本篇論文以黎曼幾何空間為基礎，提出了一種解決腦波數據非平穩性
的方法，提高跨時段(Cross-sessions)及跨受試者(Cross-subjects)在想像運動
上的分類性能。腦波訊號普遍存在著不平穩(Non-stationary)的特性，即其數
據分布隨著時間變化，而這個特性使得腦波在想像運動的分類上受到限制。
在想像運動腦波錄製過程中，由於受測者不同或受測者錄製腦波的時間、環
境不同，導致腦電訊號之間存在巨大差異，造成想像運動分類準確率不佳。
在傳統腦機介面中，雖然此情況可透過大量收集受測者的腦波資料以進行
校準，然而這將導致系統必須花費過長的校準時間以保持原有的分類準確
率。而腦機介面領域中的遷移學習方法，將可以藉由源域的資料應用於目標
域的資料中，因此，可以減少大量錄製腦波資料所需要的時間。本篇主要研
究內容如下：本論文提出CSP-RPA 方法，以黎曼幾何空間之切線空間作為
基礎，結合共同空間型樣法(Common Spatial Pattern, CSP)將不同類別之資料
事先盡可能區分開後以改良現有黎曼普氏分析架構，並且利用基於樹的特
徵選擇(Tree-based Feature Selection)方式，以減少對於少量腦波數據的特徵
維度過高所造成的過擬合(Over-fitting)情況，進而提升腦電訊號想像運動分
類的效果，最後透過BCI 競賽所提供的腦電訊號數據集驗證其演算法之有
效性，並利用t-SNE 視覺化以證明其特徵領域自適應之效果。

This thesis presents a transfer learning method based on Riemannian
geometry for improving the classification accuracy of Electroencephalographic
(EEG) signals. Non-stationarities are ubiquitous in EEG signals, which means the
statistical characteristics of EEG signals alter from time to time. The nonstationarities
of the EEG signals may be caused by different environmental factors
(e.g. user’s fatigue level, the mental and physical state of user, the location of
electrodes placement, etc.). Typically, classic Motor Imagery-based Brain-
Computer Interface (MI-based BCI) requires a calibration session in each run,
even for recorded subjects. During the calibration session, the subjects requested
to perform various Motor Imagery (MI) tasks repeatedly, which will be timeconsuming
and make user feel exhausted. As a consequence, we proposed a
transfer learning method, namely Common Spatial Pattern Riemannian Procrustes
Analysis (CSP-RPA), to shorten the calibration time while keeping MI-based BCI
work optimally. CSP-RPA is based on the tangent space of Riemannian geometric
spaces and combines the Common Spatial Pattern (CSP) method to modify the
Riemannian Procrustes Analysis (RPA) architecture. To alleviate the overfitting
in high-dimensional Riemannian manifold, the tree-based feature selection is
adopted to reduce the dimensionality after mapping data from Riemannian
manifold to tangent space. The framework was validated by the publicly available
EEG dataset 2a of the BCI competition IV. In addition, we used t-SNE (t-
Distributed Stochastic Neighbor Embedding) to visualize and prove the
effectiveness of feature domain adaptation after CSP-RPA algorithm. To sum up,
the experimental results indicate that CSP-RPA is superior to other methods, e.g.,
Re-center, Parallel Transport, RPA, under cross-sessions and cross-subjects
conditions.

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