Daniel Kaslovsky

APPM 7400: Recent Topics in Big Data

Department of Applied Mathematics
University of Colorado, Boulder

Course flier: [PDF]

Spring 2013
Thursdays, 4:00 - 5:00 PM
ECCR 257 (APPM Newton Computer Lab)

Massive quantities of data are produced by a wide range of scientific disciplines and societal interactions. Researchers are responding to this "data deluge" with new theory and computational methods for acquiring and processing large, complex, high-dimensional data. This reading course will introduce students to the state of the art research in the analysis of modern data sets. Recent and influential contributions to the literature will be read and discussed each week, allowing students to gain familiarity with the theoretical, computational, and statistical techniques crucial for the advancement of big data science.

Schedule

(papers are listed below)

January 24	Introductory Material	Papers: (1)
January 25	APPM Colloquium by Anna Gilbert - ECCR 245, 3:00 PM
January 31	Sparsity, Sparse Representation	Papers: (2), (3)
February 7	Sparse Representation and Signal/Image Processing	Papers: (4), (5)
February 14	Compressive Sensing	Papers: (6), (7), (8)
February 21	Compressive Sensing	Papers: (9), (10)
February 28	(no meeting)
March 7	Johnson-Lindenstrauss Lemma	Papers: (11), (12)
March 14	Low Rank Matrix Approximations	Papers: (13)
March 21	Random Matrix Theory, Randomized Algorithms	Papers: (14)
March 28	Spring Break
April 4	Random Matrix Theory, Randomized Algorithms	Papers: (14)
April 11	Data Models and Manifold Learning	Papers: (15), (16)
April 18	Manifold Learning and Nonlinear Dimension Reduction	Papers: (17), (18)
April 25	Graphs and Geometric Analysis of Data Sets	Papers: (19), (20)
May 2	Geometric Analysis of Data Sets	Papers: (21), (22)

Papers

(1)	Donoho and Tanner (2010). "Precise Undersampling Theorems"
(2)	Bruckstein, Donoho, and Elad (2009). "From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images"
(3)	Olshausen and Field (1996). "Emergence of Simple-cell Receptive Field Properties by Learning a Sparse Code for Natural Images"
(4)	Aharon, Elad, and Bruckstein (2006). "K-SVD: An algorithm for Designing Overcomplete Dictionaries for Sparse Representation"
(5)	Rubinstein, Bruckstein, and Elad (2010). "Dictionaries for Sparse Representation Modeling"
(6)	Candes and Wakin (2008). "An Introduction to Compressive Sampling"
(7)	Candes, Romberg, and Tao (2006). "Robust Uncertainty Principles: Exact Signal Reconstruction From Highly Incomplete Frequency Information"
(8)	Donoho (2006). "Compressed Sensing"
(9)	Candes and Tao (2005). "Decoding by Linear Programming"
(10)	Candes, Romberg, and Tao (2006). "Stable Signal Recovery from Incomplete and Inaccurate Measurements"
(11)	Dasgupta and Gupta (2002). "An Elementary Proof of a Theorem by Johnson and Lindenstrauss"
(12)	Achlioptas (2003). "Database-friendly Random Projections: Johnson-Lindenstrauss with Binary Coins"
(13)	Achlioptas and McSherry (2007). "Fast Computation of Low Rank Matrix Approximations"
(14)	Halko, Martinsson, and Tropp (2011). "Finding Structure with Randomness: Stochastic Algorithms for Constructing Approximate Matrix Decompositions"
(15)	Saul, Weinberger, Ham, Sha, and Lee (2006). "Spectral Methods for Dimensionality Reduction"
(16)	Baraniuk, Cevher, and Wakin (2010). "Low-dimensional Models for Dimensionality Reduction and Signal Recovery: A Geometric Perspective"
(17)	Belkin and Niyogi (2003). "Laplacian Eigenmaps for Dimensionality Reduction and Data Representation"
(18)	Belkin and Niyogi (2004). "Semi-supervised Learning on Riemannian Manifolds"
(19)	Coifman, Lafon, Lee, Maggioni, Nadler, Warner, and Zucker (2005). "Geometric Diffusions as a Tool for Harmonic Analysis and Structure Definition of Data: Diffusion Maps"
(20)	Lafon and Lee (2006). "Diffusion Maps and Coarse-Graining: A Unified Framework for Dimensionality Reduction, Graph Partitioning, and Data Set Parameterization"
(21)	Chen, Little, Maggioni, and Rosasco (2011). "Some Recent Advances in Multiscale Geometric Analysis of Point Clouds"
(22)	Chen and Maggioni (2011). "Multiscale Geometric Dictionaries for Point-Cloud Data"

This material is based upon work supported by the National Science Foundation under Grant Number ACI-1226362.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.