Subspace indexing on Stiefel and Grassmann manifolds

a paper by Wenqing Hu, Tiefeng Jiang, Birendra Kathariya, Vikram Abrol, Jiali Zhang and Zhu Li

published at IEEE BigData 2023 conference

(a) folder "matlab_code"

(a-1) Stiefel_Optimization.m

the object class for optimization calculus and differential geometry on Stiefel manifolds, such as tangent projection, exponential map, geodesics, gradient descent, retraction, lifting, logarithmic map, etc.

(a-2) Grassmann_Optimization.m

the object class for optimization calculus and differential geometry on Grassmann manifolds, such as tangent projection, exponential map, geodesics, gradient descent, retraction, lifting, logarithmic map, etc.

(a-3) buildVisualWordList.m

partition a given sample data set according to a tree of given height into leaf nodes

(a-4) SIFT_PCA.m

do the SIFT (Scale Invariant Feature Transform) PCA analysis

(a-5) SIFT_PCA_Recovery.m

do the SIFT PCA recovery using the Stiefel_Optimization method, compare with benchmark nearest neighbor method

(a-6) LPP_CenterMass.m

classfication analysis based on Laplacian eigenface and graph Laplacian method, as well as center of mass on Grassmann manifold. Applied to several different datasets: nwpu-aerial-images, MNIST, cifar10

(b) folder "python_code"

(b-1) Stiefel_Optimization.py

file with same name and function as matlab_code

(b-2) Grassmann_Optimization.py

file with same name and function as matlab_code

(b-3) buildVisualWordList.py

file with same name and function as matlab_code

(b-4) LPP_CenterMass.py

classfication analysis based on Laplacian eigenface and graph Laplacian method, as well as center of mass on Grassmann manifold. Applied to several different datasets: MNIST, cifar10; incorporates GMM sampling of pseudo-data inputs and labeling by pre-trained model

(b-5) LPP_Auxiliary.py

Functions to perform the Laplacian eigenface and graph Laplacian method. Include: k-nearest neighbor, graph laplacian, supervised affinity, LPP generalized eigenvalue problem

(b-6) cifar10vgg.py

build a pre-trained vgg model for cifar10, can also train a new cifar10. Pre-trained model paramter data available at https://github.com/geifmany/cifar-vgg

(b-7) umap_data_aug.py

generate new pseudo data points based on current data set using the UMAP and 2-simplices

(b-8) MNISTLeNetv2.py

build a pre-trained LeNetv2 model for MNIST.

(b-9) vox1VggFace.py

buile a pre-trained vgg model for the face data set