The main idea is to use unlabeled data in both domains to learn linear predictors for many "auxiliary" tasks, which should be somewhat related to the task of interest.
if x is a row vector representing the original feature vector and y i represents the label for auxiliary task i, the linear predictor w i is learned to predictŷ i = w i • x ′ (where x ′ is a modified version of x that excludes any features completely predictive of y i .)