Multi-scale two-directional two-dimensional principal component analysis and its application to high-dimensional biomedical signal classification Goal: Time-frequency analysis incorporating the wavelet transform followed by principal component analysis (WT-PCA) has been a powerful approach for the analysis of biomedical signals such as electromyography (EMG), electroencephalography (EEG), electrocardiography (ECG), and Doppler ultrasound. Time-frequency coefficients at various scales were usually transformed into a one-dimensional array using only a single or a few signal channels. The steady improvement of biomedicalrecording techniques has increasingly permitted the registration of a high number of channels. However, WT-PCA is not applicable to high-dimensional recordings due to the curse of dimensionality and small sample size problem. In this study, we present a multi-scale two-directional two-dimensional principal component analysis (MS2D2PCA) method for the efficient and effective extraction of essential feature information from high-dimensional signals. Multi-scale matrices constructed in the first step incorporate the spatial correlation and physiological characteristics of sub-band signals among channels. In the second step, the two-directional two-dimensional principal component analysis operates on the multi-scale matrices to reduce the dimension, rather than vectors in conventional PCA. Results are presented from an experiment to classify 20 hand movements using 89-channel EMG signals recorded in stroke survivors, which illustrates the efficiency and effectiveness of the proposed method for high-dimensional biomedical signal analysis.