Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
Buchtitelbild

2016 | OriginalPaper | Buchkapitel

1. Introduction

verfasst von : René Vidal, Yi Ma, S. Shankar Sastry

Erschienen in: Generalized Principal Component Analysis

Verlag: Springer New York

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Nächstes Kapitel Principal Component Analysis
Fußnoten
1
Under fairly broad conditions that we will elaborate in this book.
 
2
In the statistical learning literature, the most commonly used term is “mixture model.” In systems theory, the typical term is “hybrid model.” In algebraic geometry, for the case of subspaces, the typical term is a “subspace arrangement.”
 
3
In this book, we will use interchangeably “mixture,” “collection,” “union,” and “arrangement” of subspaces or models. But be aware that in the case of subspaces, the formal terminology in algebraic geometry is a “subspace arrangement.”
 
4
Or equivalently, we may impose a nonuniform prior distribution over all models.
 
5
Occam’s (or Ockham’s) razor is a principle attributed to the fourteenth-century logician and Franciscan friar William of Occam: “Pluralitas non est ponenda sine neccesitate,” which translates literally as “entities should not be multiplied unnecessarily.” In science, this principle is often interpreted thus: “when you have two competing theories that make exactly the same predictions, the simpler one is better.”
 
6
Roughly speaking, a smooth manifold is a special topological space that is locally homeomorphic to a Euclidean space and has the same dimension everywhere. A general topological space may have singularities and consist of components of different dimensions.
 
7
If the true distribution from which the data are drawn is \(q(\boldsymbol{x})\), then the maximum likelihood estimate \(p(\boldsymbol{x}\mid \theta ^{{\ast}})\) minimizes the Kullback–Leibler (KL) divergence \(KL(q\|p) =\int q(\boldsymbol{x})\log \frac{q(\boldsymbol{x})} {p(\boldsymbol{x})}\ d\boldsymbol{x}\) among the given class of distributions (see Appendix B.)
 
8
Singular distributions are probability distributions concentrated on a set of Lebesgue measure zero. Such distributions are not absolutely continuous with respect to the Lebesgue measure. The Cantor distribution is one example of a singular distribution.
 
9
As the cluster centers.
 
10
An object is called Lambertian if its apparent brightness is the same from any viewpoint.
 
11
Depending on the illumination model, the illumination space can be approximately three- or nine-dimensional.
 
12
The legitimacy of the projection process will be addressed in Chapter 5
 
13
In contrast to the previous face example, there is no rigorous mathematical justification for why local profiles from a region of similar texture must span a low-dimensional linear subspace. However, there is strong empirical evidence that a linear subspace normally gives a very good approximation.
 
14
That is, the number d i of basis elements needed to represent the ith region is typically much smaller than the number d of basis elements needed to represent the whole image.
 
15
An algebraic variety is an irreducible algebraic set. An algebraic set is called irreducible if it cannot be written as the union of two proper algebraic subsets. A subspace is one such example.
 
16
A prime ideal is an ideal that cannot be decomposed further as the intersection of two other ideals (see Appendix C). The zero-level set of a prime ideal is an irreducible algebraic set, i.e., an algebraic variety.
 
17
Notice the correspondence between a “union” of algebraic varieties and the “multiplication” of the polynomials associated with the varieties.
 
18
According to Hilbert’s Nullstellensatz (see Appendix C), there is a one-to-one correspondence between algebraic sets and radical ideals (Eisenbud 1996).
 
19
For the special case in which the ideal is generated by a single polynomial, the decomposition is equivalent to factoring the polynomial into factors.
 
20
For example, every function can be approximated arbitrarily well by a piecewise linear function with a sufficient number of pieces.
 
21
For instance, the complexity of a model can be measured as the minimum number of bits needed to fully describe the model, and the data fidelity can be measured by the distance from the sample points to the model.
 
