# `pp_msc` — Multiplicative Scatter Correction (MSC)
_Group_: **Preprocessing** · _Binding_: `n4m.sklearn.MSC` · _C ABI_: `n4m_pp_msc_*`
## Description
Multiplicative Scatter Correction.
Full binding docstring
```text
Multiplicative Scatter Correction.
Fit learns the mean reference spectrum from the training matrix. Transform
regresses each row against that reference and applies the conventional
row-wise MSC correction used by prospectr and pls.
```
### Parameters
_No constructor parameters._
## Explanations
### Bibliographic source
Geladi, P., MacDougall, D. & Martens, H. (1985). *Linearization and Scatter-Correction for Near-Infrared Reflectance Spectra of Meat*. Applied Spectroscopy 39(3), 491–500.
### Mathematical principle
Each spectrum is regressed on a reference spectrum (typically the training-set mean $\bar{\mathbf{x}}$): $\mathbf{x}_i = a_i + b_i\,\bar{\mathbf{x}} + \mathbf{e}_i$. The corrected spectrum $(\mathbf{x}_i - a_i)/b_i$ removes the additive ($a_i$) and multiplicative ($b_i$) scatter estimated by ordinary least squares. Unlike SNV, MSC needs a reference and so is stateful (the reference is fit on training data).
### Implementation
C ABI `n4m_pp_msc_*` in libn4m (create / apply / destroy lifecycle), wrapped by `n4m.sklearn.MSC`. The same numerical kernel backs every language binding.
### Usage
```python
from n4m.sklearn import MSC
op = MSC()
X_transformed = op.fit_transform(X)
```
### Benchmarks
Adaptive wall-clock per cell measured against [`full_matrix.csv`](../benchmarks/overview.md). Only backends that implement this method are listed; libraries without the method are omitted.
**Verdict** · ✓ ref / ≈ ref / ~ shape mark a reference-gate pass at strict / relaxed / qualitative tolerance · ✓ bind = pls4all binding agrees with the C++ baseline · ✗ divergent · ⚠ error · — not run. The fastest backend per column is marked 🏆.
**Reference gate**: strict — numeric equivalence (`rmse_rel_tol ≤ 1e-12`).
::::{tab-set}
:class: parity-tabs
:::{tab-item} 1 thread
:sync: threads-1
| Backend | Parity | 50×250 (ms) | 250×50 (ms) |
|---|
| C++ native · libn4m |
|---|
pls4all.cpp.blas+omp | ✓ ref | — | — |
| Python · external |
|---|
ref.python_numpy | source | — | — |
:::
::::
---
_See also_: [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)