Boaz Nadler
My research is concerned with the analysis of high dimensional data. In
many modern scientific fields,
complex datasets with relatively few samples and many variables are
collected. Examples include biological
datasets, text-document analysis, simulations of complex dynamical
systems, etc. The main challenges
are how to extract useful information from such data, how to unravel
hidden structures in them and how to represent
their main features by only a few variables.
In our research, we combine methods from probability theory, stochastic processes and harmonic analysis, to both develop novel methods for the analysis of such datasets and to analyze the mathematical characteristics of existing algorithms.
Current research focuses on the following three directions: (1) A probabilistic foundation for clustering (2) Non-linear dimensionality reduction methods, both for general data as well as for data arising from high dimensional stochastic dynamical systems, and (3) Adaptive feature extraction, specifically as a pre-processing tool prior to the application of standard learning algorithms.
Recent Publications
- [with M. Galun] Fundamental Limitations of Spectral Clustering. NIPS, 2006.
- [with S. Lafon, R.R. Coifman and I.G. Kevrekidis] Diffusion Maps, Spectral Clustering and Reaction Coordinates of Dynamical Systems. Applied and Computational Harmonic Analysis, 2006.
- [with R.R. Coifman] The prediction error in CLS and PLS: the importance of feature selection prior to multivariate calibration. Journal of Chemometrics, 2005.