Literatur
Agarwal, P., & Mustafa, N. (2004). k-means projective clustering. In ACM Symposium on Principles of Database Systems.
Agarwal, S., Lim, J., Zelnik-Manor, L., Perona, P., Kriegman, D., & Belongie, S. (2005). Beyond pairwise clustering. In IEEE Conference on Computer Vision and Pattern Recognition (Vol. 2, pp. 838–845).
Aggarwal, G., Roy-Chowdhury, A., & Chellappa, R. (2004). A system identification approach for video-based face recognition. In Proceedings of International Conference on Pattern Recognition (pp. 23–26).
Akaike, H. (1977). A new look at the statistical model selection. IEEE Transactions on Automatic Control, 16(6), 716–723.MathSciNetMATH
Aldroubi, A., Cabrelli, C., & Molter, U. (2008). Optimal non-linear models for sparsity and sampling. Journal of Fourier Analysis and Applications, 14(5–6), 793–812.MathSciNetMATHCrossRef
Aldroubi, A., & Zaringhalam, K. (2009). Nonlinear least squares in ℝ N . Acta Applicandae Mathematicae, 107(1–3), 325–337.MathSciNetMATHCrossRef
Alessandri, A., & Coletta, P. (2001). Design of Luenberger observers for a class of hybrid linear systems. In Proceedings of Hybrid Systems: Computation and Control (pp. 7–18). New York: Springer.CrossRef
Ali, S., Basharat, A., & Shah, M. (2007). Chaotic invariants for human action recognition. In Proceedings of International Conference on Computer Vision.
Amaldi, E., & Kann, V. (1998). On the approximability of minimizing nonzero variables or unsatisfied relations in linear systems. Theoretical Computer Science, 209, 237–260.MathSciNetMATHCrossRef
Anderson, B., & Johnson, R. (1982). Exponential convergence of adaptive identification and control algorithms. Automatica, 18(1), 1–13.MathSciNetMATHCrossRef
Arbelaez, P. (2006). Boundary extraction in natural images using ultrametric contour maps. In Workshop on Perceptual Organization in Computer Vision.
Arbelaez, P., Maire, M., Fowlkes, C., & Malik, J. (2009). From contours to regions: An empirical evaluation. In IEEE Conference on Computer Vision and Pattern Recognition.
Arora, S., Bhaskara, A., Ge, R., & Ma, T. (2014). Provable bounds for learning some deep representations. In Proceedings of International Conference on Machine Learning.
Avidan, S., & Shashua, A. (2000). Trajectory triangulation: 3D reconstruction of moving points from a monocular image sequence. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(4), 348–357.CrossRef
Ayazoglu, M., Li, B., Dicle, C., Sznaier, M., & Camps, O. (2011). Dynamic subspace-based coordinated multicamera tracking. In IEEE International Conference on Computer Vision (pp. 2462–2469)
Babaali, M., & Egerstedt, M. (2004). Observability of switched linear systems. In Proceedings of Hybrid Systems: Computation and Control. New York: Springer.
Bach, F. (2013). Convex relaxations of structured matrix factorizations. arXiv:1309.3117v1.
Balluchi, A., Benvenuti, L., Benedetto, M. D., & Sangiovanni-Vincentelli, A. (2002). Design of observers for hybrid systems. In Proceedings of Hybrid Systems: Computation and Control (Vol. 2289, pp. 76–89). New York: Springer.
Barbic, J., Safonova, A., Pan, J.-Y., Faloutsos, C., Hodgins, J. K., & Pollar, N. S. (2004). Segmenting motion capture data into distinct behaviors. In Graphics Interface.
Barnett, V., & Lewis, T. (1983). Outliers in statistical data (2nd ed.). New York: Wiley.MATH
Basri, R., & Jacobs, D. (2003). Lambertian reflection and linear subspaces. IEEE Transactions on Pattern Analysis and Machine Intelligence, 25(2), 218–233.CrossRef
Beck, A., & Teboulle, M. (2009). A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM Journal on Imaging Sciences, 2(1), 183–202.MathSciNetMATHCrossRef
Béjar, B., Zappella, L., & Vidal, R. (2012). Surgical gesture classification from video data. In Medical Image Computing and Computer Assisted Intervention (pp. 34–41).
Belhumeur, P., Hespanda, J., & Kriegeman, D. (1997). Eigenfaces vs. Fisherfaces: Recognition using class specific linear projection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 19(7), 711–720.CrossRef
Belhumeur, P., & Kriegman, D. (1998). What is the set of images of an object under all possible illumination conditions? International Journal of Computer Vision, 28(3), 1–16.CrossRef
Belkin, M., & Niyogi, P. (2002). Laplacian eigenmaps and spectral techniques for embedding and clustering. In Proceedings of Neural Information Processing Systems (NIPS) (pp. 585–591).
Beltrami, E. (1873). Sulle funzioni bilineari. Giornale di Mathematiche di Battaglini, 11, 98–106.MATH
Bemporad, A., Ferrari, G., & Morari, M. (2000). Observability and controllability of piecewise affine and hybrid systems. IEEE Transactions on Automatic Control, 45(10), 1864–1876.MathSciNetMATHCrossRef
Bemporad, A., Garulli, A., Paoletti, S., & Vicino, A. (2003). A greedy approach to identification of piecewise affine models. In Hybrid systems: Computation and control. Lecture notes in computer science (pp. 97–112). New York: Springer.
Bemporad, A., Roll, J., & Ljung, L. (2001). Identification of hybrid systems via mixed-integer programming. In Proceedings of IEEE Conference on Decision & Control (pp. 786–792).
Benson, H. (1994). Concave minimization: Theory, applications and algorithms. In R. Horst & P. M. Pardalos (Eds.), Handbook of global optimization (vol. 2, pp. 43-148), Springer Verlag.
Bertsekas, D. P. (1999). Nonlinear programming (2nd ed.). Optimization and computation (Vol. 2) Belmont: Athena Scientific.
Bickel, P. J. (1976). Another look at robustness: A review of reviews and some new developments. Scandinavian Journal of Statistics, 3(28), 145–168.MathSciNetMATH
Bickel, P. J., & Doksum, K. A. (2000). Mathematical statistics: Basic ideas and selected topics (2nd ed.). Upper Saddle River: Prentice Hall.MATH
Billio, M., Monfort, A., & Robert, C. (1999). Bayesian estimation of switching ARMA models. Journal of Econometrics, 93(2), 229–255.MathSciNetMATHCrossRef
Bissacco, A., Chiuso, A., Ma, Y., & Soatto, S. (2001). Recognition of human gaits. In Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (Vol. 2, pp. 52–58).
Björner, A. (1994). Subspace arrangements. In First European Congress of Mathematics, Vol. I (Paris, 1992). Progress in mathematics (Vol. 119, pp. 321–370). Basel: Birkhäuser.
Björner, A., Peeva, I., & Sidman, J. (2005). Subspace arrangements defined by products of linear forms. Journal of the London Mathematical Society 71 (2), 273–288.MathSciNetMATHCrossRef
Blake, A., North, B., & Isard, M. (1999). Learning multi-class dynamics. Advances in Neural Information Processing Systems, 11, 389–395. Cambridge: MIT Press.
Bochnak, J., Coste, M., & Roy, M. F. (1998). Real Algebraic Geometry. New York: Springer.MATHCrossRef
Bottou, L., & Bengio, J. (1995). Convergence properties of the k-means algorithms. In Neural Information Processing and Systems.
Boult, T., & Brown, L. (1991). Factorization-based segmentation of motions. In IEEE Workshop on Motion Understanding (pp. 179–186).
Boyd, S., Parikh, N., Chu, E., Peleato, B., & Eckstein, J. (2010). Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends in Machine Learning, 3(1), 1–122.MATHCrossRef
Boyd, S., & Vandenberghe, L. (2004). Convex Optimization. Cambridge: Cambridge University Press.MATHCrossRef
Brandt, S. (2002). Closed-form solutions for affine reconstruction under missing data. In In Proceedings Statistical Methods for Video Processing (ECCV’02 Workshop).
Broomhead, D. S., & Kirby, M. (2000). A new approach to dimensionality reduction theory and algorithms. SIAM Journal of Applied Mathematics, 60(6), 2114–2142.MathSciNetMATHCrossRef
Bruckstein, A., Donoho, D., & Elad, M. (2009). From sparse solutions of systems of equations to sparse modeling of signals and images. SIAM Review, 51(1), 34–81.MathSciNetMATHCrossRef
Buchanan, A., & Fitzgibbon, A. (2005). Damped Newton algorithms for matrix factorization with missing data. In IEEE Conference on Computer Vision and Pattern Recognition (pp. 316–322).
Burer, S., & Monteiro, R. D. C. (2005). Local minima and convergence in low-rank semidefinite programming. Mathematical Programming, Series A, 103(3), 427–444.MathSciNetMATHCrossRef
Burges, C. (2005). Geometric methods for feature extraction and dimensional reduction - a guided tour. In The data mining and knowledge discovery handbook (pp. 59–92). Boston: Kluwer Academic.CrossRef
Burges, C. J. C. (2010). Dimension reduction: A guided tour. Foundations and Trends in Machine Learning, 2(4), 275–365.MATHCrossRef
Burnham, K. P., & Anderson, D. R. (2002). Model selection and multimodel inference: A practical information-theoretic approach. New York: Springer.MATH
Burt, P. J., & Adelson, E. H. (1983). The Laplacian pyramid as a compact image code. IEEE Transactions on Communications, 31(4), 532–540.CrossRef
Cai, J.-F., Candés, E. J., & Shen, Z. (2008). A singular value thresholding algorithm for matrix completion. SIAM Journal of Optimization, 20(4), 1956–1982.MathSciNetMATHCrossRef
Campbell, N. (1978). The influence function as an aid in outlier detection in discriminant analysis. Applied Statistics, 27(3), 251–258.MATHCrossRef
Campbell, R. J. (1980). Robust procedures in multivariate analysis I: Robust covariance analysis. Applied Statistics, 29, 231–237.MATHCrossRef
