High dimensionality and highly correlated features are the major characteristics of hyperspectral data. Linear projections such as LDA and its variants have been used in extracting low-dimensional features from high-dimensional spectral data. Regularization of LDA has been introduced to alleviate the overfitting that often occurs in a small-sized training data set and leads to poor generalization performance. Among them, a smoothness regularized LDA seems to be effective in the feature extraction for hyperspectral data due to its capability of utilizing the high correlatedness. This paper studies the performance of the regularized LDA in hyperspectral data classification experimentally with varying conditions of the training data. In addition, a new dual smoothness regularized LDA is proposed and evaluated that makes use of both the spectral-domain and spatial-domain correlations between neighboring pixels.