阿茲海默症 (Alzheimer's disease, AD) 是一種不可逆的神經退化性疾病，其典型表現為持續性的認知能力下降，且罹患人數逐年攀升。由於一旦發病後受損的認知功能無法治癒，因此若能在早期進行準確的 AD 預測，對於臨床上的預防與及時介入具有關鍵的重要性。然而，目前的 AD 預測方法受到統計假設的限制，例如群體獨立成分分析 (GICA) 依賴統計獨立性的假設，此外，這些方法往往仰賴龐大的資料集，而在生醫場景中這類資料往往難以取得且不一定都來自同個儀器所測量。這些限制導致相關方法在資料量有限的訓練情境及跨儀器異質性情境下表現不佳。
為了應對上述挑戰，我們提出了一個創新的 GQTAD 演算法，結合了凸幾何、深度學習與量子深度網路 (QUEEN)。本方法避免使用 GICA 的獨立性假設，改以凸幾何的盲源分離 (BSS) 從靜息態功能性磁振造影 (rs-fMRI) 中提取初步特徵，而無須依賴大量的訓練資料。這些初始特徵接著輸入至深度學習架構，我們設計了 P 條平行的權重共享 3D CNN 進行空間資訊的壓縮，並透過 Transformer 編碼器進一步精煉特徵。最後，時間資訊由時間活動曲線 (TAC) 表示，並由高度糾纏的 QUEEN 處理。最終，壓縮過的空間特徵與量子特徵被整合，已完成最終的分類。
我們在具權威性的 Alzheimer’s Disease Neuroimaging Initiative (ADNI) 資料集上進行訓練及測試，並模擬真實生醫研究中常見的情境，例如資料量受限與跨儀器的差異。根據實驗結果，GQTAD 達到了 90% 的整體正確率 (OA) 與 0.92 的召回率 (recall)，相較於既有方法展現出顯著提升，並顯示其在小樣本與跨儀器條件下的廣泛適用。

Alzheimer's disease (AD) is an irreversible neurodegenerative disorder marked by a gradual decline in cognitive function. The number of people who suffer from AD is increasing year by year. Since the impaired cognitive function cannot be cured once the disease occurs, early and accurate prediction of AD has become critically importance for clinical prevention and immediate intervention. However, existing AD prediction methods are often constrained by statistical assumptions, such as the independence assumption in group independent component analysis (GICA), and typically require large datasets, which are difficult to obtain in biomedical scenarios. These limitations lead to poor performance when training with small-sample and cross-scanner heterogeneity.
To overcome these challenges, we propose GQTAD algorithm, a novel architecture that combines convex geometry, deep learning, and quantum deep networks (QUEEN). The proposed method avoids the independence assumption of GICA and instead employs blind source separation (BSS) based on convex geometry to extract source-level features, called preliminary features, from resting-state functional magnetic resonance imaging (rs-fMRI) without requiring large scale training data. The extracted preliminary features are passed into a deep learning network. We design P parallel shared weight 3D CNN tracks to compress spatial information, followed by Transformer encoder that further refine features. Finally, the temporal information represented by time activity curve (TAC) are processed through highly entangled QUEEN. Ultimately, the compressed spatial features are fused with the quantum features to complete the final classification.
We conducted experiments on the authoritative Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset under realistic biomedical conditions, including limited training datas and cross-scanner settings. The results showed that GQTAD achieved OA of 90% and a recall of 0.92, achieves superior performance compared to existing methods and demonstrating its robustness and potential for clinical application in AD prediction.

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