Candès, E. (2006). Compressive sampling. In Proceedings of the International Congress of Mathematics.
Candès, E. (2008). The restricted isometry property and its implications for compressed sensing. Comptes Rendus Mathematique, 346(9–10), 589–592.MathSciNetMATHCrossRef
Candès, E., & Donoho, D. (2002). New tight frames of curvelets and optimal representations of objects with smooth singularities. Technical Report. Stanford University.MATH
Candès, E., Li, X., Ma, Y., & Wright, J. (2011). Robust principal component analysis? Journal of the ACM, 58(3).
Candès, E., & Plan, Y. (2010). Matrix completion with noise. Proceedings of the IEEE, 98(6), 925–936.CrossRef
Candès, E., & Recht, B. (2009). Exact matrix completion via convex optimization. Foundations of Computational Mathematics, 9, 717–772.MathSciNetMATHCrossRef
Candès, E., & Recht, B. (2011). Simple bounds for low-complexity model reconstruction. Mathematical Programming Series A, 141(1–2), 577–589.MATH
Candès, E., & Tao, T. (2010). The power of convex relaxation: Near-optimal matrix completion. IEEE Transactions on Information Theory, 56(5), 2053–2080.MathSciNetCrossRef
Candès, E., & Wakin, M. (2008). An introduction to compressive sampling. IEEE Signal Processing Magazine, 25(2), 21–30.CrossRef
Cattell, R. B. (1966). The scree test for the number of factors. Multivariate Behavioral Research, 1, 245–276.CrossRef
Cetingül, H. E., Wright, M., Thompson, P., & Vidal, R. (2014). Segmentation of high angular resolution diffusion MRI using sparse riemannian manifold clustering. IEEE Transactions on Medical Imaging, 33(2), 301–317.CrossRef
Chan, A., & Vasconcelos, N. (2005a). Classification and retrieval of traffic video using auto-regressive stochastic processes. In Proceedings of 2005 IEEE Intelligent Vehicles Symposium (pp. 771–776).
Chan, A., & Vasconcelos, N. (2005b). Mixtures of dynamic textures. In IEEE International Conference on Computer Vision (Vol. 1, pp. 641–647).
Chandrasekaran, V., Sanghavi, S., Parrilo, P., & Willsky, A. (2009). Sparse and low-rank matrix decompositions. In IFAC Symposium on System Identification.
Chaudhry, R., Ravichandran, A., Hager, G., & Vidal, R. (2009). Histograms of oriented optical flow and binet-cauchy kernels on nonlinear dynamical systems for the recognition of human actions. In IEEE Conference on Computer Vision and Pattern Recognition.
Chen, G., Atev, S., & Lerman, G. (2009). Kernel spectral curvature clustering (KSCC). In Workshop on Dynamical Vision.
Chen, G., & Lerman, G. (2009a). Foundations of a multi-way spectral clustering framework for hybrid linear modeling. Foundations of Computational Mathematics, 9(5), 517–558.
Chen, G., & Lerman, G. (2009b). Spectral curvature clustering (SCC). International Journal of Computer Vision, 81(3), 317–330.
Chen, J.-Q., Pappas, T. N., Mojsilovic, A., & Rogowitz, B. E. (2003). Image segmentation by spatially adaptive color and texture features. In IEEE International Conference on Image Processing.
Chen, S., Donoho, D., & Saunders, M. (1998). Atomic decomposition by basis pursuit. SIAM Journal of Scientific Computing, 20(1), 33–61.MathSciNetMATHCrossRef
Chung, F. (1997). Spectral graph theory. Washington: Conference Board of the Mathematical Sciences.MATH
Cilibrasi, R., & Vitányi, P. M. (2005). Clustering by compression. IEEE Transactions on Information Theory, 51(4), 1523–1545.MathSciNetMATHCrossRef
Coifman, R., & Wickerhauser, M. (1992). Entropy-based algorithms for best bases selection. IEEE Transactions on Information Theory, 38(2), 713–718.MATHCrossRef
Collins, M., Dasgupta, S., & Schapire, R. (2001). A generalization of principal component analysis to the exponential family. In Neural Information Processing Systems (Vol. 14)
Collins, P., & Schuppen, J. V. (2004). Observability of piecewise-affine hybrid systems. In Proceedings of Hybrid Systems: Computation and Control. New York: Springer.
Comanicu, D., & Meer, P. (2002). Mean shift: A robust approach toward feature space analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), 24, 603–619.CrossRef
Costeira, J., & Kanade, T. (1998). A multibody factorization method for independently moving objects. International Journal of Computer Vision, 29(3), 159–179.CrossRef
Cour, T., Benezit, F., & Shi, J. (2005). Spectral segmentation with multiscale graph decomposition. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR).
Cox, T. F., & Cox, M. A. A. (1994). Multidimensional scaling. London: Chapman and Hall.MATH
Davis, C., & Cahan, W. (1970). The rotation of eigenvectors by a pertubation. SIAM Journal on Numerical Analysis, 7(1), 1–46.MathSciNetCrossRef
Davison, M. (1983). Multidimensional Scaling. New York: Wiley.MATH
De la Torre, F., & Black, M. J. (2004). A framework for robust subspace learning. International Journal of Computer Vision, 54(1), 117–142.MATH
Delsarte, P., Macq, B., & Slock, D. (1992). Signal-adapted multiresolution transform for image coding. IEEE Transactions on Information Theory, 38, 897–903.CrossRef
Dempster, A., Laird, N., & Rubin, D. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society B, 39(1), 1–38.MathSciNetMATH
Deng, W., Lai, M.-J., Peng, Z., & Yin, W. (2013). Parallel multi-block admm with o(1/k) convergence. UCLA CAM.
Deng, Y., & Manjunath, B. (2001). Unsupervised segmentation of color-texture regions in images and video. IEEE Transactions on Pattern Analysis and Machine Intelligence, 23(8), 800–810.CrossRef
DeVore, R., Jawerth, B., & Lucier, B. (1992). Image compression through wavelet transform coding. IEEE Transactions on Information Theory, 38(2), 719–746.MathSciNetMATHCrossRef
Ding, C., Zha, H., He, X., Husbands, P., & Simon, H. D. (2004). Link analysis: Hubs and authoraties on the world wide web. SIAM Review, 46(2), 256–268.MathSciNetMATHCrossRef
Do, M. N., & Vetterli, M. (2002). Contourlets: A directional multiresolution image representation. In IEEE International Conference on Image Processing.
Donoho, D. (1995). Cart and best-ortho-basis: A connection. Manuscript.MATH
Donoho, D. (1998). Sparse components analysis and optimal atomic decomposition. Technical Report, Department of Statistics, Stanford University.
Donoho, D., & Gavish, M. (2014). The optimal hard threshold for singular values is \(4/\sqrt{3}\). IEEE Transactions on Information Theory, 60(8), 5040–5053.MathSciNetCrossRef
Donoho, D., & Grimes, C. (2003). Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data. National Academy of Sciences, 100(10), 5591–5596.MathSciNetMATHCrossRef
Donoho, D. L. (2005). Neighborly polytopes and sparse solution of underdetermined linear equations. Technical Report. Stanford University.
Donoho, D. L. (2006). For most large underdetermined systems of linear equations the minimal ℓ 1-norm solution is also the sparsest solution. Communications on Pure and Applied Mathematics, 59(6), 797–829.MathSciNetMATHCrossRef
Donoho, D. L., & Elad, M. (2003). Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ 1 minimization. Proceedings of National Academy of Sciences, 100(5), 2197–2202.MathSciNetMATHCrossRef
Donoho, D. L., Vetterli, M., DeVore, R., & Daubechies, I. (1998). Data compression and harmonic analysis. IEEE Transactions on Information Theory, 44(6), 2435–2476.MathSciNetMATHCrossRef
Donoser, M., Urschler, M., Hirzer, M., & Bischof, H. (2009). Saliency driven total variation segmentation. In Proceedings of the International Conference on Computer Vision (ICCV).
Doretto, G., Chiuso, A., Wu, Y., & Soatto, S. (2003). Dynamic textures. International Journal of Computer Vision, 51(2), 91–109.MATHCrossRef
Doretto, G., & Soatto, S. (2003). Editable dynamic textures. In IEEE Conference on Computer Vision and Pattern Recognition (Vol. II, pp. 137–142).
Doretto, G., & Soatto, S. (2006). Dynamic shape and appearance models. IEEE Transactions on Pattern Analysis and Machine Intelligence, 28(12), 2006–2019.CrossRef
Doucet, A., Logothetis, A., & Krishnamurthy, V. (2000). Stochastic sampling algorithms for state estimation of jump Markov linear systems. IEEE Transactions on Automatic Control, 45(1), 188–202.MathSciNetMATHCrossRef
Duda, R., Hart, P., & Stork, D. (2000). Pattern Classification (2nd ed.). Wiley, New York.MATH
Eckart, C., & Young, G. (1936). The approximation of one matrix by another of lower rank. Psychometrika, 1, 211–218.MATHCrossRef
Effros, M., & Chou, P. (1995). Weighted universal transform coding: Universal image compression with the Karhunen-Loéve transform. In IEEE International Conference on Image Processing (Vol. 2, pp. 61–64).
Efros, A. A., & Leung, T. K. (1999). Texture synthesis by non-parametric sampling. In IEEE International Conference on Computer Vision (pp. 1033–1038). Corfu, Greece.CrossRef
Eisenbud, D. (1996). Commutative algebra: With a view towards algebraic geometry. Graduate texts in mathematics. New York: Springer.
Elad, M., & Bruckstein, A. (2001). On sparse signal representations. In IEEE International Conference on Image Processing.
Elad, M., & Bruckstein, A. (2002). A generalized uncertainty principle and sparse representation in pairs of bases. IEEE Transactions on Information Theory, 48(9), 2558–2567.MathSciNetMATHCrossRef
Elad, M., Figueiredo, M. A. T., & Ma, Y. (2010). On the role of sparse and redundant representations in image processing. Proceedings of the IEEE, 98(6), 972–982.CrossRef
