Principal manifold learning by sparse grids
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| Title: | Main Title: Principal manifold learning by sparse grids |
| Description: | Abstract: In this paper, we deal with the construction of lower-dimensional manifolds from high-dimensional data which is an important task in data mining, machine learning and statistics. Here, we consider principal manifolds as the minimum of a regularized, non-linear empirical quantization error functional. For the discretization we use a sparse grid method in latent parameter space. This approach avoids, to some extent, the curse of dimension of conventional grids like in the GTM approach. The arising non-linear problem is solved by a descent method which resembles the expectation maximization algorithm.We present our sparse grid principal manifold approach, discuss its properties and report on the results of numerical experiments for one-, two and three-dimensional model problems. |
| Identifier: | 10.1007/s00607-009-0045-8 (DOI) |
Responsible Party
| Creators: | Christian Feuersänger (Author), Michael Griebel (Author) |
| Publisher: | Springer |
| Publication Year: | 2013 |
Topic
| TR32 Topic: | Other |
| Related Subproject: | D5 |
| Subjects: | Keywords: Sparse Grids, Regularized Principal Manifolds, High-Dimensional Data |
File Details
| Filename: | 2009_Feuersaenger_Computing.pdf |
| Data Type: | Text - Article |
| Size: | 33 Pages |
| File Size: | 5.7 MB |
| Dates: | Accepted: 28.04.2009 Issued: 28.07.2009 |
| Mime Type: | application/pdf |
| Data Format: | |
| Language: | English |
| Status: | Completed |
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| Download Permission: | Only Project Members |
| General Access and Use Conditions: | For internal use only |
| Access Limitations: | For internal use only |
| Licence: | [TR32DB] Data policy agreement |
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Specific Information - Publication
| Publication Status: | Published |
| Review Status: | Peer reviewed |
| Publication Type: | Article |
| Article Type: | Journal |
| Source: | Computing |
| Volume: | 85 |
| Number of Pages: | 33 (267 - 299) |
Metadata Details
| Metadata Creator: | Harrie-Jan Hendricks-Franssen |
| Metadata Created: | 03.12.2013 |
| Metadata Last Updated: | 03.12.2013 |
| Subproject: | D5 |
| Funding Phase: | 1 |
| Metadata Language: | English |
| Metadata Version: | V50 |
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| Page Visits: | 746 |
| Metadata Downloads: | 0 |
| Dataset Downloads: | 0 |
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