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
- Compute the N×N pairwise distance matrix.
- 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.
- Accumulate the field. Maintain a vector
field[i]= Σ_{s ∈ selected} 1/d(i,s)² for every unselected sample i. - Iterate. At each step, add the sample with the minimum field value (least covered by the current selection). Update the field vector.
- The remaining samples form the test set.
Field Strength vs. Kennard–Stone
KennardStoneSplit | FieldStrengthSplit | |
|---|---|---|
| Selection criterion | Max minimum distance to nearest selected | Min cumulative inverse-squared field |
| Coverage model | Distance to nearest neighbour only | Influence of all selected samples |
| Sensitivity to nearest neighbour | High | Smoothed |
| Exact split sizes | Yes | Yes |
| Deterministic | Yes | Yes |
| Peak memory | O(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.