Elder, J., & Zucker, S. (1996). Computing contour closures. In Proceedings of the European Conference on Computer Vision (ECCV).
Elhamifar, E., Sapiro, G., & Vidal, R. (2012a). Finding exemplars from pairwise dissimilarities via simultaneous sparse recovery. In Neural Information Processing and Systems.
Elhamifar, E., Sapiro, G., & Vidal, R. (2012b). See all by looking at a few: Sparse modeling for finding representative objects. In IEEE Conference on Computer Vision and Pattern Recognition.
Elhamifar, E., & Vidal, R. (2009). Sparse subspace clustering. In IEEE Conference on Computer Vision and Pattern Recognition.
Elhamifar, E., & Vidal, R. (2010). Clustering disjoint subspaces via sparse representation. In IEEE International Conference on Acoustics, Speech, and Signal Processing.
Elhamifar, E., & Vidal, R. (2011). Sparse manifold clustering and embedding. In Neural Information Processing and Systems.
Elhamifar, E., & Vidal, R. (2013). Sparse subspace clustering: Algorithm, theory, and applications. IEEE Transactions on Pattern Analysis and Machine Intelligence, 35(11), 2765–2781.CrossRef
Ezzine, J., & Haddad, A. H. (1989). Controllability and observability of hybrid systems. International Journal of Control, 49(6), 2045–2055.MathSciNetMATHCrossRef
Favaro, P., Vidal, R., & Ravichandran, A. (2011). A closed form solution to robust subspace estimation and clustering. In IEEE Conference on Computer Vision and Pattern Recognition.
Fazel, M., Hindi, H., & Boyd, S. (2003). Log-det heuristic for matrix rank minimization with applications to Hankel and Euclidean distance matrices. In Proceedings of the American Control Conference (pp. 2156–2162).
Fei-Fei, L., Fergus, R., & Perona, P. (2004). Learning generative visual models from few training examples: An incremental bayesian approach tested on 101 object categories. In Workshop on Generative Model Based Vision.
Felzenszwalb, P. F., & Huttenlocher, D. P. (2004). Efficient graph-based image segmentation. International Journal of Computer Vision (IJCV), 59(2), 167–181.CrossRef
Feng, J., Xu, H., Mannor, S., & Yang, S. (2013). Online PCA for contaminated data. In NIPS.
Feng, X., & Perona, P. (1998). Scene segmentation from 3D motion. In IEEE Conference on Computer Vision and Pattern Recognition (pp. 225–231).
Ferguson, T. (1961). On the rejection of outliers. In Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability.
Ferrari-Trecate, G., Mignone, D., & Morari, M. (2002). Moving horizon estimation for hybrid systems. IEEE Transactions on Automatic Control, 47(10), 1663–1676.MathSciNetCrossRef
Ferrari-Trecate, G., Muselli, M., Liberati, D., & Morari, M. (2003). A clustering technique for the identification of piecewise affine systems. Automatica, 39(2), 205–217.MathSciNetMATHCrossRef
Feuer, A., Nemirovski, A. (2003). On sparse representation in pairs of bases. IEEE Transactions on Information Theory, 49(6), 1579–1581.MathSciNetMATHCrossRef
Figueiredo, M. A. T., & Jain, A. K. (2002). Unsupervised learning of finite mixture models. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24(3), 381–396.CrossRef
Fischler, M. A., & Bolles, R. C. (1981). RANSAC random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography. Communications of the ACM, 26, 381–395.MathSciNetCrossRef
Fisher, Y. (1995). Fractal Image Compression: Theory and Application. Springer-Verlag Telos.CrossRef
Fitzgibbon, A., & Zisserman, A. (2000). Multibody structure and motion: 3D reconstruction of independently moving objects. In European Conference on Computer Vision (pp. 891–906).
Forgy, E. (1965). Cluster analysis of multivariate data: Efficiency vs. interpretability of classifications (abstract). Biometrics, 21, 768–769.
Freixenet, J., Munoz, X., Raba, D., Marti, J., & Cuff, X. (2002). Yet another survey on image segmentation. In Proceedings of the European Conference on Computer Vision (ECCV).
Frey, B., Colmenarez, A., & Huang, T. (1998). Mixtures of local linear subspaces for face recognition. In IEEE Conference on Computer Vision and Pattern Recognition.
Gabriel, K. R. (1978). Least squares approximation of matrices by additive and multiplicative models. Journal of the Royal Statistical Society B, 40, 186–196.MathSciNetMATH
Ganesh, A., Wright, J., Li, X., Candès, E., & Ma, Y. (2010). Dense error correction for low-rank matrices via principal component pursuit. In International Symposium on Information Theory.
Geman, S., & McClure, D. (1987). Statistical methods for tomographic image reconstruction. In Proceedings of the 46th Session of the ISI, Bulletin of the ISI (Vol. 52, pp. 5–21).
Georghiades, A., Belhumeur, P., & Kriegman, D. (2001). 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.CrossRef
Gersho, A., & Gray, R. M. (1992). Vector Quantization and Signal Compression. Boston: Kluwer Academic.MATHCrossRef
Gevers, T., & Smeulders, A. (1997). Combining region splitting and edge detection through guided Delaunay image subdivision. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR).
Ghahramani, Z., & Beal, M. (2000). Variational inference for Bayesian mixtures of factor analysers. Advances in Neural Information Processing Systems, 12, 449–455.
Ghahramani, Z., & Hinton, G. (1996). The EM algorithm for mixtures of factor analyzers. Technical Report CRG-TR-96-1, University of Toronto, Canada.
Ghahramani, Z., & Hinton, G. E. (1998). Variational learning for switching state-space models. Neural Computation, 12(4), 963–996.
Ghoreyshi, A., & Vidal, R. (2007). Epicardial segmentation in dynamic cardiac MR sequences using priors on shape, intensity, and dynamics, in a level set framework. In IEEE International Symposium on Biomedical Imaging (pp. 860–863).
Gnanadesikan, R., & Kettenring, J. (1972). Robust estimates, residuals, and outlier detection with multiresponse data. Biometrics, 28(1), 81–124.CrossRef
Goh, A., & Vidal, R. (2007). Segmenting motions of different types by unsupervised manifold clustering. In IEEE Conference on Computer Vision and Pattern Recognition.
Goh, A., & Vidal, R. (2008). Unsupervised Riemannian clustering of probability density functions. In European Conference on Machine Learning.
Goldfarb, D., & Ma, S. (2009). Convergence of fixed point continuation algorithms for matrix rank minimization. Preprint.
Golub, H., & Loan, C. V. (1996). Matrix Computations (2nd ed.). Baltimore: Johns Hopkins University Press.MATH
Govindu, V. (2005). A tensor decomposition for geometric grouping and segmentation. In IEEE Conference on Computer Vision and Pattern Recognition (pp. 1150–1157).
Gower, J. (1966). Some distance properties of latent root and vector methods used in multivariate analysis. Biometrika, 53, 325–338.MathSciNetMATHCrossRef
Gross, D. (2011). Recovering low-rank matrices from few coefficients in any basis. IEEE Trans on Information Theory, 57(3), 1548–1566.MathSciNetCrossRef
Gruber, A., & Weiss, Y. (2004). Multibody factorization with uncertainty and missing data using the EM algorithm. In IEEE Conference on Computer Vision and Pattern Recognition (Vol. I, pp. 707–714).
H.Aanaes, Fisker, R., Astrom, K., & Carstensen, J. M. (2002). Robust factorization. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24(9), 1215–1225.CrossRef
Haeffele, B., Young, E., & Vidal, R. (2014). Structured low-rank matrix factorization: Optimality, algorithm, and applications to image processing. In International Conference on Machine Learning.
Hamkins, J., & Zeger, K. (2002). Gaussian source coding with spherical codes. IEEE Transactions on Information Theory, 48(11), 2980–2989.MathSciNetMATHCrossRef
Hampel, F., Ronchetti, E., Rousseeuw, P., & Stahel, W. (1986). Robust statistics: The approach based on influence functions. New York: Wiley.MATH
Hampel, F. R. (1974). The influence curve and its role in robust estiamtion. Journal of the American Statistical Association, 69, 383–393.MathSciNetMATHCrossRef
Han, M., & Kanade, T. (2000). Reconstruction of a scene with multiple linearly moving objects. In Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (Vol. 2, pp. 542–549).
Han, M., & Kanade, T. (2001). Multiple motion scene reconstruction from uncalibrated views. In Proceedings of IEEE International Conference on Computer Vision (Vol. 1, pp. 163–170).
Hansen, M., & Yu, B. (2001). Model selection and the principle of minimum description length. Journal of American Statistical Association, 96, 746–774.MathSciNetMATHCrossRef
Haralick, R., & Shapiro, L. (1985). Image segmentation techniques. Computer Vision, Graphics, and Image Processing, 29(1), 100–132.CrossRef
Hardt, M. (2014). Understanding alternating minimization for matrix completion. In Symposium on Foundations of Computer Science.
Haro, G., Randall, G., & Sapiro, G. (2006). Stratification learning: Detecting mixed density and dimensionality in high dimensional point clouds. In Neural Information Processing and Systems.
Haro, G., Randall, G., & Sapiro, G. (2008). Translated poisson mixture model for stratification learning. International Journal of Computer Vision, 80(3), 358–374.CrossRef
Hartley, R., & Schaffalitzky, F. (2003). Powerfactorization: An approach to affine reconstruction with missing and uncertain data. In Proceedings of Australia-Japan Advanced Workshop on Computer Vision.
