Diversified query expansion (DQE) based approaches aim to select a set of expansion terms with less redundancy among them while covering as many query aspects as possible. Recently they have experimentally demonstrate their effectiveness for the task of search result diversification. One challenge faced by existing DQE approaches is how to ensure the aspect coverage. In this paper, we propose a novel method for DQE, called compact aspect embedding, which exploits trace norm regularization to learn a low rank vector space for the query, with each eigenvector of the learnt vector space representing an aspect, and the absolute value of its corresponding eigenvalue representing the association strength of that aspect to the query. Meanwhile, each expansion term is mapped into the vector space as well. Based on this novel representation of the query aspects and expansion terms, we design a greedy selection strategy to choose a set of expansion terms to explicitly cover all possible aspects of the query.We test our method on several TREC diversification data sets, and show that our method significantly outperforms the state-of-the-art search result diversification approaches.