My research interests include high-dimensional data analysis, multiscale methods, clustering algorithms, and machine learning. My research has utilized tools from statistics, linear algebra, random matrix theory, probability, and harmonic analysis. My dissertation research used multiscale singular value decompositions to estimate the instrinsic dimension of high-dimensional data sets. More recently I am working on a multiscale, spectral method for estimating the number of clusters in a data set.
- A Little, X Mountrouidou, D Moseley; ``Spectral Clustering Technique for Classifying Network Attacks," IEEE International Conference on Intelligent Data and Security (IDS), New York City, April 2016.
- A Little, A Byrd; ``A Multiscale Spectral Method for Learning Number of Clusters," 14th IEEE International Conference on Machine Learning and Applications (ICMLA), Miami, Dec. 2015.
- A Little, M Maggioni, L Rosasco; ``Multiscale Geometric Methods for Estimating Intrinsic Dimension," 9th International Conference on Sampling Theory and Applications (SampTA), Singapore, May 2011.
- A Little, Y Jung, M Maggioni; ``Multiscale Estimation of Intrinsic Dimensionality of Data Sets," Association for the Advancement of Artificial Intelligence (AAAI) Fall Symposium (FS-09-04), 2009.
- J Lee, A Little, Y Jung, M Maggioni; ``Estimation of Intrinsic Dimensionality of Samples from Noisy Low-dimensional Manifolds in High Dimensions with Multiscale SVD," IEEE Workshop on Statistical Signal Processing (SSP), Cardiff, 2009.
Journal Articles and Book Chapters
- A Little, M Maggioni, L Rosasco; ``Multiscale geometric methods for data sets I: Multiscale SVD, noise and curvature," to appear in Applied and Computational Harmonic Analysis (ACHA), 2016.
- L Hart, A Little; ``Translating Evidence into Practice: Interpreting Measures of Risk," to appear in The Nurse Practitioner, August 2016.
- G. Chen, A.V. Little, M. Maggioni; ``Multi-Resolution Geometric Analysis for Data in High Dimensions," in Excursions in Harmonic Analysis, Vol. 1, Editors T.D. Andrews et al., Birkhauser, 2013.
- G Chen, A Little, M Maggioni; ``Some recent advances in the geometric analysis of point clouds," in Wavelets and Multiscale Analysis: Theory and Applications, Editors J. Cohen and A. Zayed, Birkhauser, 2011.
- T Ladner, A Little, K Marks, A Russel; ``Positive Solutions to a Diffusive Logistic Equation with Constant Yield Harvesting," Rose-Hulman Undergraduate Math Journal, ISSN Vol. 6, Issue 1, 2005.
- A Little, Advisor: M Maggioni; "Estimating the Intrinsic Dimension of High-Dimensional Data Sets: A Multiscale, Geometric Approach," Duke University, 2011