Hartley, R., & Vidal, R. (2004). The multibody trifocal tensor: Motion segmentation from 3 perspective views. In IEEE Conference on Computer Vision and Pattern Recognition (Vol. I, pp. 769–775).
Hartley, R., & Zisserman, A. (2004). Multiple view geometry in computer vision (2nd ed.). Cambridge: Cambridge University Press.MATHCrossRef
Hastie, T. (1984). Principal curves and surfaces. Technical Report, Stanford University.
Hastie, T., Tibshirani, R., & Friedman, J. (2001). The Elements of Statistical Learning. New York: Springer.MATHCrossRef
He, H., & Garcia, E. (2009). Learning from imbalanced data. IEEE Transactions on Knowledge and Data Engineering, 21(9), 1263–1284.CrossRef
He, H., & Ma, Y. (2013). Imbalanced Learning: Foundations, Algorithms, and Applications. New York: Wiley.MATHCrossRef
Hinton, G., Osindero, S., & Teh, Y.-W. (2006). A fast learning algorithm for deep belief nets. Neural Computation, 18(7), 1527–1554.MathSciNetMATHCrossRef
Ho, J., Yang, M., Lim, J., Lee, K., & Kriegman, D. (2003). Clustering appearances of objects under varying illumination conditions. In Proceedings of International Conference on Computer Vision and Pattern Recognition.
Hong, W., Wright, J., Huang, K., & Ma, Y. (2006). Multi-scale hybrid linear models for lossy image representation. IEEE Transactions on Image Processing, 15(12), 3655–3671.MathSciNetCrossRef
Horn, R. A., & Johnson, C. R. (1985). Matrix Analysis. Cambridge: Cambridge University Press.MATHCrossRef
Hotelling, H. (1933). Analysis of a complex of statistical variables into principal components. Journal of Educational Psychology, 24, 417–441.MATHCrossRef
Householder, A. S., & Young, G. (1938). Matrix approximation and latent roots. American Mathematical Monthly, 45, 165–171.MathSciNetMATHCrossRef
Huang, K., Ma, Y., & Vidal, R. (2004). Minimum effective dimension for mixtures of subspaces: A robust GPCA algorithm and its applications. In IEEE Conference on Computer Vision and Pattern Recognition (Vol. II, pp. 631–638).
Hubert, L., Meulman, J., & Heiser, W. (2000). Two purposes for matrix factorization: A historical appraisal. SIAM Review, 42(1), 68–82.MathSciNetMATHCrossRef
Hwang, I., Balakrishnan, H., & Tomlin, C. (2003). Observability criteria and estimator design for stochastic linear hybrid systems. In Proceedings of European Control Conference.
Hyndman, M., Jepson, A., & Fleet, D. J. (2007). Higher-order autoregressive models for dynamic textures. In British Machine Vision Conference (pp. 76.1–76.10). doi:10.​5244/​C.​21.​76.
Jacobs, D. (2001). Linear fitting with missing data: Applications to structure-from-motion. Computer Vision and Image Understanding, 82, 57–81.MATHCrossRef
Jain, A. (1989). Fundamentals of Digital Image Processing. Upper Saddle River: Prentice Hall.MATH
Jain, P., Meka, R., & Dhillon, I. (2010). Guaranteed rank minimization via singular value projection. In Neural Information Processing Systems (pp. 937–945).
Jancey, R. (1966). Multidimensional group analysis. Australian Journal of Botany, 14, 127–130.CrossRef
Jarret, K., Kavukcuoglu, K., Ranzato, M., & LeCun, Y. (2009). What is the best multi-stage architecture for object recognition. In International Conference on Computer Vision.
Jhuo, I.-H., Liu, D., Lee, D., & Chang, S.-F. (2012). Robust visual domain adaptation with low-rank reconstruction. In IEEE Conference on Computer Vision and Pattern Recognition (pp. 2168–2175).
Johnson, C. (1990). Matrix completion problems: A survey. In Proceedings of Symposia in Applied Mathematics.
Jolliffe, I. (2002). Principal Component Analysis (2nd ed.). New York: Springer.MATH
Jordan, M. (1874). Mémoire sur les formes bilinéaires. Journal de Mathématiques Pures et Appliqués, 19, 35–54.MATH
Juloski, A., Heemels, W., & Ferrari-Trecate, G. (2004). Data-based hybrid modelling of the component placement process in pick-and-place machines. In Control Engineering Practice. Amsterdam: Elsevier.
Kamvar, S., Klein, D., & Manning, C. (2002). Interpreting and extending classical agglomerative clustering methods using a model-based approach. Technical Report 2002-11, Stanford University Department of Computer Science.
Kanatani, K. (1998). Geometric information criterion for model selection. International Journal of Computer Vision (pp. 171–189).
Kanatani, K. (2001). Motion segmentation by subspace separation and model selection. In IEEE International Conference on Computer Vision (Vol. 2, pp. 586–591).
Kanatani, K. (2002). Evaluation and selection of models for motion segmentation. In Asian Conference on Computer Vision (pp. 7–12).
Kanatani, K. (2003). How are statistical methods for geometric inference justified? In Workshop on Statistical and Computational Theories of Vision, IEEE International Conference on Computer Vision.
Kanatani, K., & Matsunaga, C. (2002). Estimating the number of independent motions for multibody motion segmentation. In European Conference on Computer Vision (pp. 25–31).
Kanatani, K., & Sugaya, Y. (2003). Multi-stage optimization for multi-body motion segmentation. In Australia-Japan Advanced Workshop on Computer Vision (pp. 335–349).
Ke, Q., & Kanade, T. (2005). Robust ℓ 1-norm factorization in the presence of outliers and missing data. In IEEE Conference on Computer Vision and Pattern Recognition.
Keshavan, R., Montanari, A., & Oh, S. (2010a). Matrix completion from a few entries. IEEE Transactions on Information Theory.
Keshavan, R., Montanari, A., & Oh, S. (2010b). Matrix completion from noisy entries. Journal of Machine Learning Research, 11, 2057–2078.
Keshavan, R. H. (2012). Efficient algorithms for collaborative filtering. Ph.D. Thesis. Stanford University.
Kim, J., Fisher, J., Yezzi, A., Cetin, M., & Willsky, A. (2005). A nonparametric statistical method for image segmentation using information theory and curve evolution. PAMI, 14(10), 1486–1502.MathSciNet
Kim, S. J., Doretto, G., Rittscher, J., Tu, P., Krahnstoever, N., & Pollefeys, M. (2009). A model change detection approach to dynamic scene modeling. In Sixth IEEE International Conference on Advanced Video and Signal Based Surveillance, 2009 (AVSS ’09) (pp. 490–495).
Kim, S. J., Koh, K., Lustig, M., Boyd, S., & Gorinevsky, D. (2007). An interior-point method for large-scale l1-regularized least squares. IEEE Journal on Selected Topics in Signal Processing, 1(4), 606–617.CrossRef
Kim, T., Lee, K., & Lee, S. (2010). Learning full pairwise affinities for spectral segmentation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR).
Kleinberg, J. M. (1999). Authorative sources in a hyberlinked environment. Journal of the ACM, 48, 604–632.MathSciNetCrossRef
Kontogiorgis, S., & Meyer, R. (1989). A variable-penalty alternating direction method for convex optimization. Mathematical Programming, 83, 29–53.MathSciNetMATH
Kruskal, J. (1964). Nonmetric multidimensional scaling: A numerical method. Psychometrika.
Kurita, T. (1995). An efficient clustering algorithm for region merging. IEICE Transactions of Information and Systems, E78-D(12), 1546–1551.
Lanczos, C. (1950). An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. Journal of Research of the National Bureau of Standards, 45, 255–282.MathSciNetCrossRef
Lang, S. (1993). Algebra (3rd ed.). Reading: Addison-Wesley.MATH
Lee, J. A., & Verleysen, M. (2007). Nonlinear Dimensionality Reduction (1st ed.). New York: Springer.MATHCrossRef
Lee, K.-C., Ho, J., & Kriegman, D. (2005). Acquiring linear subspaces for face recognition under variable lighting. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27(5), 684–698.CrossRef
Leonardis, A., Bischof, H., & Maver, J. (2002). Multiple eigenspaces. Pattern Recognition, 35(11), 2613–2627.MATHCrossRef
LePennec, E., & Mallat, S. (2005). Sparse geometric image representation with bandelets. IEEE Transactions on Image Processing, 14(4), 423–438.MathSciNetCrossRef
Levina, E., & Bickel, P. J. (2006). Texture synthesis and non-parametric resampling of random fields. Annals of Statistics, 34(4), 1751–1773.MathSciNetMATHCrossRef
Li, B., Ayazoglu, M., Mao, T., Camps, O. I., & Sznaier, M. (2011). Activity recognition using dynamic subspace angles. In Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (pp. 3193–3200). New York: IEEE.
Lin, Z., Chen, M., Wu, L., & Ma, Y. (2011). The augmented Lagrange multiplier method for exact recovery of corrupted low-rank matrices. arXiv:1009.5055v2.
Lions, P., & Mercier, B. (1979). Splitting algorithms for the sum of two nonlinear operators. SIAM Journal on Numerical Analysis, 16(6), 964–979.MathSciNetMATHCrossRef
Liu, G., Lin, Z., Yan, S., Sun, J., & Ma, Y. (2013). Robust recovery of subspace structures by low-rank representation. IEEE Trans. Pattern Analysis and Machine Intelligence, 35(1), 171–184.CrossRef
Liu, G., Lin, Z., & Yu, Y. (2010). Robust subspace segmentation by low-rank representation. In International Conference on Machine Learning.
Liu, Y. K., & Zalik, B. (2005). Efficient chain code with Huffman coding. Pattern Recognition, 38(4), 553–557.CrossRef
Lloyd, S. (1957). Least squares quantization in PCM. Technical Report. Bell Laboratories. Published in 1982 in IEEE Transactions on Information Theory, 28, 128–137.
Luenberger, D. G. (1973). Linear and Nonlinear Programming. Reading: Addison-Wesley.MATH
