Representation Learning for Clustering: A Statistical Framework

We address the problem of communicating domain knowledge from a user to the designer of a clustering algorithm. We propose a protocol in which the user provides a clustering of a relatively small random sample of a data set. The algorithm designer then uses that sample to come up with a data representation under which $k$-means clustering results in a clustering (of the full data set) that is aligned with the user's clustering. We provide a formal statistical model for analyzing the sample complexity of learning a clustering representation with this paradigm. We then introduce a notion of capacity of a class of possible representations, in the spirit of the VC-dimension, showing that classes of representations that have finite such dimension can be successfully learned with sample size error bounds, and end our discussion with an analysis of that dimension for classes of representations induced by linear embeddings.Comment: To be published in Proceedings of UAI 201

Computational fluid dynamics research

The focus of research in the computational fluid dynamics (CFD) area is two fold: (1) to develop new approaches for turbulence modeling so that high speed compressible flows can be studied for applications to entry and re-entry flows; and (2) to perform research to improve CFD algorithm accuracy and efficiency for high speed flows. Research activities, faculty and student participation, publications, and financial information are outlined

Plasmon dispersion in semimetallic armchair graphene nanoribbons

The dispersion relations for plasmons in intrinsic and extrinsic semimetallic armchair graphene nanoribbons (acGNR) are calculated in the random phase approximation using the orthogonal p_z-orbital tight binding method. Our model predicts new plasmons for acGNR of odd atomic widths N=5,11,17,... Our model further predicts plasmons in acGNR of even atomic width N=2,8,14,... related to those found using a Dirac continuum model, but with different quantitative dispersion characteristics. We find that the dispersion of all plasmons in semimetallic acGNR depends strongly on the localization of the p_z electronic wavefunctions. We also find that overlap integrals for acGNR behave in a more complex way than predicted by the Dirac continuum model, suggesting that these plasmons will experience a small damping for all q not equal to 0. Plasmons in extrinsic semimetallic acGNR with the chemical potential in the lowest (highest) conduction (valence) band are found to have dispersion characteristics nearly identical to their intrinsic counterparts, with negligible differencs in dispersion arising from the slight differences in overlap integrals for the interband and intraband transitions.Comment: 8 pages, 9 figure