---
abstract: 'Many manifold embedding algorithms fail apparently when the data manifold has a large aspect ratio (such as a long, thin strip). Here, we formulate success and failure in terms of finding a smooth embedding, showing also that the problem is pervasive and more complex than previously recognized. Mathematically, success is possible under very broad conditions, provided that embedding is done by carefully selected eigenfunctions of the Laplace-Beltrami operator $\Delta$. Hence, we propose a bicriterial [*Independent Eigencoordinate Selection (IES)*]{} algorithm that selects smooth embeddings with few eigenvectors. The algorithm is grounded in theory, has low computational overhead, and is successful on synthetic and large real data.'
author:
- |
    Yu-Chia Chen\
    Department of Electrical & Computer Engineering\
    University of Washington\
    Seattle, WA 98195\
    `yuchaz@uw.edu`\
    Marina Meilă\
    Department of Statistics\
    University of Washington\
    Seattle, WA 98195\
    `mmp2@uw.edu`\
---

Acknowledgements {#acknowledgements .unnumbered}
================

The authors acknowledge partial support from the U.S. Department of Energy, Solar Energy Technology Office award DE-EE0008563 and from the NSF DMS PD 08-1269 and NSF IIS-0313339 awards. They are grateful to the Tkatchenko and Pfaendtner labs and in particular to Stefan Chmiela and Chris Fu for providing the molecular dynamics data and for many hours of brainstorming and advice.