Luo, Z. Q., & Tseng, P. (1993). One the convergence rate of dual ascent methods for strictly convex minimization. Mathematics of Operations Research, 18, 846–867.MathSciNetMATHCrossRef
Ma, S. (2012). Alternating proximal gradient method for convex minimization. Technical Report.
Ma, Y., Derksen, H., Hong, W., & Wright, J. (2007). Segmentation of multivariate mixed data via lossy coding and compression. IEEE Transactions on Pattern Analysis and Machine Intelligence, 29(9), 1546–1562.CrossRef
Ma, Y., Soatto, S., Kosecka, J., & Sastry, S. (2003). An Invitation to 3D Vision: From Images to Geometric Models. New York: Springer.MATH
Ma, Y., & Vidal, R. (2005). Identification of deterministic switched ARX systems via identification of algebraic varieties. In Hybrid Systems: Computation and Control (pp. 449–465). New York: Springer.CrossRef
Ma, Y., Yang, A. Y., Derksen, H., & Fossum, R. (2008). Estimation of subspace arrangements with applications in modeling and segmenting mixed data. SIAM Review, 50(3), 413–458.MathSciNetMATHCrossRef
MacQueen, J. (1967). Some methods for classification and analysis of multivariate observations. In Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability (pp. 281–297).
Madiman, M., Harrison, M., & Kontoyiannis, I. (2004). Minimum description length vs. maximum likelihood in lossy data compression. In Proceedings of the 2004 IEEE International Symposium on Information Theory.
Malik, J., Belongie, S., Leung, T., & Shi, J. (2001). Contour and texture analysis for image segmentation. International Journal of Computer Vision, 43(1), 7–27.MATHCrossRef
Mallat, S. (1999). A Wavelet Tour of Signal Processing (2nd ed.). London: Academic.MATH
Mallows, C. (1973). Some comments on C p . Technometrics, 15, 661–675.MATH
Martin, D., Fowlkes, C., Tal, D., & Malik, J. (2001). A Database of Human Segmented Natural Images and its Application to Evaluating Segmentation Algorithms and Measuring Ecological Statistics. In IEEE International Conference on Computer Vision.
McLanchlan, G. J., & Krishnan, T. (1997). The EM Algorithms and Extentions. Wiley Series in Probability and Statistics. John Wiley & Sons, Inc.
Meila, M. (2005). Comparing clusterings: An axiomatic view. In Proceedings of the International Conference on Machine Learning.
Mercer, J. (1909). Functions of positive and negative types and their connection with the theory of integral equations. Philosophical Transactions, Royal Society London, A, 209(1909), 415–446.MATHCrossRef
Meyer, F. (2000). Fast adaptive wavelet packet image compression. IEEE Transactions on Image Processing, 9(5), 792–800.CrossRef
Meyer, F. (2002). Image compression with adaptive local cosines. IEEE Transactions on Image Processing, 11(6), 616–629.CrossRef
Minka, T. (2000). Automatic choice of dimensionality for PCA. In Neural Information Processing Systems (Vol. 13, pp. 598–604).
Mobahi, H., Rao, S., Yang, A., & Sastry, S. (2011). Segmentation of natural images by texture and boundary compression. International Journal of Computer Vision, 95(1), 86–98.CrossRef
Mori, G., Ren, X., Efros, A., & Malik, J. (2004). Recovering human body configurations: Combining segmentation and recognition. In IEEE Conference on Computer Vision and Pattern Recognition.
Muresan, D., & Parks, T. (2003). Adaptive principal components and image denoising. In IEEE International Conference on Image Processing.
Murphy, K. (1998). Switching Kalman filters. Technical Report. U.C. Berkeley.
Nascimento, J. C., Figueiredo, M. A. T., & Marques, J. S. (2005). Recognition of human activities using space dependent switched dynamical models. In IEEE International Conference on Image Processing (pp. 852–855).
Neal, R., & Hinton, G. (1998). A view of the EM algorithm that justifies incremental, sparse, and other variants. In M. Jordan (Ed.), Learning in graphical models (pp. 355–368). Boston: Kluwer Academic.CrossRef
Nemirovskii, A. S., & Yudin, D. B. (1979). Complexity of problems and efficiency of optimization methods (in Russian). Moscow: Nauka.
Nesterov, Y. (1983). A method of solving a convex programming problem with convergence rate O(1∕k 2). Soviet Mathematics Doklady, 27(2), 372–376.MATH
Ng, A., Weiss, Y., & Jordan, M. (2001). On spectral clustering: Analysis and an algorithm. In Proceedings of Neural Information Processing Systems (NIPS) (pp. 849–856).
Niessen, H., & A.Juloski (2004). Comparison of three procedures for identification of hybrid systems. In Conference on Control Applications.
Nunez, F., & Cipriano, A. (2009). Visual information model based predictor for froth speed control in flotation process. Minerals Engineering, 22(4), 366–371.CrossRef
Ofli, F., Chaudhry, R., Kurillo, G., Vidal, R., & Bajcsy, R. (2013). Berkeley MHAD: A comprehensive multimodal human action database. In IEEE Workshop on Applications of Computer Vision.
Olshausen, B., & D.J.Field (1996). Emergence of simple-cell receptive field properties by learning a sparse code for natural images. Nature, 381(6583), 607–609.CrossRef
Orlik, P. (1989). Introduction to Arrangements. Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics (Vol. 72). Providence: American Mathematics Society.
Overschee, P. V., & Moor, B. D. (1993). Subspace algorithms for the stochastic identification problem. Automatica, 29(3), 649–660.MathSciNetMATHCrossRef
Patel, V. M., Gopalan, R., Li, R., & Chellappa, R. (2014). Visual domain adaptation: A survey of recent advances. IEEE Signal Processing Magazine, 32(3), 53–69.CrossRef
Pavlovic, V., Moulin, P., & Ramchandran, K. (1998). An integrated framework for adaptive subband image coding. IEEE Transactions on Signal Processing, 47(4), 1024–1038.CrossRef
Pavlovic, V., Rehg, J. M., Cham, T. J., & Murphy, K. P. (1999). A dynamic Bayesian network approach to figure tracking using learned dynamic models. In Proceedings of the International Conference on Computer Vision (pp. 94–101).
Pearson, K. (1901). On lines and planes of closest fit to systems of points in space. The London, Edinburgh and Dublin Philosphical Magazine and Journal of Science, 2, 559–572.MATHCrossRef
Peng, Z., Yan, M., & Yin, W. (2013). Parallel and distributed sparse optimization. In Asilomar.
Polito, M., & Perona, P. (2002). Grouping and dimensionality reduction by locally linear embedding. In Proceedings of Neural Information Processing Systems (NIPS).
Qiu, Q., Patel, V. M., Turaga, P., & Chellappa, R. (2012). Domain adaptive dictionary learning. In European Conference on Computer Vision (Vol. 7575, pp. 631–645).
Rabiee, H., Kashyap, R., & Safavian, S. (1996). Adaptive multiresolution image coding with matching and basis pursuits. In IEEE International Conference on Image Processing.
Rahimi, A., Darrell, T., & Recht, B. (2005). Learning appearance manifolds from video. In IEEE Conference on Computer Vision and Pattern Recognition (Vol. 1, pp. 868–875).
Ramchandran, K., & Vetterli, M. (1993). Best wavelet packets bases in a rate-distortion sense. IEEE Transactions on Image Processing, 2, 160–175.CrossRef
Ramchandran, K., Vetterli, M., & Herley, C. (1996). Wavelets, subband coding, and best basis. Proceedings of the IEEE, 84(4), 541–560.CrossRef
Rand, W. M. (1971). Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association, 66(336), 846–850.CrossRef
Rao, S., Mobahi, H., Yang, A., & Sastry, S. (2009). Natural image segmentation with adaptive texture and boundary encoding. In Asian Conference on Computer Vision, 1 (pp. 135–146).
Rao, S., Tron, R., Ma, Y., & Vidal, R. (2008). Motion segmentation via robust subspace separation in the presence of outlying, incomplete, or corrupted trajectories. In IEEE Conference on Computer Vision and Pattern Recognition.
Rao, S., Tron, R., Vidal, R., & Ma, Y. (2010). Motion segmentation in the presence of outlying, incomplete, or corrupted trajectories. IEEE Transactions on Pattern Analysis and Machine Intelligence, 32(10), 1832–1845.CrossRef
Rao, S., Yang, A. Y., Wagner, A., & Ma, Y. (2005). Segmentation of hybrid motions via hybrid quadratic surface analysis. In IEEE International Conference on Computer Vision (pp. 2–9).
Ravichandran, A., Chaudhry, R., & Vidal, R. (2009). View-invariant dynamic texture recognition using a bag of dynamical systems. In IEEE Conference on Computer Vision and Pattern Recognition.
Ravichandran, A., Chaudhry, R., & Vidal, R. (2013). Categorizing dynamic textures using a bag of dynamical systems. IEEE Transactions on Pattern Analysis and Machine Intelligence, 35(2), 342–353.CrossRef
Ravichandran, A., & Vidal, R. (2008). Video registration using dynamic textures. In European Conference on Computer Vision.
Ravichandran, A., & Vidal, R. (2011). Video registration using dynamic textures. IEEE Transactions on Pattern Analysis and Machine Intelligence, 33(1), 158–171.CrossRef
Ravichandran, A., Vidal, R., & Halperin, H. (2006). Segmenting a beating heart using polysegment and spatial GPCA. In IEEE International Symposium on Biomedical Imaging (pp. 634–637).
Recht, B., Fazel, M., & Parrilo, P. (2010). Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization. SIAM Review, 52(3), 471–501.MathSciNetMATHCrossRef
Ren, X., Fowlkes, C., & Malik, J. (2005). Scale-invariant contour completion using condition random fields. In IEEE International Conference on Computer Vision.
