The transition of search engine users' intents has been studied for a long time. The knowledge of intent transition, once discovered, can yield a better understanding of how di®erent topics are related and be used in many applications, such as building recommender systems, ranking and etc. In this paper, we study the problem of finding the transition probabilities of digital library users' intents among different topics. We use the click-through data from CiteSeerX and extract the click chains. Each document in the click chain is represented by a topical vector generated by LDA models. We then model the task of finding the topical transition probabilities as a multiple output linear regression problem, in which the input and output are two consecutive topical vectors in the click chain and the elements in the weight matrix correspond to the transition probabilities. Given the constraints of our task, we propose a new algorithm based on the exponentiated gradient. Our algorithm provides a good interpretability as well as a small sum-of-squares error comparable to existing regression methods. We are particular interested in the off-diagonal elements of the learned weight matrix since they represent the transition probabilities of different topics. The authors' interpretation of these transitions are given at the end of the paper.