A circuit framework for robust manifold learning
Författare
Summary, in English
Manifold learning and nonlinear dimensionality reduction addresses the problem of detecting possibly nonlinear structure in highdimensional data and constructing lower-dimensional configurations representative of this structure. A popular example is the Isomap algorithm which uses local information to approximate geodesic distances and adopts multidimensional scaling to produce lowerdimensional representations. Isomap is accurate on a global scale in contrast to many competing methods which approximate locally. However, a drawback of the Isomap algorithm is that it is topologically instable, that is, incorrectly chosen algorithm parameters or perturbations of data may drastically change the resulting configurations. We propose new methods for more robust approximation of the geodesic distances using a viewpoint of electric circuits. In this way, we achieve both the stability of local methods and the global approximation property of global methods, while compromising with local accuracy. This is demonstrated by a study of the performance of the proposed and competing methods on different data sets.
Avdelning/ar
Publiceringsår
2007
Språk
Engelska
Sidor
323-332
Publikation/Tidskrift/Serie
Neurocomputing
Volym
71
Issue
1-3
Dokumenttyp
Artikel i tidskrift
Förlag
Elsevier
Ämne
- Mathematics
Nyckelord
- Laplacian Eigenmaps
- Manifold learning
- Topological instability
- Multidimensional scaling
- Isomap
Status
Published
Forskningsgrupp
- Harmonic Analysis and Applications
ISBN/ISSN/Övrigt
- ISSN: 0925-2312