In many applications, it is very expensive or time consuming to obtain a lot of labeled examples. One practically important problem is: can the labeled data from other related sources help predict the target task, even if they have 1) different feature spaces (e.g., image versus text data), 2) different data distributions, and 3) different output spaces? This paper proposes a solution and discusses the conditions where this is highly likely to produce better results. It first unifies the feature spaces of the target and source data sets by spectral embedding, even when they are with completely different feature spaces. The principle is to devise an optimization objective that preserves the original structure of the data, while at the same time, maximizes the similarity between the two. A linear projection model, as well as a nonlinear approach are derived on the basis of this principle with closed forms. Second, a judicious sample selection strategy is applied to select only those related source examples. At last, a Bayesian-based approach is applied to model the relationship between different output spaces. The three steps can bridge related heterogeneous sources in order to learn the target task. Among the 20 experiment data sets, for example, the images with wavelet-transformed-based features are used to predict another set of images whose features are constructed from color-histogram space; documents are used to help image classification, etc. By using these extracted examples from heterogeneous sources, the models can reduce the error rate by as much as 50 percent, compared with the methods using only the examples from the target task. © 2012 IEEE.