Noise Reduced Common PCA for High-Dimensional, Low-Sample Size Multi-View Data

High-Dimensional Low-Sample Size (HDLSS) data pose significant challenges in fields like medicine and neuroscience. Traditional principal component analysis (PCA) often fails under these conditions, leading to unstable eigenvalue estimation. This study introduces Noise Reduced-Common Principal Component Analysis (NR-CPCA), a method that combines Common Principal Component Analysis (CPCA) with a noise reduction technique to enhance eigenvalue stability and reliability in HDLSS data. By comparing eigenvalue estimations from NR-CPCA and traditional CPCA across various dimensions (1000, 2000, 3000) and sample sizes (10 to 120), we demonstrate that NR-CPCA mitigates noise effects more effectively, ensuring stable principal component selection. Simulation results confirm that NR-CPCA reduces variability in eigenvalue estimation, making it a valuable tool for dimensionality reduction in multi-view data. Despite limitations in simulation-based validation, NR-CPCA shows promise for real-world applications in data-intensive fields. Future research should focus on refining this method and applying it to diverse datasets to fully realize its potential. NR-CPCA provides an important advancement for researchers dealing with HDLSS data, promoting more accurate analysis and contributing to progress in data science, biology, and neuroscience.