Analyzing high-dimensional point clouds is a classical challenge in visual analytics. Traditional techniques, such as projections or axis-based techniques, suffer from projection artifacts, occlusion, and visual complexity. We propose to split data analysis into two parts to address these shortcomings. First, a structural overview phase abstracts data by its density distribution. This phase performs topological analysis to support accurate and nonoverlapping presentation of the high-dimensional cluster structure as a topological landscape profile. Utilizing a landscape metaphor, it presents clusters and their nesting as hills whose height, width, and shape reflect cluster coherence, size, and stability, respectively. A second local analysis phase utilizes this global structural knowledge to select individual clusters or point sets for further, localized data analysis. Focusing on structural entities significantly reduces visual clutter in established geometric visualizations and permits a clearer, more thorough data analysis. This analysis complements the global topological perspective and enables the user to study subspaces or geometric properties, such as shape.