  In this work, a cut high-dimensional model representation (cut-HDMR)
expansion based on multiple anchors is constructed via the clustering method.
Specifically, a set of random input realizations is drawn from the parameter
space and grouped by the centroidal Voronoi tessellation (CVT) method. Then for
each cluster, the centroid is set as the reference, thereby the corresponding
zeroth-order term can be determined directly. While for non-zero order terms of
each cut-HDMR, a set of discrete points is selected for each input component,
and the Lagrange interpolation method is applied. For a new input, the cut-HDMR
corresponding to the nearest centroid is used to compute its response.
Numerical experiments with high-dimensional integral and elliptic stochastic
partial differential equation as backgrounds show that the CVT based multiple
anchors cut-HDMR can alleviate the negative impact of a single inappropriate
anchor point, and has higher accuracy than the average of several expansions.
