Capacity Preserving Mapping for High-dimensional Data Visualization
This addresses a fundamental problem in data visualization for researchers and practitioners dealing with high-dimensional data, though it appears incremental as it builds on existing methods.
The paper tackles the crowding issue in high-dimensional data visualization by adjusting the capacity of high-dimensional balls to prepare for embedding, demonstrating effectiveness on synthetic and real datasets.
We provide a rigorous mathematical treatment to the crowding issue in data visualization when high dimensional data sets are projected down to low dimensions for visualization. By properly adjusting the capacity of high dimensional balls, our method makes right enough room to prepare for the embedding. A key component of the proposed method is an estimation of the correlation dimension at various scales which reflects the data density variation. The proposed adjustment to the capacity applies to any distance (Euclidean, geodesic, diffusion) and can potentially be used in many existing methods to mitigate the crowding during the dimension reduction. We demonstrate the effectiveness of the new method using synthetic and real datasets.