series of subspace arrangements. Journal of pure and applied algebra, 209(1):91–98, 2007.
- 28
David L Donoho and Michael Elad. Optimally sparse representation in general (nonorthogonal) dictionaries via $l_1$ minimization. Proceedings of the National Academy of Sciences, 100(5):2197–2202, 2003.
- 29
Richard O Duda, Peter E Hart, and David G Stork. Pattern classification. John Wiley & Sons, 2012.
- 30
Michael Elad. Sparse and redundant representations. Springer, 2010.
- 31
Michael Elad and Alfred M Bruckstein. A generalized uncertainty principle and sparse representation in pairs of bases. Information Theory, IEEE Transactions on, 48(9):2558–2567, 2002.
- 32
Ehsan Elhamifar and Rene Vidal. Sparse subspace clustering: algorithm, theory, and applications. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 35(11):2765–2781, 2013.
- 33
Ehsan Elhamifar and René Vidal. Clustering disjoint subspaces via sparse representation. In Acoustics Speech and Signal Processing (ICASSP), 2010 IEEE International Conference on, 1926–1929. IEEE, 2010.
- 34
Kjersti Engan, Sven Ole Aase, and J Hakon Husoy. Method of optimal directions for frame design. In Acoustics, Speech, and Signal Processing, 1999. Proceedings., 1999 IEEE International Conference on, volume 5, 2443–2446. IEEE, 1999.
- 35
David G Feingold, Richard S Varga, and others. Block diagonally dominant matrices and generalizations of the gerschgorin circle theorem. Pacific J. Math, 12(4):1241–1250, 1962.
- 36
W. Feller. An Introduction to Probability Theory and Its Applications. Number v. 1 in An Introduction to Probability Theory and Its Applications. Wiley, 1968. URL: https://books.google.co.in/books?id=wYkQAQAAIAAJ.
- 37
Philippe Flajolet and Robert Sedgewick. Analytic combinatorics. cambridge University press, 2009.
- 38
Guojun Gan, Chaoqun Ma, and Jianhong Wu. Data clustering: theory, algorithms, and applications. SIAM, 2020.
- 39
Charles William Gear. Multibody grouping from motion images. International Journal of Computer Vision, 29(2):133–150, 1998.
- 40
Athinodoros S. Georghiades, Peter N. Belhumeur, and David J. Kriegman. From few to many: illumination cone models for face recognition under variable lighting and pose. IEEE transactions on pattern analysis and machine intelligence, 23(6):643–660, 2001.
- 41
D. Gopal, A. Deshmukh, A.S. Ranadive, and S. Yadav. An Introduction to Metric Spaces. CRC Press, 2020. ISBN 9781000087994. URL: https://books.google.co.in/books?id=13jtDwAAQBAJ.
- 42
Vivek K Goyal, Martin Vetterli, and Nguyen T Thao. Quantized overcomplete expansions in ir/sup n: analysis, synthesis, and algorithms. IEEE Transactions on Information Theory, 44(1):16–31, 1998.
- 43
Rémi Gribonval, Holger Rauhut, Karin Schnass, and Pierre Vandergheynst. Atoms of all channels, unite! average case analysis of multi-channel sparse recovery using greedy algorithms. Journal of Fourier analysis and Applications, 14(5-6):655–687, 2008.
- 44
Phillip Griffiths and Joseph Harris. Principles of algebraic geometry. John Wiley & Sons, 2014.
- 45
Joe Harris. Algebraic geometry: a first course. Volume 133. Springer Science & Business Media, 2013.
- 46
John A Hartigan. Clustering algorithms. 1975.
- 47
Robin Hartshorne. Algebraic geometry. Volume 52. Springer Science & Business Media, 1977.
- 48
Jean-Baptiste Hiriart-Urruty and Claude Lemaréchal. Convex analysis and minimization algorithms I: Fundamentals. Volume 305. Springer science & business media, 2013.
- 49
Jeffrey Ho, Ming-Hsuan Yang, Jongwoo Lim, Kuang-Chih Lee, and David Kriegman. Clustering appearances of objects under varying illumination conditions. In Computer Vision and Pattern Recognition, 2003. Proceedings. 2003 IEEE Computer Society Conference on, volume 1, I–11. IEEE, 2003.
- 50
Kenneth Hoffman and Ray Kunze. Linear algebra, prentice-hall. Inc., Englewood Cliffs, New Jersey, pages 122–125, 1971.
- 51
Anil K Jain and Richard C Dubes. Algorithms for clustering data. Prentice-Hall, Inc., 1988.
- 52
Anil K Jain, M Narasimha Murty, and Patrick J Flynn. Data clustering: a review. ACM computing surveys (CSUR), 31(3):264–323, 1999.
- 53
Kenichi Kanatani. Motion segmentation by subspace separation and model selection. image, 1:1, 2001.
- 54
Paul Joseph Kelly and Max L Weiss. Geometry and convexity: a study in mathematical methods. John Wiley & Sons, 1979.
- 55
Andrei Nikolaevich Kolmogorov and Albert T Bharucha-Reid. Foundations of the theory of probability: Second English Edition. Courier Dover Publications, 2018.
- 56
Serge Lang. Algebra revised third edition. Volume 1. Springer Science and Media, 2002.
- 57
Stuart Lloyd. Least squares quantization in pcm. IEEE transactions on information theory, 28(2):129–137, 1982.
