Field Strength Split

Field-strength splitting (He et al. 2026) is a greedy distance-based strategy for building calibration sets in near-infrared spectroscopy. It is conceptually similar to KennardStoneSplit, but instead of selecting the sample farthest from the nearest already-selected sample, it selects the sample with the lowest cumulative field generated by all already-selected samples.

The field analogy comes from electrostatics: each selected sample acts as a point charge that repels other samples with a force proportional to 1/d². The next sample added is always the one least covered by the existing selection.

How it works

  1. Compute the N×N pairwise distance matrix.
  2. Initialise. Score each sample by its total isolation: Σⱼ 1/d(i,j)². The most isolated sample — the one with the lowest score — is selected first.
  3. Accumulate the field. Maintain a vector field[i] = Σ_{s ∈ selected} 1/d(i,s)² for every unselected sample i.
  4. Iterate. At each step, add the sample with the minimum field value (least covered by the current selection). Update the field vector.
  5. The remaining samples form the test set.

Field Strength vs. Kennard–Stone

KennardStoneSplitFieldStrengthSplit
Selection criterionMax minimum distance to nearest selectedMin cumulative inverse-squared field
Coverage modelDistance to nearest neighbour onlyInfluence of all selected samples
Sensitivity to nearest neighbourHighSmoothed
Exact split sizesYesYes
DeterministicYesYes
Peak memoryO(N²)O(N²)

The field-strength criterion produces a smoother distribution because it accounts for all selected samples, not just the nearest one. In practice the two methods tend to agree on well-separated datasets and differ most in dense, overlapping regions where a single nearest-neighbour criterion can over-represent boundaries.

API reference

References

He, Z.; Yun, Y.; Tan, Y.; Ye, Z.; Li, H. A new sample selection method based on field strength distribution for developing near-infrared spectroscopy calibration models. Journal of Chemometrics 2026, e70094. https://doi.org/10.1002/cem.70094.