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This paper concerns clustering-by-directions algorithm. The algorithm introduces a novel approach to interactive query expansion. It is designed to support users of search engines in forming Web search queries. When a user executes a query, the algorithm shows potential directions in which the search can be continued. This paper describes the algorithm, and it presents an enhancement which reduces the computational complexity of the algorithm. Moreover, in this paper, a new type of interface is introduced. It is based on a tag cloud, in which terms are located in a radial arrangement. This paper also presents the new experimental results and the evaluation of the algorithm.