# `pp_emsc` — Extended Multiplicative Scatter Correction (EMSC)

_Group_: **Preprocessing** · _Binding_: `n4m.sklearn.EMSC` · _C ABI_: `n4m_pp_emsc_*`

## Description

Extended Multiplicative Scatter Correction (polynomial).

### Parameters

| Name | Type | Default |
|------|------|---------|
| `degree` | `int` | `2` |

## Explanations

### Bibliographic source

Martens, H. & Stark, E. (1991). *Extended multiplicative signal correction and spectral interference subtraction*. Journal of Pharmaceutical and Biomedical Analysis 9(8), 625–635.

### Mathematical principle

EMSC augments the MSC regression basis with polynomial wavelength terms (and optionally known interferent spectra), so the model $\mathbf{x}_i = a_i + b_i\bar{\mathbf{x}} + d_i\boldsymbol{\lambda} + e_i\boldsymbol{\lambda}^2 + \dots$ separates chemical signal from smooth physical baselines more flexibly than plain MSC.

### Implementation

C ABI `n4m_pp_emsc_*` in libn4m (create / apply / destroy lifecycle), wrapped by `n4m.sklearn.EMSC`. The same numerical kernel backs every language binding.

### Usage

```python
from n4m.sklearn import EMSC
op = EMSC()
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

<div class="parity-table-wrap">
<table class="docutils parity-grouped">
<thead><tr><th scope="col">Backend</th><th scope="col">Parity</th><th class="size-col" scope="col">50×250 (ms)</th><th class="size-col" scope="col">250×50 (ms)</th></tr></thead>
<tbody class="lang-band lang-cpp"><tr class="lang-band-row" data-lang="cpp"><th colspan="4" scope="rowgroup"><span class="lang-band-dot"></span>C++ native · libn4m</th></tr>
<tr class="bk-row"><td class="bk-name"><code>pls4all.cpp.blas+omp</code></td><td class="parity parity-ref-strict">✓ ref</td><td class="ms">—</td><td class="ms">—</td></tr>
</tbody>
<tbody class="lang-band lang-python"><tr class="lang-band-row" data-lang="python"><th colspan="4" scope="rowgroup"><span class="lang-band-dot"></span>Python · external</th></tr>
<tr class="bk-row"><td class="bk-name"><code>ref.python_numpy</code></td><td class="parity parity-ref-source">source</td><td class="ms">—</td><td class="ms">—</td></tr>
</tbody>
</table>
</div>

:::

::::


---

_See also_: [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)