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Extreme energy ratio (EER) is a recently proposed feature extractor to learn spatial filters for electroencephalogram (EEG) signal classification. It is theoretically equivalent and computationally superior to the common spatial patterns (CSP) method which is a widely used technique in brain-computer interfaces (BCIs). However, EER may seriously overfit on small training sets due to the presence of large noise. Moreover, it is a totally supervised method that cannot take advantage of unlabeled data. To overcome these limitations, we propose a regularization constraint utilizing local temporal information of unlabeled trails. It can encourage the temporal smoothness of source signals discovered, and thus alleviate their tendency to overfit. By combining this regularization trick with the EER method, we present a semi-supervised feature extractor termed semi-supervised extreme energy ratio (SEER). After solving two eigenvalue decomposition problems, SEER recovers latent source signals that not only have discriminative energy features but also preserve the local temporal structure of test trails. Compared to the features found by EER, the energy features of these source signals have a stronger generalization ability, as shown by the experimental results. As a nonlinear extension of SEER, we further present the kernel SEER and provide the derivation of its solutions.