Ren, X., Fowlkes, C., & Malik, J. (2008). Learning probabilistic models for contour completion in natural images. International Journal of Computer Vision, 77, 47–63.CrossRef
Rissanen, J. (1978). Modeling by shortest data description. Automatica, 14, 465–471.MATHCrossRef
Rose, K. (1998). Deterministic annealing for clustering, compression, classification, regression, and related optimization problems. Proceedings of the IEEE, 86(11), 2210–2239.CrossRef
Roweis, S., & Saul, L. (2000). Nonlinear dimensionality reduction by locally linear embedding. Science, 290(5500), 2323–2326.CrossRef
Roweis, S., & Saul, L. (2003). Think globally, fit locally: Unsupervised learning of low dimensional manifolds. Journal of Machine Learning Research, 4, 119–155.MathSciNetMATH
Saisan, P., Bissacco, A., Chiuso, A., & Soatto, S. (2004). Modeling and synthesis of facial motion driven by speech. In European Conference on Computer Vision (Vol. 3, pp. 456–467).
Santis, E., Benedetto, M. D., & Giordano, P. (2003). On observability and detectability of continuous-time linear switching systems. In Proceedings of IEEE Conference on Decision & Control (pp. 5777–5782).
Schindler, K., & Suter, D. (2005). Two-view multibody structure-and-motion with outliers. In IEEE Conference on Computer Vision and Pattern Recognition.
Schölkopf, B., & Smola, A. (2002). Learning with kernels. Cambridge: MIT Press.MATH
Schölkopf, B., Smola, A., & Muller, K. R. (1998). Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation, 10, 1299–1319.CrossRef
Selim, S., & Ismail, M. A. (1984). K-means-type algorithms: A generalized convergence theorem and characterization of local optimality. IEEE Transaction on Pattern Analysis and Machine Intelligence, 6(1), 81–87.MATHCrossRef
Sha, F., & Saul, L. (2005). Analysis and extension of spectral methods for nonlinear dimensionality reduction. In Proceedings of International Conference on Machine Learning (pp. 784–791).
Shabalin, A., & Nobel, A. (2010). Reconstruction of a low-rank matrix in the presence of gaussian noise (pp. 1–34). arXiv preprint 1007.4148
Shakernia, O., Vidal, R., & Sastry, S. (2003). Multi-body motion estimation and segmentation from multiple central panoramic views. In IEEE International Conference on Robotics and Automation (Vol. 1, pp. 571–576).
Shapiro, J. M. (1993). Embedded image coding using zerotrees of wavelet coefficients. IEEE Transactions on Signal Processing, 41(12), 3445–3463.MATHCrossRef
Shashua, A., & Levin, A. (2001). Multi-frame infinitesimal motion model for the reconstruction of (dynamic) scenes with multiple linearly moving objects. In Proceedings of IEEE International Conference on Computer Vision (Vol. 2, pp. 592–599).
Shekhar, S., Patel, V. M., Nguyen, H. V., & Chellappa, R. (2013). Generalized domain-adaptive dictionaries. In IEEE Conference on Computer Vision and Pattern Recognition.
Shi, J., & Malik, J. (1998). Motion segmentation and tracking using normalized cuts. In IEEE International Conference on Computer Vision (pp. 1154–1160).
Shi, J., & Malik, J. (2000). Normalized cuts and image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(8), 888–905.CrossRef
Shi, T., Belkin, M., & Yin, B. (2008). Data spectroscopy: Eigenspace of convolution operators and clustering. arXiv:0807.3719v1.
Shizawa, M., & Mase, K. (1991). A unified computational theory for motion transparency and motion boundaries based on eigenenergy analysis. In IEEE Conference on Computer Vision and Pattern Recognition (pp. 289–295).
Shum, H.-Y., Ikeuchi, K., & Reddy, R. (1995). Principal component analysis with missing data and its application to polyhedral object modeling. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17(9), 854–867.CrossRef
Sikora, T., & Makai, B. (1995). Shape-adaptive DCT for generic coding of video. IEEE Transactions on Circuits and Systems For Video Technology, 5, 59–62.CrossRef
Soltanolkotabi, M., & Candès, E. J. (2013). A geometric analysis of subspace clustering with outliers. Annals of Statistics, 40(4), 2195–2238.MathSciNetMATHCrossRef
Soltanolkotabi, M., Elhamifar, E., & Candès, E. J. (2014). Robust subspace clustering. Annals of Statistics, 42(2), 669–699.MathSciNetMATHCrossRef
Souvenir, R., & Pless, R. (2005). Manifold clustering. In Proceedings of International Conference on Computer Vision (Vol. I, pp. 648–653).
Spielman, D., Wang, H., & Wright, J. (2012). Exact recovery of sparsity-used dictionaries. Conference on Learning Theory (COLT).
Starck, J.-L., Elad, M., & Donoho, D. (2003). Image decomposition: Separation of texture from piecewise smooth content. In Proceedings of the SPIE (Vol. 5207, pp. 571–582).
Sturm, P. (2002). Structure and motion for dynamic scenes - the case of points moving in planes. In Proceedings of European Conference on Computer Vision (pp. 867–882).
Sun, A., Ge, S. S., & Lee, T. H. (2002). Controllability and reachability criteria for switched linear systems. Automatica, 38, 775–786.MathSciNetMATHCrossRef
Szigeti, F. (1992). A differential algebraic condition for controllability and observability of time varying linear systems. In Proceedings of IEEE Conference on Decision and Control (pp. 3088–3090).
Szummer, M., & Picard, R. W. (1996). Temporal texture modeling. In IEEE International Conference on Image Processing (Vol. 3, pp. 823–826).
Taubin, G. (1991). Estimation of planar curves, surfaces, and nonplanar space curves defined by implicit equations with applications to edge and range image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(11), 1115–1138.CrossRef
Tenenbaum, J. B., de Silva, V., & Langford, J. C. (2000). A global geometric framework for nonlinear dimensionality reduction. Science, 290(5500), 2319–2323.CrossRef
Tibshirani, R. (1996). Regression shrinkage and selection via the LASSO. Journal of the Royal Statistical Society B, 58(1), 267–288.MathSciNetMATH
Tipping, M., & Bishop, C. (1999a). Mixtures of probabilistic principal component analyzers. Neural Computation, 11(2), 443–482.
Tipping, M., & Bishop, C. (1999b). Probabilistic principal component analysis. Journal of the Royal Statistical Society, 61(3), 611–622.
Torgerson, W. (1958). Theory and Methods of Scaling. New York: Wiley.
Torr, P., & Davidson, C. (2003). IMPSAC: Synthesis of importance sampling and random sample consensus. IEEE Transactions on Pattern Analysis and Machine Intelligence, 25(3), 354–364.CrossRef
Torr, P., Szeliski, R., & Anandan, P. (2001). An integrated Bayesian approach to layer extraction from image sequences. IEEE Transactions on Pattern Analysis and Machine Intelligence, 23(3), 297–303.CrossRef
Torr, P. H. S. (1998). Geometric motion segmentation and model selection. Philosophical Transactions of the Royal Society of London, 356(1740), 1321–1340.MathSciNetMATHCrossRef
Tremeau, A., & Borel, N. (1997). A region growing and merging algorithm to color segmentation. Pattern Recognition, 30(7), 1191–1204.CrossRef
Tron, R., & Vidal, R. (2007). A benchmark for the comparison of 3-D motion segmentation algorithms. In IEEE Conference on Computer Vision and Pattern Recognition.
Tse, D., & Viswanath, P. (2005). Fundamentals of Wireless Communications. Cambridge: Cambridge University Press.MATHCrossRef
Tseng, P. (2001). Convergence of a block coordinate descent method for nondifferentiable minimization. Journal of Optimization Theory and Applications, 109(3), 475–494.MathSciNetMATHCrossRef
Tu, Z., & Zhu, S. (2002). Image segmentation by data-driven Markov Chain Monte Carlo. PAMI, 24(5), 657–673.CrossRef
Turaga, P., Veeraraghavan, A., Srivastava, A., & Chellappa, R. (2011). Statistical computations on special manifolds for image and video-based recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence, 33(11), 2273–2286.CrossRef
Turk, M., & Pentland, A. (1991). Face recognition using eigenfaces. In Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (pp. 586–591).
Udell, M., Horn, C., Zadeh, R., & Boyd, S. (2015). Generalized low rank models. Working manuscript.
Ueda, N., Nakan, R., & Ghahramani, Z. (2000). SMEM algorithm for mixture models. Neural Computation, 12, 2109–2128.CrossRef
Varma, M., & Zisserman, A. (2003). Texture classification: Are filter banks necessary? In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition.
Vasilescu, M., & Terzopoulos, D. (2002). Multilinear analysis of image ensembles: Tensorfaces. In Proceedings of European Conference on Computer Vision (pp. 447–460).
Vecchio, D. D., & Murray, R. (2004). Observers for a class of hybrid systems on a lattice. In Proceedings of Hybrid Systems: Computation and Control. New York: Springer.
Vetterli, M., & Kovacevic, J. (1995). Wavelets and subband coding. Upper Saddle River: Prentice-Hall.MATH
Vidal, R. (2004). Identification of PWARX hybrid models with unknown and possibly different orders. In American Control Conference (pp. 547–552).
Vidal, R. (2005). Multi-subspace methods for motion segmentation from affine, perspective and central panoramic cameras. In IEEE Conference on Robotics and Automation (pp. 1753–1758).
Vidal, R., Chiuso, A., & Soatto, S. (2002a). Observability and identifiability of jump linear systems. In IEEE Conference on Decision and Control (pp. 3614–3619).
