Manifold based fisher method for semi-supervised feature selection

Fisher criterion is one of most widely used methods for supervised feature selection. Traditional Fisher based feature selection methods focus on maximizing the distances inter-class and minimizing the distances of samples within the same class. But, they ignore the geometric structure of data in measuring the importance of the features. In this paper, we propose a new semi-supervised feature selection algorithm based on the Fisher criterion and manifold assumption. It redefines the inter-classes scatter matrix by maximizing the margins between different classes. The new inter-class scatter matrix is more robust to data with complex distribution. Also, the proposed algorithm includes a new term which keeps locally reconstruction coefficients of data. We show that the capability of the evaluated feature in keeping the reconstruction coefficients is vital in measuring the importance of this feature, especially in semi-supervised cases. Experiments on benchmark data are conducted to show effectiveness of the proposed method.