對比主成分分析（cPCA）是在某些特定情境下有用的降維技術，該情境下資料集在不同條件下收集，例如治療與對照實驗，特別用於視覺化和探索僅屬於一個資料集的模式。在本研究中，我們提出了一種新的方法來處理高維度、低樣本數（HDLSS）資料情境下的cPCA。這種方法稱為cPCA-NR，它借鑑了Yata和Aoshima（2012）提出的降噪（NR）方法，以減輕噪音資料點的不良影響，提高降維過程的穩健性和可靠性。在模擬研究中，我們證明了cPCA-NR在分類準確度和聚類性能方面優於傳統PCA。此外，該方法對噪音資料表現出強大的韌性，在高噪音水準的情境下達到了顯著的改進。這些結果突顯了cPCA-NR的優越性能，確定其作為各種應用的寶貴工具，例如圖像識別、異常檢測和資料視覺化。;Contrastive Principal Component Analysis (cPCA) is a useful dimensionality reduction technique under some specific scenarios in which datasets are collected under different conditions, e.g., a treatment and a control experiment, especially in visualizing and exploring patterns that are specific to one dataset. In this study, we propose a new methodology to deal with cPCA in high-dimension, low-sample-size (HDLSS) data situations. The proposed method, called cPCA-NR, gives an idea of applying the noise-reduction (NR) method proposed by Yata and Aoshima (2012) to mitigates the adverse effects of noisy data points, improving the robustness and reliability of the dimensionality reduction process. In simulation study, we demonstrate that the cPCA-NR outperforms traditional PCA in terms of classification accuracy and clustering performance. Moreover, the proposed method exhibits strong resilience to noisy data, achieving notable improvements in scenarios with high levels of noise. The results highlight the superior performance of cPCA-NR, establishing its potential as a valuable tool for various applications, such as image recognition, anomaly detection, and data visualization.
