Geometric median reducer over time (multivariate).

Returns a custom reducer for reduce_over() computing, per pixel, the band-vector minimising the sum of Euclidean distances to the observed band-vectors: the geometric (L1, spatial) median. Unlike a per-band median, whose result can be a spectrum no real observation ever had, the geometric median is a genuine multivariate central tendency: every distance couples all bands.

Usage

geomedian(iters = 12L, eps = 1e-07)

Arguments

iters

Weiszfeld iterations (fixed, unrolled).

eps

Distance regulariser (guards the weight at zero distance).

Value

A reducer fn(x, dims) for reduce_over().

Details

Solved by Weiszfeld iteration (a fixed-point weighted mean, weights inverse distance to the current estimate), unrolled to a fixed iters steps so it compiles to a static kernel. Timesteps with any NaN band are ignored; pixels with no valid timestep return NaN.

The input must be a (band, t, y, x) cube: stack each band's (t, y, x) stack along "band", then reduce over "t"; the band axis survives.

See also

medoid(), reduce_over(); band_project() and mlp_project() for projections over the surviving band axis.