在 Hi-C 皮爾森相關矩陣中識別 A 和 B 染色體區室的標準作法是基於主成份分析，然而其運作原理卻鮮少被討論。對於 Hi-C 皮爾森相關矩陣，我們提出其第一主成份的變異解釋率通常很高，並且該解釋率反應了 PC1 與皮爾森相關矩陣上之區室的匹配程度。此外，我們提出了一種啟發式算法，透過 Hi-C 皮爾森相關矩陣的共變異矩陣估計出第一主成份的型態，而不需要直接進行主成份分析。我們的啟發式算法可以使用隨機抽樣有效的實現以加快計算速度，為了解決高解析度下的記憶體瓶頸，我們使用一種最近發表的區室識別工具 POSSUMM 改進了算法，它接受稀疏的 Hi-C O/E 矩陣作為輸入。在我們的實驗中，我們的算法在時間或是記憶體使用上，其基準測試的表現優於使用 Scikit-learn 和 POSSUMM 等軟體工具的幂迭代法（Power iteration），同時與作為基準答案的第一主成份有高相似度。程式碼公開於下列網址 https://github.com/ZhiRongDev/HiCPEP。

The PCA-based method is the standard for identifying A and B compartments in the Hi-C Pearson matrix. However, the reason why it works is rarely discussed. For the Hi-C Pearson matrix, we propose that the explained variance ratio of PC1 is usually high, and the ratio will reflect how the PC1 matches the compartments on the Pearson matrix. Besides, we propose a heuristic algorithm to estimate the pattern of PC1 according to the Hi-C Pearson's covariance matrix without explicitly performing PCA. Our method can be implemented efficiently using random sampling techniques to accelerate calculations. To address the memory bottleneck at finer matrix resolutions, we adapt the algorithm using principles from POSSUMM, a recently published compartment identification tool that takes the sparse Hi-C O/E matrix as input. In our experiments, our algorithm outperforms Power iteration methods, such as those implemented in Scikit-learn and POSSUMM, in terms of the time or memory usage, while maintaining a high degree of similarity to the ground truth PC1. The code is freely available at
https://github.com/ZhiRongDev/HiCPEP.

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