CSP-HEIDI Visualising Closest Subspace Points in  \(R^d\) Clusters and Classes

High-dimensional datasets present a fundamental challenge: understanding how data points relate to each other across different feature combinations. Existing visualization methods typically show global structure through dimensionality reduction or highlight relationships in the full feature space, but they fail to reveal which specific feature subspaces drive point-to-point connections. We present CSP-HEIDI ( Source code ), a visualization framework that resolves this ambiguity by analyzing k-nearest neighbor (k-NN) relationships across the complete feature subspaces. Central to our approach is the Interpretable Expression Matrix (IEM), which replaces scalar distances with minimal Boolean expressions (minterms). By employing a logic minimization strategy, CSP-HEIDI isolates the “root cause” subspaces that are sufficient to maintain neighborhood connections, discarding redundant supersets. Through a novel Concentric Spiral Arrangement, these expressions are organized to reveal structural topology. We demonstrate on biological and synthetic datasets that CSP-HEIDI successfully disentangles intra-cluster cohesion from inter-cluster bridging. The visualization explicitly reveals how high-discriminability features act as “identity anchors” within clusters, while low-discriminability dimensions function as specific “semantic bridges” between them. This offers a qualitative, “white-box” alternative to projection methods, enabling researchers to diagnose the precise logic governing cluster cohesion and overlap.