- 58
David G Luenberger, Yinyu Ye, and others. Linear and nonlinear programming. Volume 2. Springer, 1984.
- 59
James MacQueen and others. Some methods for classification and analysis of multivariate observations. In Proceedings of the fifth Berkeley symposium on mathematical statistics and probability, volume 1, 281–297. Oakland, CA, USA., 1967.
- 60
Joy Morris. Combinatorics: enumeration, graph theory, and design theory. 2017.
- 61
Deanna Needell and Joel A Tropp. Cosamp: iterative signal recovery from incomplete and inaccurate samples. Applied and Computational Harmonic Analysis, 26(3):301–321, 2009.
- 62
Andrew Y Ng, Michael I Jordan, Yair Weiss, and others. On spectral clustering: analysis and an algorithm. Advances in neural information processing systems, 2:849–856, 2002.
- 63
Jorge Nocedal and Stephen Wright. Numerical optimization. Springer Science & Business Media, 2006.
- 64
A. Papoulis and S.U. Pillai. Probability, Random Variables, and Stochastic Processes. McGraw-Hill series in electrical and computer engineering. McGraw-Hill, 2002. ISBN 9780072817256. URL: https://books.google.co.in/books?id=Mal4OgAACAAJ.
- 65
Neal Parikh and Stephen Boyd. Proximal algorithms. Foundations and Trends in optimization, 1(3):127–239, 2014.
- 66
Conrad J Poelman and Takeo Kanade. A paraperspective factorization method for shape and motion recovery. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 19(3):206–218, 1997.
- 67
Ralph Tyrell Rockafellar. Convex analysis. Princeton university press, 2015.
- 68
S.M. Ross. A First Course in Probability. Pearson Education, Incorporated, 2014. ISBN 9780321794772. URL: https://books.google.co.in/books?id=7yqBNAEACAAJ.
- 69
S.M. Ross. Introduction to Probability Models. Academic Press. Academic Press, 2014. ISBN 9780124079489. URL: https://books.google.co.in/books?id=bKjSsgEACAAJ.
- 70
Ron Rubinstein, Alfred M Bruckstein, and Michael Elad. Dictionaries for sparse representation modeling. Proceedings of the IEEE, 98(6):1045–1057, 2010.
- 71
Jianbo Shi and Jitendra Malik. Normalized cuts and image segmentation. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 22(8):888–905, 2000.
- 72
H. Stark, J.W. Woods, B. Thilaka, and A. Kumar. Probability, Statistics, and Random Processes for Engineers. Always learning. Pearson Education, 2012. ISBN 9780273752288. URL: https://books.google.co.in/books?id=PMngoQEACAAJ.
- 73
Carlo Tomasi and Takeo Kanade. Detection and tracking of point features. School of Computer Science, Carnegie Mellon Univ. Pittsburgh, 1991.
- 74
Carlo Tomasi and Takeo Kanade. Shape and motion from image streams under orthography: a factorization method. International Journal of Computer Vision, 9(2):137–154, 1992.
- 75
Ivana Tosic and Pascal Frossard. Dictionary learning. Signal Processing Magazine, IEEE, 28(2):27–38, 2011.
- 76
W.F. Trench. Introduction to Real Analysis. Open Textbook Library. Prentice Hall/Pearson Education, 2003. ISBN 9780130457868. URL: https://books.google.co.in/books?id=NkFkQgAACAAJ.
- 77
Joel A Tropp. Greed is good: algorithmic results for sparse approximation. Information Theory, IEEE Transactions on, 50(10):2231–2242, 2004.
- 78
Joel A Tropp. Just relax: convex programming methods for subset selection and sparse approximation. ICES report, 2004.
- 79
Joel A Tropp. Just relax: convex programming methods for identifying sparse signals in noise. Information Theory, IEEE Transactions on, 52(3):1030–1051, 2006.
- 80
Joel A Tropp and Anna C Gilbert. Signal recovery from random measurements via orthogonal matching pursuit. Information Theory, IEEE Transactions on, 53(12):4655–4666, 2007.
- 81
Jacobus Hendricus Van Lint, Richard Michael Wilson, and Richard Michael Wilson. A course in combinatorics. Cambridge university press, 2001.
- 82
Vladimir Vapnik. The nature of statistical learning theory. Springer Science & Business Media, 2013.
- 83
René Vidal. A tutorial on subspace clustering. IEEE Signal Processing Magazine, 28(2):52–68, 2010.
- 84
Ulrike Von Luxburg. A tutorial on spectral clustering. Statistics and computing, 17(4):395–416, 2007.
- 85
Silke Wagner and Dorothea Wagner. Comparing clusterings: an overview. 2007.
- 86
Rui Xu and Donald Wunsch. Survey of clustering algorithms. IEEE Transactions on neural networks, 16(3):645–678, 2005.
- 87
Lihi Zelnik-Manor and Pietro Perona. Self-tuning spectral clustering. In Advances in neural information processing systems, 1601–1608. 2004.
- 88
Wikipedia contributors. Ordered pair — Wikipedia, the free encyclopedia. URL: https://en.wikipedia.org/wiki/Ordered_pair.
- 89
Wikipedia contributors. Relation (mathematics) — Wikipedia, the free encyclopedia. URL: https://en.wikipedia.org/wiki/Relation_(mathematics).
- 90
Wikipedia contributors. Tuple — Wikipedia, the free encyclopedia. URL: https://en.wikipedia.org/wiki/Tuple.