This thesis is about the implementation of two out-of-sample extension algorithms, namely “Multi Scale Geometric Harmonics” and the “Laplacian Pyramids”, for empirical functions on data sets with the manifold assumption. The challenge is to design the software interfaces for the algorithms, improve the efficiency of the existing implementation, test and document it, and then to include everything as an open source solution in the python package datafold. The new implementations are demonstrated on suitable examples. The tests showed very good agreement with the examples from the original papers where the algorithms were first proposed.

Keywords: out-of-sample extension, Geometric Harmonics, Laplacian Pyramids