Abstract In this paper, we consider semi-supervised classi- fification on evolutionary data, where the distribution of the data and the underlying concept that we aim to learn change over time due to shortterm noises and long-term drifting, making a single aggregated classififier inapplicable for long-term classifification. The drift is smooth if we take a localized view over the time dimension, which enables us to impose temporal smoothness assumption for the learning algorithm. We fifirst discuss how to carry out such assumption using temporal regularizers defifined in a structural way with respect to the Hilbert space, and then derive the online algorithm that effificiently fifinds the closed-form solution to the classifification functions. Experimental results on real-world evolutionary mailing list data demonstrate that our algorithm outperforms classical semi-supervised learning algorithms in both algorithmic stability and classifification accuracy