Patch Alignment for Graph Embedding

Luo, Yong; Tao, Dacheng; Xu, Chao

doi:10.1007/978-1-4614-4457-2_4

Cited by 1 publication

(2 citation statements)

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“…It has attracted more and more researchers’ attention because of its good effect in research applications such as pattern recognition, machine learning and feature extraction. Such representative approaches include isometric feature mapping (ISOMAP) [5], locally linear embedding (LLE) [6], Laplacian Eigenmaps (LEs) [7], Cauchy graph embedding [8] etc. Since non‐linear manifold learning suffers from the out‐of‐sample problem [9], i.e.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, the LPP method is barely able to capture the intrinsic structures of data while existing outliers and noise. Second, LPP employs squared L2‐norm for distance measurement, which could magnify the influence of large distance of samples and thus leading to many violations of local topology preserving at small distance pairs [8]. As a result, the actual projections solution will deviate from the ideal ones when data contain outliers.…”

Section: Introductionmentioning

confidence: 99%

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Robust locality preserving projections using angle‐based adaptive weight method

Gao

Zhong

et al. 2020

IET Computer Vision

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Locality preserving projections (LPP) method is a classical manifold learning method for dimensionality reduction. However, LPP is sensitive to outliers since squared L2‐norm may exaggerate the distance of outliers. Besides, the normalisation constraint of LPP may impair its robustness during embedding. Motivated by this observation, the authors propose a novel robust LPP using angle‐based adaptive weight (RLPP‐AAW) method. RLPP‐AAW not only considers the distance metric of training samples, but also take the reconstruction error into account, so as to reduce the influence of outliers and noise in the embedding process. In the RLPP‐AAW, based on the angle between distance metric and reconstruction error, a novel way is used to combine them in the objective function. Besides, RLPP‐AAW employs the L21‐norm criterion, which retains rotational invariance and is more robust than squared L2‐norm. An iterative algorithm is presented to solve the objective function of RLPP‐AAW. Experimental results on the benchmark databases illustrate the effectiveness of the proposed algorithm.

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