Learning Reduced Order Dynamics via Geometric Representations
Imran Nasim, Melanie Weber
SCML 2024
Any notion of "closeness" in pattern matching should have the property that if A is close to B, and B is close to C, then A is close to C. Traditionally, this property is attained because of the triangle inequality (d(A, C) ≤ d(A, B) + d(B, C), where d represents a notion of distance). However, the full power of the triangle inequality is not needed for this property to hold. Instead, a "relaxed triangle inequality" suffices, of the form d(A, C) < c(d(A, B) + d(B, C)), where c is a constant that is not too large. In this paper, we show that one of the measures used for distances between shapes in (an experimental version of) IBM's QBIC1 ("Query by Image Content") system (Niblack et al., 1993) satisfies a relaxed triangle inequality, although it does not satisfy the triangle inequality.
Imran Nasim, Melanie Weber
SCML 2024
Albert Atserias, Anuj Dawar, et al.
Journal of the ACM
P.C. Yue, C.K. Wong
Journal of the ACM
Segev Shlomov, Avi Yaeli
CHI 2024