meigen0 function

Nystrom extension of Moran eigenvectors

This function estimates Moran eigenvectors at unobserved sites using the Nystrom extension.

meigen0( meig, coords0, coords_z0 = NULL, s_id0 = NULL )

Arguments

• meig: Moran eigenvectors and eigenvalues. Output from meigen or meigen_f
• coords0: Matrix of spatial point coordinates of prediction sites (N_0 x 2)
• coords_z0: Optional. One- or two-column matrix whose t-th column represents the t-th temporal coordinate of prediction times (N_0 x 1 or N_0 x 2).
• s_id0: Optional. ID specifying groups modeling spatial effects (N_0 x 1). If specified, Moran eigenvectors are extracted by groups. It is useful e.g. for multilevel modeling (s_id is the groups) and panel data modeling (s_id is given by individual location id). Default is NULL

Returns

• sf: Matrix of the first L eigenvectors at unobserved sites (N_0 x L)

• ev: Vector of the first L eigenvalues (L x 1)

• sf_z: List. t-th element is the matrix of the t-th temporal eigenvectors (N x L_t)

• ev_z: List. t-th element is the vector of the t-th temporal eigenvalues (L_t x 1)

• other: List of other outputs, which are internally used

References

Drineas, P. and Mahoney, M.W. (2005) On the Nystrom method for approximating a gram matrix for improved kernel-based learning. Journal of Machine Learning Research, 6 (2005), 2153-2175.

Author(s)

Daisuke Murakami

See Also

meigen, meigen_f