Probabilistic Kernel Function for Fast Angle Testing

The paper introduces two projection-based probabilistic kernel functions for angle comparison and thresholding in high-dimensional Euclidean spaces, with application to Approximate Nearest Neighbor Search. It resides in the 'Probabilistic and Kernel-Based Angle Testing' leaf, which contains only two papers total (including this one). This leaf sits within the broader 'Angle-Based Similarity and Distance Computation' branch, indicating a relatively sparse research direction focused specifically on kernel-driven angle testing methods. The small sibling count suggests this is a specialized niche rather than a crowded subfield.

The taxonomy reveals neighboring leaves addressing related but distinct problems: 'Euclidean Distance Approximation via Angular Information' (two papers) focuses on distance estimation rather than direct angle testing, while 'Vector Similarity Search and Nearest Neighbor Retrieval' (one paper) emphasizes search algorithms without the probabilistic kernel framework. The parent branch 'Angle-Based Similarity and Distance Computation' contains four leaves total, suggesting moderate activity in angular similarity methods broadly, but the specific intersection of probabilistic kernels and angle testing remains underdeveloped. The scope note explicitly excludes general distance approximation, clarifying that this work targets angle-specific kernel functions.

Among sixteen candidates examined across three contributions, no clearly refuting prior work was identified. The first contribution (two projection-based kernel functions) examined two candidates with no refutations; the second (deterministic relationship without asymptotic conditions) examined four candidates with no refutations; the third (two configuration structures for projection vectors) examined ten candidates with no refutations. This limited search scope—sixteen papers total, not hundreds—suggests the analysis captures the most semantically proximate work but cannot claim exhaustive coverage. The absence of refutations within this sample indicates the specific combination of deterministic projection structures and non-asymptotic guarantees may be novel.

Given the sparse taxonomy leaf (one sibling paper) and the limited literature search (sixteen candidates), the work appears to occupy a relatively unexplored intersection of probabilistic angle testing and deterministic projection design. The analysis does not extend to exhaustive citation networks or broader kernel method literature, so the novelty assessment reflects top-K semantic proximity rather than comprehensive field coverage. The application to ANNS and reported performance gains suggest practical differentiation, though the theoretical positioning within kernel methods warrants deeper investigation beyond the examined sample.