Structure-Preserving Nonlinear Sufficient Dimension Reduction

This repository contains the implementation of the paper Structure-Preserving Nonlinear Sufficient Dimension Reduction for Tensor Regression. The paper introduces novel nonlinear sufficient dimension reduction (SDR) methods specifically designed for tensor regression and classification problems. It employs a Tensor Product Space framework within multiple Reproducing Kernel Hilbert Spaces (RKHS) and proposes Tucker and CANDECOMP/PARAFAC (CP) Tensor Envelope frameworks.

Features

• Implements Nonlinear Dimension Folding (NDF) using kernel-based sufficient dimension reduction.
• Establishes a relationship between the Conventional SDR Subspace and the Tensor Envelope Subspace.
• Develops two optimization algorithms leveraging Tucker and CP Tensor Decomposition.
• Implements both population-level and sample-level estimations using a Coordinate Mapping approach.
• Provides comparison with other dimension reduction techniques such as PCA, UMAP, t-SNE, LDA, SIR, and GSIR.
• Evaluates the performance through simulations and real-world EEG & CSIQ data analysis.

Dependencies

The following R packages are required:

• matrixcalc
• MASS
• class
• umap
• Rtsne
• Rcpp
• kernlab
• expm
• doParallel
• foreach

Installation

1. Clone the repository:

   git clone https://github.com/DJLin0219/NonlinearTensorSDR.git
   cd NonlinearTensorSDR

2. Install required R packages:

   install.packages(c("matrixcalc", "MASS", "class", "umap", "Rtsne", "Rcpp", "kernlab", "expm", "doParallel", "foreach"))

3. Compile the C++ source files:

   file_path <- "/path/to/repository"
   sourceCpp(paste(file_path, "NDF.cpp", sep="/"))

Results

• Simulation Studies: Demonstrate the effectiveness of our methods in estimating the true subspace structure and outperforming existing approaches.
• EEG Data Analysis: Shows the improved classification accuracy of our method in distinguishing alcoholic vs. non-alcoholic subjects.
• CSIQ Data Analysis: Provides better Pearson correlation values compared to GSIR when assessing image quality distortions.

Citation

If you use this code in your research, please cite (The paper will be posted to arxiv soon).

Contact

For any questions or issues, please open an issue in this repository or contact [email protected].

License

This project is licensed under the MIT License.