Orthogonal Neighborhood Preserving Projections: A Projection-Based Dimensionality Reduction Technique

By Effrosini Kokiopoulou, Y. Saad. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2007

312 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/87d4c95794676e5e8f7a9f9f05cd1e2f468906dd

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In Computational Mechanics

In Computer Vision and Pattern Recognition

Citations in the corpus

Maximum Neighborhood Margin Discriminant Projection for Classification (2014, unknown): “Moreover, making the projection orthogonal (i.e., Φ 𝑇 Φ = 𝐼 ) will tend to preserve distances between any points 𝑥 𝑖 and 𝑥 𝑗 in the projected subspace [53].”
Fast Approximate kNN Graph Construction for High Dimensional Data via Recursive Lanczos Bisection (2009, background): “…Laplacian eigenmaps (Belkin and Niyogi, 2003), locality preserving projections (LPP) (He and Niyogi, 2004), and orthogonal neighborhood preserving projections (ONPP) (Kokiopoulou and Saad, 2007), compute a low dimensional embedding of the data by preserving the local neighborhoods for each point.”
Trace optimization and eigenproblems in dimension reduction methods (2011, methodology): “However, as was suggested in [25], one can exploit the fact that V can be restricted (again implicitly) to lie in the span of Φ( X ), since V must project Φ( X ).”
Flexible Orthogonal Neighborhood Preserving Embedding (2017, background): “in [Kokiopoulou and Saad, 2007] pointed out that this kind of orthogonal constraint tends to make the projected points different from one another, which makes NPE can not preserve the overall geometry very well.”
Feature dimensionality reduction: a review (2022, methodology): “Locally preserved projection (LPP) is a recently proposed method of dimensionality reduction that attempts to capture the manifold structure of data [103, 104].”
Learning shared subspace for multi-label dimensionality reduction via dependence maximization (2015, background): “The orthogonal constraint ΘΘ 1⁄4 I is added for two considerations: (1) to avoid the scaling problem; (2) to preserve as much shared information as possible [46].”
Dimensionality Reduction: A Comparative Review (2008, methodology): “These variants include factor analysis [117], Gaussian Process Latent Variable Models [80], principal curves [28], kernel maps [118], conformal eigenmaps [113], Geodesic Nullspace Analysis [24], Structure Preserving Embedding [114], variants of multidimensional scaling [3, 38, 45, 62, 92], technique”