Vidal, R., Chiuso, A., Soatto, S., & Sastry, S. (2003a). Observability of linear hybrid systems. In Hybrid Systems: Computation and Control (pp. 526–539). New York: Springer.
Vidal, R., & Favaro, P. (2014). Low rank subspace clustering (LRSC). Pattern Recognition Letters, 43, 47–61.CrossRef
Vidal, R., & Hartley, R. (2004). Motion segmentation with missing data by PowerFactorization and Generalized PCA. In IEEE Conference on Computer Vision and Pattern Recognition (Vol. II, pp. 310–316).
Vidal, R., & Ma, Y. (2004). A unified algebraic approach to 2-D and 3-D motion segmentation. In European Conference on Computer Vision (pp. 1–15).
Vidal, R., Ma, Y., & Piazzi, J. (2004). A new GPCA algorithm for clustering subspaces by fitting, differentiating and dividing polynomials. In IEEE Conference on Computer Vision and Pattern Recognition (Vol. I, pp. 510–517).
Vidal, R., Ma, Y., & Sastry, S. (2003b). Generalized Principal Component Analysis (GPCA). In IEEE Conference on Computer Vision and Pattern Recognition (Vol. I, pp. 621–628).
Vidal, R., Ma, Y., Soatto, S., & Sastry, S. (2006). Two-view multibody structure from motion. International Journal of Computer Vision, 68(1), 7–25.CrossRef
Vidal, R., & Ravichandran, A. (2005). Optical flow estimation and segmentation of multiple moving dynamic textures. In IEEE Conference on Computer Vision and Pattern Recognition (Vol. II, pp. 516–521).
Vidal, R., & Sastry, S. (2003). Optimal segmentation of dynamic scenes from two perspective views. In IEEE Conference on Computer Vision and Pattern Recognition (Vol. 2, pp. 281–286).
Vidal, R., Soatto, S., Ma, Y., & Sastry, S. (2002b). Segmentation of dynamic scenes from the multibody fundamental matrix. In ECCV Workshop on Visual Modeling of Dynamic Scenes.
Vidal, R., Soatto, S., Ma, Y., & Sastry, S. (2003c). An algebraic geometric approach to the identification of a class of linear hybrid systems. In IEEE Conference on Decision and Control (pp. 167–172).
Vidal, R., Tron, R., & Hartley, R. (2008). Multiframe motion segmentation with missing data using PowerFactorization and GPCA. International Journal of Computer Vision, 79(1), 85–105.CrossRef
Wallace, C., & Boulton, D. (1968). An information measure for classification. The Computer Journal, 11, 185–194.MATHCrossRef
Wallace, C., & Dowe, D. (1999). Minimum message length and Kolmogrov complexity. The Computer Journal, 42(4), 270–283.MATHCrossRef
Wallace, G. K. (1991). The JPEG still picture compression standard. Communications of the ACM. Special issue on digital multimedia systems, 34(4), 30–44.
Wang, J., Jia, Y., Hua, X., Zhang, C., & Quan, L. (2008a). Normalized tree partitioning for image segmentation. In IEEE Conference on Computer Vision and Pattern Recognition.
Wang, J. M., Fleet, D. J., & Hertzmann, A. (2008b). Gaussian process dynamical models for human motion. IEEE Transactions on Pattern Analysis and Machine Intelligence, 30(2), 283–298.
Wang, Y.-X., & Xu, H. (2013). Noisy sparse subspace clustering. In International Conference on Machine learning.
Ward, J. (1963). Hierarchical grouping to optimize and objective function. Journal of the American Statistical Association, 58, 236–244.MathSciNetCrossRef
Wei, S., & Lin, Z. (2010). Analysis and improvement of low rank representation for subspace segmentation. Technical Report MSR-TR-2010-177, Microsoft Research Asia.
Weinberger, K. Q., & Saul, L. (2004). Unsupervised learning of image manifolds by semidefinite programming. In Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (pp. 988–955).
Wiberg, T. (1976). Computation of principal components when data are missing. In Symposium on Computational Statistics (pp. 229–326).
Wilks, S. S. (1962). Mathematical Staistics. New York: Wiley.
Williams, C. (2002). On a connection between kernel PCA and metric multidimensional scaling. Machine Learning, 46, 11–19.MATHCrossRef
Wolf, L., & Shashua, A. (2001a). Affine 3-D reconstruction from two projective images of independently translating planes. In Proceedings of IEEE International Conference on Computer Vision (pp. 238–244).
Wolf, L., & Shashua, A. (2001b). Two-body segmentation from two perspective views. In IEEE Conference on Computer Vision and Pattern Recognition (pp. 263–270).
Wolf, L., & Shashua, A. (2003). Learning over sets using kernel principal angles. Journal of Machine Learning Research, 4(10), 913–931.MathSciNetMATH
Woolfe, F., & Fitzgibbon, A. (2006). Shift-invariant dynamic texture recognition. In Proceedings of European Conference on Computer Vision, pages II: 549–562.
Wright, J., Ganesh, A., Kerui, M., & Ma, Y. (2013). Compressive principal component analysis. IMA Journal on Information and Inference, 2(1), 32–68.MATHCrossRef
Wright, J., Ganesh, A., Rao, S., Peng, Y., & Ma, Y. (2009a). Robust principal component analysis: Exact recovery of corrupted low-rank matrices via convex optimization. In NIPS.
Wright, J., Ma, Y., Tao, Y., Lin, Z., & Shum, H.-Y. (2009b). Classification via minimum incremental coding length (MICL). SIAM Journal on Imahing Sciences, 2(2), 367–395.
Wu, Y., Zhang, Z., Huang, T., & Lin, J. (2001). Multibody grouping via orthogonal subspace decomposition. In IEEE Conference on Computer Vision and Pattern Recognition (Vol. 2, pp. 252–257).
Xiong, F., Camps, O., & Sznaier, M. (2011). Low order dynamics embedding for high dimensional time series. In IEEE International Conference on Computer Vision (pp. 2368–2374).
Xiong, F., Camps, O., & Sznaier, M. (2012). Dynamic context for tracking behind occlusions. In European Conference on Computer Vision. Lecture notes in computer science (Vol. 7576, pp. 580–593). Berlin/Heidelberg: Springer.
Xu, H., Caramanis, C., & Sanghavi, S. (2010). Robust pca via outlier pursuit. In Neural Information Processing Systems (NIPS).
Yan, J., & Pollefeys, M. (2006). A general framework for motion segmentation: Independent, articulated, rigid, non-rigid, degenerate and non-degenerate. In European Conference on Computer Vision (pp. 94–106).
Yang, A., Wright, J., Ma, Y., & Sastry, S. (2008). Unsupervised segmentation of natural images via lossy data compression. Computer Vision and Image Understanding, 110(2), 212–225.CrossRef
Yang, A. Y., Rao, S. R., & Ma, Y. (2006). Robust statistical estimation and segmentation of multiple subspaces. In CVPR workshop on 25 years of RANSAC.
Yang, J., Wright, J., Huang, T., & Ma, Y. (2010). Image super-resolution via sparse representation. IEEE Transactions on Image Processing, 19(11), 2861–2873.MathSciNetCrossRef
Yang, M. H., Ahuja, N., & Kriegman, D. (2000). Face detection using mixtures of linear subspaces. In IEEE International Conference on Automatic Face and Gesture Recognition.
Yu, G., Sapiro, G., & Mallat, S. (2010). Image modeling and enhancement via structured sparse model selection. In International Conference on Image Processing.
Yu, G., Sapiro, G., & Mallat, S. (2012). Solving inverse problems with piecewise linear estimators: From gaussian mixture models to structured sparsity. IEEE Transactions on Image Processing, 21(5), 2481–2499.MathSciNetCrossRef
Yu, S. (2005). Segmentation induced by scale invariance. In IEEE Conference on Computer Vision and Pattern Recognition.
Yuan, L., Wen, F., Liu, C., & Shum, H. (2004). Synthesizing dynamic texture with closed-loop linear dynamic system. In European Conference on Computer Vision (pp. 603–616).
Yuan, X., & Yang, J. (2009). Sparse and low-rank matrix decomposition via alternating direction methods. Preprint.
Zelnik-Manor, L., & Irani, M. (2003). Degeneracies, dependencies and their implications in multi-body and multi-sequence factorization. In IEEE Conference on Computer Vision and Pattern Recognition (Vol. 2, pp. 287–293).
Zhang, K., Zhang, L., & Yang, M. (2014). Fast compressive tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence, 36(10).
Zhang, T., Szlam, A., & Lerman, G. (2009). Median k-flats for hybrid linear modeling with many outliers. In Workshop on Subspace Methods.
Zhang, T., Szlam, A., Wang, Y., & Lerman, G. (2010). Randomized hybrid linear modeling via local best-fit flats. In IEEE Conference on Computer Vision and Pattern Recognition (pp. 1927–1934).
Zhang, Z., & Zha, H. (2005). Principal manifolds and nonlinear dimensionality reduction via tangent space alignment. SIAM Journal on Scientific Computing, 26(1), 313–338.MathSciNetMATHCrossRef
Zhou, F., la Torre, F. D., & Hodgins, J. K. (2008). Aligned cluster analysis for temporal segmentation of human motion. In International Conference on Automatic Face and Gesture Recognition.
Zhou, M., Wang, C., Chen, M., Paisley, J., Dunson, D., & Carin, L. (2010a). Nonparametric bayesian matrix completion. In Sensor Array and Multichannel Signal Processing Workshop.
Zhou, Z., Wright, J., Li, X., Candès, E., & Ma, Y. (2010b). Stable principal component pursuit. In International Symposium on Information Theory.
Zhu, Q., Song, G., & Shi, J. (2007). Untangling cycles for contour grouping. In Proceedings of the International Conference on Computer Vision (ICCV).
Metadaten
Titel
Introduction
verfasst von
René Vidal
Yi Ma
S. Shankar Sastry
Copyright-Jahr
2016
Verlag
Springer New York
Buch
Generalized Principal Component Analysis

Print ISBN: 978-0-387-87810-2

Electronic ISBN: 978-0-387-87811-9

Copyright-Jahr: 2016

DOI
https://doi.org/10.1007/978-0-387-87811-9_1

Neuer Inhalt

    Bildnachweise