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Visual exploratory data analysis represents a well-accepted imaging modality for high-dimensional DCE-MRI-derived breast cancer data. We employ this paradigm for discriminating between malignant and benign lesions based on different shape descriptors thanks to proven and novel dimension reduction algorithms. We demonstrate that shape structure changes such as weighted 3D Krawtchouck moments outperform global averaging moments such as geometric moment invariants in terms of discrimination of benign/malignant lesions. The best visualization of tumor shapes in a two-dimensional space is achieved based on nonlinear mapping methods, especially the ones that consider neighborhood ranks.