3 papers
cs.LG2026
Non-negative Matrix Factorisation with Topological Regularisation
Matias de Jong van Lier, Shizuo Kaji, Keunsu Kim
We investigate the learning of interpretable bases in non-negative matrix factorisation (NMF) by regularising the topology of the learned basis functions. Our approach is motivated…
math.DS2026
Polynomial Interpolation of a Vector Field on a Convex Polyhedral Domain
Junyan Chu, Shizuo Kaji
We present a computational method for reconstructing a vector field on a convex polytope of arbitrary dimension from discrete samples. We specifi…
math.DG2025
Polyhedra of Constant Gaussian Curvature
Soto Hisakawa, Shizuo Kaji, Ryo Kawai
Topology and geometry are deeply intertwined in the study of surfaces, though their interaction manifests differently in smooth and discrete settings. In the smooth category, a cla…