降维（子空间学习）的matlab代码程序 Matlab codes for dimensionality reduction (subspace learning)

Matlab codes for dimensionality reduction (subspace learning)

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If you find these algoirthms and data sets useful, we appreciate it very much if you can cite our related works:  ( Publications sort by topic )

• Deng Cai, Xiaofei He, Jiawei Han, and Hong-Jiang Zhang, "Orthogonal Laplacianfaces for Face Recognition", in IEEE TIP, 2006.
  Bibtex source
• Deng Cai, Xiaofei He, and Jiawei Han, "Document Clustering Using Locality Preserving Indexing", in IEEE TKDE, 2005. 
  Bibtex source
• Deng Cai, Xiaofei He and Jiawei Han, "Semi-Supervised Discriminant Analysis", ICCV'07. 
  Bibtex source
• Deng Cai, Xiaofei He, Yuxiao Hu, Jiawei Han and Thomas Huang, "Learning a Spatially Smooth Subspace for Face Recognition", CVPR'07. 
  Bibtex source
• Xiaofei He, Shuicheng Yan, Yuxiao Hu, Partha Niyogi, and Hong-Jiang Zhang, "Face Recognition Using Laplacianfaces", in IEEE TPAMI, 2005.
  Bibtex source
• Xiaofei He and Partha Niyogi, "Locality Preserving Projections", NIPS 16, 2003. 
  Bibtex source

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Algorithms

• Some general functions
  • EuDist2: Calculate the Euclidean distance matrix of two data matrix.
  • mySVD: An efficient SVD.
  • NormalizeFea: Normalize the data matrix.
  • constructW: Function used to construct the affinity matrix.
  • constructKernel: Function used to construct the kernel matrix.

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• PCA: Principal Component Analysis

• KPCA: Kernel Principal Component Analysis

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• LGE: (Regularized) Linear Graph Embedding (Provides a general framework for graph based subspace learning. This function will be called by LPP, NPE, IsoProjection, LSDA, MMP ...)

• OLGE: (Regularized) Orthogonal Linear Graph Embedding (Provides a general framework for graph based subspace learning (orthogonal basis vectors). This function will be called by OLPP. It is also very easy to develop ONPE, OIsoProjection, OLSDA, MMP...)

• TensorLGE: Tensor Linear Graph Embedding (Provides a general framework for graph based tensor subspace learning. This function will be called by TensorLPP. It is also very easy to develop TensorNPE, TensorIsoProjection, TensorLSDA, TensorMMP...)

• KGE: (Regularized) Kernel Graph Embedding (Provides a general framework for graph based kernel subspace learning. This function will be called by KernelLPP. It is also very easy to develop KernelNPE, KernelIsoProjection, KernelLSDA, KernelMMP...)
  • Deng Cai, Xiaofei He and Jiawei Han, "Spectral Regression for Efficient Regularized Subspace Learning", ICCV'07.
    Bibtex source
  • Deng Cai, Xiaofei He, Yuxiao Hu, Jiawei Han and Thomas Huang, "Learning a Spatially Smooth Subspace for Face Recognition", CVPR'07.
    Bibtex source

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• LDA: (Regularized) Linear Discriminant Analysis (Generally, LDA can also use LGE as a subroutine. However, we can use the special graph structure of LDA to obtain some computational benefits.)

• KDA: (Regularized) Kernel Discriminant Analysis (Generally, KDA can also use KGE as a subroutine. However, we can use the special graph structure of KDA to obtain some computational benefits.)
  • Deng Cai, Xiaofei He and Jiawei Han, "SRDA: An Efficient Algorithm for Large-Scale Discriminant Analysis", IEEE TKDE 2008. 
    Bibtex source
  • Deng Cai, Xiaofei He, Jiawei Han, "Speed Up Kernel Discriminant Analysis", The VLDB Journal, 2011. 
    Bibtex source

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• LPP: Locality Preserving Projection (You need to download LGE.m as well as constructW.m).

• OLPP: Orthogonal Locality Preserving Projections (You need to download OLGE.m as well as constructW.m)

• TensorLPP: Tensor Locality Preserving Projections (You need to download TensorLGE.m as well as constructW.m)

• KernelLPP: Kernel Locality Preserving Projections (You need to download KGE.m as well as constructW.m)
  • Deng Cai, Xiaofei He, Jiawei Han, and Hong-Jiang Zhang, "Orthogonal Laplacianfaces for Face Recognition", in IEEE TIP, 2006. 
    Bibtex source
  • Xiaofei He, Deng Cai, and Partha Niyogi, "Tensor Subspace Analysis", NIPS 2005. 
    Bibtex source
  • Xiaofei He, Shuicheng Yan, Yuxiao Hu, Partha Niyogi, and Hong-Jiang Zhang, "Face Recognition Using Laplacianfaces", in IEEE TPAMI, 2005. 
    Bibtex source
  • Xiaofei He and Partha Niyogi, "Locality Preserving Projections", NIPS 16, 2003. 
    Bibtex source

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• NPE: Neighborhood Preserving Embedding (You need to download LGE.m)
  • Xiaofei He, Deng Cai, Shuicheng Yan and Hong-Jiang Zhang, "Neighborhood Preserving Embedding," ICCV 2005. 
    Bibtex source

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• IsoProjection: Isometric Projection (You need to download LGE.m)

  dijkstra.mexw32 (for 32bit Windows) 
  dijkstra.mexw64 (for 64bit Windows) 
  dijkstra.mexglx (for Linux): dijkstra algorithm (You can download the source code at here)

  • Deng Cai, Xiaofei He, and Jiawei Han, "Isometric Projection," AAAI 2007. 
    Bibtex source

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• LSDA: Locality Sensitive Discriminant Analysis (You need to download LGE.m)
  • Deng Cai, Xiaofei He, Kun Zhou, Jiawei Han and Hujun Bao, "Locality Sensitive Discriminant Analysis," IJCAI'07.
    Bibtex source

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• SDA: Semi-Supervised Discriminant Analysis
  • Deng Cai, Xiaofei He and Jiawei Han, "Semi-Supervised Discriminant Analysis", ICCV'07. 
    Bibtex source

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• MMP: Maximum Margin Projection
  • Xiaofei He, Deng Cai, Jiawei Han, "Learning a Maximum Margin Subspace for Image Retrieval," TKDE 2008
    Bibtex source

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• GenSpatialSmoothRegularizer: Generate the spatially smooth regularizer 
  
  • Deng Cai, Xiaofei He, Yuxiao Hu, Jiawei Han and Thomas Huang, "Learning a Spatially Smooth Subspace for Face Recognition", CVPR'07. 
    Bibtex source

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