CSE 291. Unsupervised Learning

CSE 291B. Unsupervised Learning

Winter 2009
Professor: Lawrence Saul
Lectures: Tue/Thu 11:00 am - 12:20 pm
Location: Warren Lecture Hall 2209
Office hours: after class and/or by appointment.
Units: 2 or 4

Course Description

The lectures in this course will survey leading algorithms for unsupervised learning and high dimensional data analysis. The first part of the course will cover probabilistic generative models of high dimensional data, including Gaussian mixture models, factor analysis, nonnegative matrix factorization, exponential family PCA, probabilistic latent semantic analysis, and latent Dirichlet allocation. The second part of the course will cover spectral methods for dimensionality reduction, including multidimensional scaling, Isomap, maximum variance unfolding, locally linear embedding, graph Laplacian methods, spectral clustering, and kernel PCA. The third part of the course will consist of student presentations on related topics of interest.

Prerequisites

The course is aimed at graduate students in machine learning and related fields. Students should have earned a high grade in a previous, related course, such as CSE 250A, CSE 250B, ECE 271A, or ECE 271B. The course will be taught by lecture in the same style as CSE 250A, though at a more advanced mathematical level.

Grading

Students may take the course for either two or four units of credit. For two units, students will be required to give a 20-minute oral presentation on an assigned reading or research project. They may also be required to submit "scribe notes" (handwritten or typeset) on a small subset of lectures. For four units, students will additionally be required to complete occasional (but challenging) problem sets.

HW 1 (out Jan 29, due Feb 12)
HW 2 (out Mar 3, due Mar 17)

Syllabus

Tue Jan 6	Course overview. Review of clustering: k-means algorithm, Gaussian mixture modeling.
Thu Jan 8	Review of linear dimensionality reduction: principal component analysis, factor analysis.
Tue Jan 13	EM algorithms for factor analysis, principal component analysis, and mixture of factor analyzers.
Thu Jan 15	Nonnegative matrix factorization: cost functions and multiplicative updates.
Tue Jan 20	Nonnegative matrix factorization: auxiliary functions and proofs of convergence.
Thu Jan 22	Exponential family PCA.
Tue Jan 27	Random projection trees: guest lecture by Yoav Freund
Thu Jan 29	Document modeling: bag-of-words representation, probabilistic latent semantic indexing, Dirichlet models.
Tue Feb 3	Latent Dirichlet allocation.
Thu Feb 5	Variational approximations for inference.
Tue Feb 10	Singular value decomposition, low-rank matrix approximations, multidimensional scaling.
Thu Feb 12	Manifold learning, Isomap algorithm.
Tue Feb 17	Nystrom approximation; maximum variance unfolding (MVU).
Thu Feb 19	Spectral clustering, normalized cuts, graph partitioning.
Tue Feb 24	Laplacian eigenmaps, locally linear embedding (LLE).
Thu Feb 26	Low rank factorizations for MVU, kernel PCA; class evaluations.

Student Presentations

Tue Mar 3	Boyko Kakaradov, Josh Lewis, Cheng-Xian Li, Adam Koerner
Thu Mar 5	Aditya Menon, Tim Mullen, Matt Rodriguez, Andrea Vattani, Priya Velu
Tue Mar 10	Pouya Bozorgmehr, Heejin Choi, Eric Christiansen, Timothy Fair
Thu Mar 12	Kristen Jackie, Han Kim, Justin Ma, Kei Ma, Vicente Malave
Thu Mar 19	Peter Shin, Il-Young Son, Andrew Stout, Walter Talbott, Robert Thomas, Alex Tsiatas, Kai Wang, Wensong Xu

Readings

Probabilistic PCA

S. Roweis (1998). EM algorithms for PCA and SPCA. In M. I. Jordan, M. S. Kearns, and S. A. Solla (eds.), Advances in Neural Information Processing Systems 10, pages 626-632. MIT Press: Cambridge, MA.

M. E. Tipping and C. M. Bishop (1999). Mixtures of probabilistic principal component analysers. Neural Computation 11(2), 443-482.

Nonnegative matrix factorization

D. D. Lee and H. S. Seung (1999). Learning the parts of objects with nonnegative matrix factorization. Nature 401: 788-791.
D. D. Lee and H. S. Seung (2001). Algorithms for nonnegative matrix factorization. In T. K. Leen, T. G. Dietterich, and V. Tresp (eds.), Advances in Neural Information Processing Systems 14, pages 556-562. MIT Press: Cambridge, MA.

Exponential family PCA

M. Collins, S. Dasgupta, and R. E. Schapire (2002). A generalization of principal component analysis to the exponential family. In T. G. Dietterich, S. Becker, and Z. Ghahramani (eds.), Advances in Neural Information Processing Systems 13, pages 617-624. MIT Press: Cambridge, MA.

