Efficient Inter-Geodesic Distance Computation and Fast Classical Scaling
Multidimensional scaling (MDS) is a dimensionality reduction tool used for information analysis, data visualization and manifold learning. Most MDS procedures embed data points in low-dimensional euclidean (flat) domains, such that distances between the points are as close as possible to given inter...
| Veröffentlicht in: | IEEE transactions on pattern analysis and machine intelligence. - 1979. - 42(2020), 1 vom: 29. Jan., Seite 74-85 |
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| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2020
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| Zugriff auf das übergeordnete Werk: | IEEE transactions on pattern analysis and machine intelligence |
| Schlagworte: | Journal Article |
| Zusammenfassung: | Multidimensional scaling (MDS) is a dimensionality reduction tool used for information analysis, data visualization and manifold learning. Most MDS procedures embed data points in low-dimensional euclidean (flat) domains, such that distances between the points are as close as possible to given inter-point dissimilarities. We present an efficient solver for classical scaling, a specific MDS model, by extrapolating the information provided by distances measured from a subset of the points to the remainder. The computational and space complexities of the new MDS methods are thereby reduced from quadratic to quasi-linear in the number of data points. Incorporating both local and global information about the data allows us to construct a low-rank approximation of the inter-geodesic distances between the data points. As a by-product, the proposed method allows for efficient computation of geodesic distances |
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| Beschreibung: | Date Revised 04.03.2020 published: Print-Electronic Citation Status PubMed-not-MEDLINE |
| ISSN: | 1939-3539 |
| DOI: | 10.1109/TPAMI.2018.2877961 |