Large numbers of dimensions not only cause clutter in multi-dimensional visualizations, but also make it difficult for users to navigate the data space. Effective dimension management, such as dimension ordering, spacing and filtering, is critical for visual exploration of such datasets. Dimension ordering and spacing explicitly reveal dimension relationships in arrangement-sensitive multi-dimensional visualization techniques, such as Parallel Coordinates, Star Glyphs, and Pixel-Oriented techniques. They facilitate the visual discovery of patterns within the data. Dimension filtering hides some of the dimensions to reduce clutter while preserving the major information of the dataset. In this paper, we propose an interactive hierarchical dimension ordering, spacing and filtering approach, called DOSFA. DOSFA is based on dimension hierarchies derived from similarities among dimensions. It is a scalable multi-resolution approach making dimensional management a tractable task. On the one hand, it automatically generates default settings for dimension ordering, spacing and filtering. On the other hand, it allows users to efficiently control all aspects of this dimension management process via visual interaction tools for dimension hierarchy manipulation. A case study visualizing a dataset containing over 200 dimensions reveals how our proposed approach greatly improves the effectiveness of high dimensional visualization techniques.