本文在分析現有的降維技術，特別是主成分分析（PCA）、對比主成分分析 （CPCA）和(2D)²PCA的基礎上，提出了一種結合對比分析的雙向二維主成分分析（Contrastive (2D)²PCA）方法。該方法旨在通過引入對比機制，有效抑制背景雜訊和非目標變異，突出目標資料的判別特徵。在理論層面，本文闡述了該方法的構想，即在保持資料矩陣結構的同時，利用背景資料集來引導特徵提取，從而提升降維效果和辨識能力。此外，針對對比參數的選擇問題，文章討論了相關策略與挑戰，並提出了初步的算法設計框架。整體來說，該方法為在背景雜訊較多的應用場景中進行有效特徵提取提供了一個新的思路。在模擬研究中，對比（2D）²PCA在資料的變異性捕捉、資料重建與分類性能與運算時間方面均優於傳統PCA與其他相關方法，展現出其在影像分析、模式識別等領域的潛力與價值。;Building upon ananalysis of existing dimensionality reduction techniques, including PCA, contrastive PCA (CPCA), and (2D)²PCA, this paper proposes a novel contrastive bi-directional 2D PCA (Contrastive (2D)²PCA) approach. The method aims to incorporate a contrastive mechanism to effectively suppress background noise and non-target variations, thereby emphasizing discriminative features of the target data. Theoretically, the approach involves leveraging background datasets to guide feature extraction while preserving the matrix structure of data, ultimately enhancing dimensionality reduction and recognition performance. The paper also discusses strategies and challenges related to selecting contrastive parameters, along with an initial algorithmic framework. Over all, this method offers a new perspective for efficient feature extraction in scenarios with significant background interference. In simulation study, Contrastive (2D)² PCA out performs conventional PCA and related techniques in capturing data variance, reconstruction accuracy, and classification performance. The results highlight its potential applications in medical imaging, pattern recognition, and related fields.
