1：Experimental Design and Method Selection:

The proposed kNCN-SRC method involves two stages: first, selecting k nearest neighbors using nearest centroid neighbor (NCN) classification based on Euclidean distance and spatial distribution; second, classifying the test sample using sparse representation classification (SRC) with the selected neighbors. L1 norm optimization (Basis Pursuit method) is used for sparse representation.

2：Sample Selection and Data Sources:

Four public finger vein databases are used: FV-USM, SDUMLA-HMT, HKPU, and THU-FVDT2. Images are normalized to unit L2 norm, resized (e.g., to 30x10 or 20x10 pixels), and split into training and test sets as per database specifications.

3：Images are normalized to unit L2 norm, resized (e.g., to 30x10 or 20x10 pixels), and split into training and test sets as per database specifications. List of Experimental Equipment and Materials:

3. List of Experimental Equipment and Materials: A computer with a 2.6 GHz CPU and 4.0 GB RAM, running MATLAB 2015a software. No specific hardware for image capture is detailed, as databases provide pre-captured images.

4：6 GHz CPU and 0 GB RAM, running MATLAB 2015a software. No specific hardware for image capture is detailed, as databases provide pre-captured images. Experimental Procedures and Operational Workflow:

4. Experimental Procedures and Operational Workflow: For each test sample, compute distances to training samples, select k nearest centroid neighbors, perform SRC on the reduced set, compute residuals, and classify based on minimum residual. Parameters like k are varied for optimization.

5：Data Analysis Methods:

Recognition accuracy and Kappa Coefficient (kc) are calculated. Sparsity Concentration Index (SCI) is used to evaluate sparsity. Processing time per image is measured.