1 EmbeddingMethodsinMotivatingCaseStudy

Isomap is a nonlinear dimensionality reduction method and finds low-dimensional embedding of high-dimensional data by preserving the pairwise geodesic distances between data pointsinmanifold. In2-dimensional embedding manifoldM,thegeodesic polygonal curvePi,j canbeprojected on the straight line connected it two endpoints. Every line segment ofPi,j has a corresponding line segmentinthethestraightline. The hyper-parameters searched over include the dimension of node representation as well as hyper-parameters specific to each model.