Nonlinear Dimensionality Reduction via Path-Based Isometric Mapping

Najafi, A ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1109/TPAMI.2015.2487981
  3. Publisher: IEEE Computer Society
  4. Abstract:
  5. Nonlinear dimensionality reduction methods have demonstrated top-notch performance in many pattern recognition and image classification tasks. Despite their popularity, they suffer from highly expensive time and memory requirements, which render them inapplicable to large-scale datasets. To leverage such cases we propose a new method called "Path-Based Isomap". Similar to Isomap, we exploit geodesic paths to find the low-dimensional embedding. However, instead of preserving pairwise geodesic distances, the low-dimensional embedding is computed via a path-mapping algorithm. Due to the much fewer number of paths compared to number of data points, a significant improvement in time and memory complexity with a comparable performance is achieved. The method demonstrates state-of-the-art performance on well-known synthetic and real-world datasets, as well as in the presence of noise
  6. Keywords:
  7. Conformal mapping ; Geodesy ; Image classification ; Mapping ; Nonlinear analysis ; Pattern recognition ; Geodesic paths ; Large-scale datasets ; Low dimensional embedding ; Manifold learning ; Memory requirements ; Nonlinear dimensionality reduction ; Optimization criteria ; State-of-the-art performance ; Embedded systems
  8. Source: IEEE Transactions on Pattern Analysis and Machine Intelligence ; Volume 38, Issue 7 , 2016 , Pages 1452-1464 ; 01628828 (ISSN)
  9. URL: http://ieeexplore.ieee.org/document/7293680