Simulations data for symmetry-3748042

1. Research Context This dataset contains MATLAB scripts that regenerate all visual results in the manuscript *"A K-means Clustering Algorithm with Total Bregman Divergence for Point Cloud Denoising"*. The codes implement novel geometric metrics (TLD, TED, TID) for robust 3D point cloud denoising, outperforming traditional Euclidean-based methods.  2. Data Generation Methodology All results were produced through controlled numerical simulations: - Fig.1 (Isosurfaces): Generated by `fig1.m` using isosurface function. - Fig.2 (Point Cloud Denoising): Created by processing MATLAB's built-in `teapotGeometry` dataset with SNR=4137:1000 using Algorithm 1. - Fig.3-4 (Loss Functions): Computed through 100 Monte Carlo trials on randomly generated SPD matrices (Eq.85). - Table 1 (Performance Metrics): Derived by running denoising experiments at three SNR levels (10/2/1) in:  - `Table1_Euclid.m` (Euclidean baseline)  - `Table1_TLD.m` (Total Logarithm Divergence)  - `Table1_TED.m` (Total Exponential Divergence)  - `Table1_TID.m` (Total Inverse Divergence)  3. File Contents & Naming Conventions  `fig1.m`: Generates 3D isosurfaces for Euclidean/TLD/TED/TID metrics                 `fig2.m`: Implements teapot denoising visualization (Algorithm 1)                    `fig3.m`: Compares loss functions of Euclidean/TLD/TED/TID means                     `fig4.m`: Validates TLD superiority over Log-Euclidean Metric                       | `Table1_Euclid.m`:Computes TPR/FPR/SNRG for Euclidean metric at SNR=10/2/1                  `Table1_TLD.m`: Computes TPR/FPR/SNRG for TLD at SNR=10/2/1 `Table1_TED.m`: Computes TPR/FPR/SNRG for TED at SNR=10/2/1 `Table1_TID.m`: Computes TPR/FPR/SNRG for TID at SNR=10/2/1   4. Key Parameters & Output Metrics SNR Configuration (critical for Table 1): % In Table1_*.m files:num_data = 4148;    % Signal points (fixed) num_noise = 415;    % SNR=10 (num_noise = num_data/10) num_noise = 2074;   % SNR=2 (num_noise = num_data/2) num_noise = 4148;   % SNR=1 (num_noise = num_data)``` Output Metrics Definition: TPR=TP / (TP + FN): True Positive Rate | FPR= FP / (FP + TN): False Positive Rate | SNRG = (TP/FP)×(TN/FN) - 1 : Signal-to-Noise Ratio Growth |  5. Data Value & Reusability Reproducibility: Executing scripts in order regenerates all manuscript figures/table exactly Benchmarking: Enables direct performance comparison of new denoising algorithms against TBD metrics Parameter Studies: Easily modify:  - `dist_num` (neighborhood size in Algorithm 1)  - `dim` (SPD matrix dimension in Table1_*.m)  - Noise models (currently Gaussian) - Educational Utility: Demonstrates practical implementation of:  - Total Bregman Divergences on matrix manifolds  - Influence function analysis (Section 4.2)  - Anisotropy indices (Section 4.1)   6. Recommended Workflow 1. Run `fig1.m → fig2.m → fig3.m → fig4.m` for visual results 2. For Table 1:   ```matlab  % In each Table1_*.m file:  num_noise = 415;  % Set SNR=10  % Run and record TPR/FPR/SNRG  num_noise = 2074; % Set SNR=2  % Run and record...  num_noise = 4148; % Set SNR=1  ``` 3. Compare outputs across scripts to replicate Table 1  7. Technical Specifications - Software: MATLAB R2023a (min R2021b) - Toolboxes Required: Statistics and Machine Learning, Computer Vision - Dataset Dependency: `teapot.ply` from MATLAB's `teapotGeometry` ---  Key Improvements Over Initial Submission1. Explicit SNR Control: Documented exact parameter locations for SNR configuration 2. Metric Formulae: Provided mathematical definitions of TPR/FPR/SNRG 3. Reproducibility Pathway: Clear step-by-step execution sequence 4. Extension Guidance: Highlighted modifiable parameters for new studies 5. Technical Context: Added computation requirements and dependencies