חיפוש בערכים וקטוריים: חיפוש תמונתי עם פרויקציות על מרחבי q-מטריקה

תקציר מקורי באנגליתarXiv:2506.06557v3 Announce Type: replace-cross Abstract: An ultrametric space or infinity-metric space is defined by a dissimilarity function that satisfies a strong triangle inequality in which every side of a triangle is not larger than the larger of the other two. We show that search in ultrametric spaces with a vantage point tree has worst-case complexity equal to the depth of the tree. Since datasets of interest are not ultrametric in general, we employ a projection operator that transforms an arbitrary dissimilarity function into an ultrametric space while preserving nearest neighbors. We further learn an approximation of this projection operator to efficiently compute ultrametric distances between query points and points in the dataset. We proceed to solve a more general problem in