Locality Preserving Projections

By Xiaofei He, Partha Niyogi. 2003

4,727 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. Dacheng Tao
2. Yi Yang
3. Luc Van Gool
4. Yoshua Bengio
5. Gong Cheng
6. Feiping Nie
7. Xuelong Li
8. Chunhua Shen

Citations in the corpus

• A Comprehensive Survey of Graph Embedding: Problems, Techniques, and Applications (2017, background): “(4) AgLPP [79] anchor graph,W ¼ ZL 1ZT , Lkk ¼ P Zik, Zik ¼ Ks ðXi;UkÞP j Ks ðXi;UjÞ a ¼ argmin aT ULUT a aT UDUT a LGRM [98] KNN,Wij ¼ exp kXi Xjk2 2t2 y ¼ argmin y T ðLleþmLgÞy yT y ARE [88] KNN,Wij ¼ exp r2ðXiXjÞ t ,WAREij ¼ g; Xi 2 Fþ&Xj 2 Fþ 1;LðXiÞ 6¼ LðXjÞ 0; otherwise 8< : a ¼ argmax a T XLA”
• Graph Embedding Techniques, Applications, and Performance: A Survey (2017, methodology): “[35] survey a list of such methods including Principal Component Analysis (PCA) [36], Linear Discrimant Analysis (LDA) [37], ISOMAP [38], Multidimesional Scaling (MDS) [39], Locality Preserving Properties (LPP) [40] and Kernel Eigenmaps [41].”
• SIFT-Bag kernel for video event analysis (2008, unknown): “Locality Preserving Projection [15].”
• Hyperspectral and LiDAR Data Fusion: Outcome of the 2013 GRSS Data Fusion Contest (2014, methodology): “Classification maps produced by using (a) the original hyperspectral data, (b) MPs of hyperspectral data, (c) MPs of LiDAR data, (d) the stacked features , (e) the features fused by LPP on , and (f) the proposed fused features. connected.”
• Local and Global Regressive Mapping for Manifold Learning with Out-of-Sample Extrapolation (2010, background): “As a compromise, Locality Preserving Projection (LPP) (He & Niyogi 2003) and Spectral Regression (SR) (Cai, He, & Han 2007) were proposed, which introduce linear projection matrix to LE.”
• Bregman Divergence-Based Regularization for Transfer Subspace Learning (2010, background): “To demonstrate the effectiveness of the proposed TSL in text categorization, we compare the proposed TSL examples, e.g., TFLDA, TLPP, TMFA, and TDLA, with conventional subspace learning algorithms, e.g., FLDA, LPP, MFA, DLA, and the SDA.”
• Smooth Representation Clustering (2014, methodology): “…term: where W = ( w ij ) is the weight matrix measuring the spatial closeness of points and L = D − W is the Laplacian matrix, in which D is the diagonal degree matrix with A common way to construct W is to use the k nearest neighbor ( k -nn) graph with a heat kernel or 0 - 1 weights [9].”
• Orthogonal Neighborhood Preserving Projections: A Projection-Based Dimensionality Reduction Technique (2007, methodology): “Projection-based techniques consist of replacing the original data X by a matrix of the form Y ¼ V >X; where V 2 Rm d: ð1Þ Thus, each vector xi is replaced by yi ¼ V >xi, a member of the d-dimensional space Rd.”
• Clustering and projected clustering with adaptive neighbors (2014, methodology): “We compare the PCAN method with two popular dimension reduction methods, Principal Component Analysis (PCA) [11] and Locality Preserving Projections(LPP) [8].”
• Matching on Balanced Nonlinear Representations for Treatment Effects Estimation (2017, methodology): “For PCA-NNM, LPP-NNM, RNNM and our method, we can choose the dimension of feature space where the matching is conducted.”
• Bearing performance degradation assessment using locality preserving projections (2011, methodology): “The details of LPP are described in algorithm (He & Niyogi, 2004).”
• Tensor Subspace Analysis (2005, methodology): “The typical linear subspace learning algorithms include Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), and Locality Preserving Projection (LPP).”
• CoType: Joint Extraction of Typed Entities and Relations with Knowledge Bases (2016, methodology): “e Znegative feature samples. In D L, each relation mention z i is heuristically associated with a set of candidate types R i. Existing embedding methods rely on either the local consistent assumption [19] (i.e., objects strongly connected tend to be similar) or the distributional assumption [30] (i.”
• Coupled Kernel Embedding for Low-Resolution Face Image Recognition (2012, methodology): “In order to make the projection of each LR image and the corresponding HR projected image with identical labels as close as possible in the new feature space, they further introduce a locality-preserving objective [22], [23] into the optimization criterion, and this presents a satisfactory performan”
• Enhancing Person Re-identification in a Self-Trained Subspace (2017, background): “Different with our approach, [48] is extended from linear discriminant analysis (LDA), while our approach seems more like a semi-supervised locality preserving projections (LPP) [51].”
• 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 ordinal discriminative features for age estimation (2012, background): “Manifold learning uncovers the nonlinear structure by integrating the descriptions of a set of local patches using the neighborhood graph [16].”