I. Rish, G. Grabarnik, G. Cecchi, F. Pereira, and G. J. Gordon (2008). Closed-form supervised dimensionality reduction with generalized linear models. In Proceedings of the Twenty Fifth International Conference on Machine Learning (ICML-08), pages 832-839. Helsinki, Finland.

Document modeling

T. Hoffman (1999). Probabilistic latent semantic analysis. In Proceedings of the Fifteenth Annual Conference on Uncertainty in Artificial Intelligence (UAI-99), pages 289-296. Stockholm, Sweden.

D. Blei, A. Ng, and M. I. Jordan (2003). Latent Dirichlet allocation. Journal of Machine Learning Research 3:993-1022.

Multidimensional scaling and Nystrom approximation

J. C. Platt (2004). Fast embedding of sparse music similarity graphs. In S. Thrun, L. K. Saul, and B. Schoelkopf (eds.) (2004). Advances in Neural Information Processing Systems 16, pages 571-578. MIT Press: Cambridge, MA.
J. C. Platt (2005). FastMap, MetricMap, and landmark MDS are all Nystrom algorithms. In Proceedings of the Tenth International Workshop on Artificial Intelligence and Statistics (AISTATS-05), pp. 261-268. Barbados, West Indies.

Isomap and extensions

J.B. Tenenbaum, V. de Silva and J. C. Langford (2000). A global geometric framework for nonlinear dimensionality reduction. Science, vol. 290, pp. 2319--2323.

V. de Silva and J. B. Tenenbaum (2003). Global versus local methods in nonlinear dimensionality reduction. In S. Becker, S. Thrun, and K. Obermayer (eds.), Advances in Neural Information Processing Systems 15, pages 705-712. MIT Press: Cambridge, MA.

Maximum variance unfolding

K. Q. Weinberger and L. K. Saul (2006). An introduction to nonlinear dimensionality reduction by maximum variance unfolding. In Proceedings of the Twenty First National Conference on Artificial Intelligence (AAAI-06), pages 1683-1686. Boston, MA.
J. Sun, S. Boyd, L. Xiao, and P. Diaconis (2006). The fastest mixing Markov process on a graph and a connection to a maximum variance unfolding problem. SIAM Review 48(4):681-699.
K. Q. Weinberger, F. Sha, Q. Zhu, and L. K. Saul (2007). Graph Laplacian regularization for large-scale semidefinite programming. In B. Schoelkopf, J. Platt, and T. Hofmann (eds.), Advances in Neural Information Processing Systems 19, pages 1489-1496. MIT Press: Cambridge, MA.

Spectral clustering

J. Shi and J. Malik (2000). Normalized cuts and image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI) 22(8): 888-905.
A. Ng, M. Jordan, and Y. Weiss (2002). On spectral clustering: analysis and an algorithm. In T. Dietterich, S. Becker and Z. Ghahramani (eds.), Advances in Neural Information Processing Systems 14, pages 849-856. MIT Press: Cambridge, MA.

Graph Laplacian methods

M. Belkin and P. Niyogi (2003). Laplacian eigenmaps for dimensionality reduction and data representation, Neural Computation 15(6): 1373-1396.
M. Belkin and P. Niyogi (2004). Semi-supervised learning on Riemannian manifolds, Machine Learning 56:209-239.

Locally linear embedding and related work

S. T. Roweis and L. K. Saul (2000). Nonlinear dimensionality reduction by locally linear embedding. Science 290: 2323-2326.
L. K. Saul and S. T. Roweis (2003). Think globally, fit locally: unsupervised learning of low dimensional manifolds. Journal of Machine Learning Research 4:119-155.
D. Donoho and C. Grimes (2003). Hessian eigenmaps: locally linear embedding techniques for high dimensional data. Proceedings of the National Academy of Sciences 10:5591-5596.
Z. Zhang (2004). Principal manifolds and nonlinear dimension reduction via local tangent space alignment. SIAM Journal of Scientific Computing 26:313-338.
Z. Zhang and J. Wang (2007). MLLE: modified locally linear embedding using multiple weights. In B. Schoelkopf, J. Platt, and T. Hofmann (eds.), Advances in Neural Information Processing Systems 19, pages 1593-1600. MIT Press: Cambridge, MA.

Kernel PCA

B. Schoelkopf, A. J. Smola, K. R. Mueller (1998). Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation 10:1299-1319.
J. Hamm, D. D. Lee, S. Mika, and B. Schoelkopf (2004). A kernel view of the dimensionality reduction of manifolds. In Proceedings of the Twenty First International Confernence on Machine Learning (ICML-04), pages 369-376. Banff, Canada.
K. Q. Weinberger, F. Sha, and L. K. Saul (2004). Learning a kernel matrix for nonlinear dimensionality reduction. In Proceedings of the Twenty First International Confernence on Machine Learning (ICML-04), pages 839-846. Banff, Canada.