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The focus of this paper is on joint feature re-extraction and classification in cases when the training data set is small. An iterative semi-supervised support vector machine (SVM) algorithm is proposed, where each iteration consists both feature re-extraction and classification, and the feature re-extraction is based on the classification results from the previous iteration. Feature extraction is first discussed in the framework of Rayleigh coefficient maximization. The effectiveness of common spatial pattern (CSP) feature, which is commonly used in Electroencephalogram (EEG) data analysis and EEG-based brain computer interfaces (BCIs), can be explained by Rayleigh coefficient maximization. Two other features are also defined using the Rayleigh coefficient. These features are effective for discriminating two classes with different means or different variances. If we extract features based on Rayleigh coefficient maximization, a large training data set with labels is required in general; otherwise, the extracted features are not reliable. Thus we present an iterative semi-supervised SVM algorithm embedded with feature re-extraction. This iterative algorithm can be used to extract these three features reliably and perform classification simultaneously in cases where the training data set is small. Each iteration is composed of two main steps: (i) the training data set is updated/augmented using unlabeled test data with their predicted labels; features are re-extracted based on the augmented training data set. (ii) The re-extracted features are classified by a standard SVM. Regarding parameter setting and model selection of our algorithm, we also propose a semi-supervised learning-based method using the Rayleigh coefficient, in which both training data and test data are used. This method is suitable when cross-validation model selection may not work for small training data set. Finally, the results of data analysis are presented to demonstrate the validity of our approach.