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In many applications, domain-specific entities are easily compared and categorized if they are represented as high-dimensional feature vectors. To detect object similarities and to quantify coherent groups, analysts often visualize the vectors directly, aiming to identify clusters visually. However, common visualizations for high-dimensional data often suffer from information loss, occlusions and visual clutter for large and noisy data. In this case, structure is misleading and false insights are derived. We use topological concepts to provide a structural view of the points. We analyze them in their original space and depict their clustering structure using intuitive landscapes. We describe the visual analysis process to define and simplify the structural view and to perform local analysis by linking individual features to other visualizations.