---
kind: concept
slug: data-resampling
title: Data resampling for class imbalance
summary: >-
  Resampling changes how many rows of each class a model trains on: undersampling removes majority rows, oversampling copies or synthesises minority rows. One card compares five methods on tabular Porto Seguro data; another uses density-based SMOTE inside a sensor feature-selection pipeline. Accuracy alone hides the failure, and the reported numbers are single runs.
tags: [class-imbalance, tabular, evaluation]
papers: ["2108.00071", "2008.12987"]
related: [synthetic-minority-oversampling, class-balanced-loss, long-tailed-recognition, dataset-curation, data-augmentation, feature-selection]
status: draft
updated_at: 2026-11-06
---

## Overview

When one class is rare, a model can score high accuracy by predicting the common
class every time. On the Porto Seguro Safe Driver data, the no-resampling
logistic regression reaches accuracy 0.96 with no positive predictions
[arxiv:2108.00071 tab. 2]. The imbalance ratio is the count of negatives divided
by the count of positives [arxiv:2108.00071 §2.1], and the chapter argues that
accuracy, precision and recall should be read from the confusion matrix
[arxiv:2108.00071 §3.1] [arxiv:2108.00071 §3.2].

Resampling is the family of fixes that change the training data rather than the
model. Undersampling removes majority rows, oversampling copies or creates
minority rows, and hybrids combine the two [arxiv:2108.00071 §4]. Each variant
below changes the class counts. The chapter does not state whether it resampled
before or after the train/test split [arxiv:2108.00071 §4], so the sketch in
this page splits first. The SECOM card also oversamples before its feature
selection step and does not say where the train/test split falls
[arxiv:2008.12987 §3].

## Variants

### Random undersampling

Removes majority rows at random until the classes are equal
[arxiv:2108.00071 §4.1.1]. In the chapter's single run it was the only
undersampler that found positives: accuracy 0.59 and AUC 0.63 against 0.96 and
0.62 without resampling [arxiv:2108.00071 tab. 4] [arxiv:2108.00071 tab. 5].

### Tomek links

Finds pairs of opposite-class instances where no third instance is closer to
either member, and removes the majority member of each pair
[arxiv:2108.00071 §4.1.2]. In the chapter it removed rows but left the
classifier predicting only the majority class: accuracy 0.96, precision and
recall 0, AUC 0.62 [arxiv:2108.00071 tab. 6] [arxiv:2108.00071 tab. 7].

### Edited nearest neighbours (ENN)

Removes a majority instance when most of its k nearest neighbours are
minority instances. The chapter's default is k = 3, and it does not say how a
tie is handled for even k [arxiv:2108.00071 §4.1.3]. As with Tomek links, the
classifier still predicted only the majority class: accuracy 0.96, AUC 0.64
[arxiv:2108.00071 tab. 6] [arxiv:2108.00071 fig. 8, p. 12].

### Random oversampling

Copies minority rows at random until the classes are equal
[arxiv:2108.00071 §4.2.1]. Accuracy 0.59, precision 0.54 and recall 0.60 as
printed, AUC 0.63 [arxiv:2108.00071 tab. 8] [arxiv:2108.00071 tab. 9]. The
chapter's conclusion is that oversampling did better than undersampling here
[arxiv:2108.00071 §5]. The gap is 0.01 AUC, from one run each.

### SMOTE

Creates new minority points by interpolating between a minority instance and
nearby minority instances. The chapter defers the interpolation details to the
original SMOTE paper and does not state them [arxiv:2108.00071 §4.2.2]. Accuracy
0.58, AUC 0.62 [arxiv:2108.00071 tab. 10] [arxiv:2108.00071 tab. 11]. See the
[SMOTE concept page](/concepts/synthetic-minority-oversampling) for the one
other card that uses it.

### ADASYN

An extension of SMOTE that makes more synthetic points for minority instances
judged harder to learn, using their density distribution
[arxiv:2108.00071 §4.2.2] [arxiv:2108.00071 §4.2.3]. Accuracy 0.58, AUC 0.62
[arxiv:2108.00071 tab. 12] [arxiv:2108.00071 tab. 13].

### Density-based SMOTE (DBSMOTE)

A density-based SMOTE variant. The SECOM paper uses it to oversample the
failure class before a genetic-algorithm feature selection, on 104 failure
cases [arxiv:2008.12987 §3.2]. Its neighbour count and sampling amount are not
stated [arxiv:2008.12987 §3.2]. The paper does not run it with and without
oversampling, so it gives no measured effect of this step. Card:
[AI-based Modeling and Data-driven Evaluation for Smart Manufacturing Processes](/papers/2008.12987).
See the [SMOTE concept page](/concepts/synthetic-minority-oversampling) for the
base method.

### Hybrid methods and named-only approaches

SMOTE+ENN and SMOTE+Tomek are named and left to a library, and are not
evaluated [arxiv:2108.00071 §4.3]. Cost-sensitive learning, one-class learning,
bagging and boosting are named but not covered [arxiv:2108.00071 §5]. For
loss-side weighting, see [class-balanced loss](/concepts/class-balanced-loss).

## Reported results

Author-reported, one run per method, logistic regression, 70/30 split, seed 0.
The values are as printed, before the corrections under Contradictions. All
rows are from [arxiv:2108.00071].

| Method | Accuracy | Recall (as printed) | AUC | Source |
|---|---|---|---|---|
| No resampling (baseline) | 0.96 | 0 | 0.62 | tab. 2, tab. 3, fig. 6 |
| Random undersampling | 0.59 | 0.60 | 0.63 | tab. 4, tab. 5, fig. 8 |
| Tomek links | 0.96 | 0 | 0.62 | tab. 6, tab. 7, fig. 10 |
| ENN | 0.96 | 0 | 0.64 | tab. 6, tab. 7, fig. 8 |
| Random oversampling | 0.59 | 0.60 | 0.63 | tab. 8, tab. 9, fig. 12 |
| SMOTE | 0.58 | 0.59 | 0.62 | tab. 10, tab. 11, fig. 14 |
| ADASYN | 0.58 | 0.59 | 0.62 | tab. 12, tab. 13, fig. 16 |

The differences among the resampled methods are 0.01 to 0.02 AUC and 0.01
accuracy. None of these were tested for significance, and no intervals are
reported. The hybrids are not in the table because they were not evaluated.

The SECOM card is not in this table. Its tables compare feature-selection
methods, not resampling methods [arxiv:2008.12987 tab. 2]. Its 90.2% test
accuracy comes from the full pipeline with DBSMOTE as one stage, and it is not
comparable with the Porto Seguro numbers above [arxiv:2008.12987 tab. 2].

## When to use which

| Situation | Use | Why |
|---|---|---|
| Rare class, and you have only accuracy to report | Report confusion-matrix counts with precision, recall and F1 | A classifier that never predicts the rare class scores 0.96 accuracy here [arxiv:2108.00071 tab. 2] [arxiv:2108.00071 §3.1]. |
| Large majority class and you need the rare cases found | Random undersampling as a first baseline | In this run it was the only undersampler that found positives [arxiv:2108.00071 tab. 4]. One run, so compare it with your own split. |
| You want to keep every majority row | Random oversampling, or SMOTE or ADASYN | Oversampling was the chapter's conclusion [arxiv:2108.00071 §5]. SMOTE and ADASYN did not beat random copying on AUC in this run [arxiv:2108.00071 tab. 9] [arxiv:2108.00071 tab. 11] [arxiv:2108.00071 tab. 13]. |
| Removing borderline majority rows as the main fix | Not supported by this card | Both Tomek links and ENN left the classifier predicting only the majority class [arxiv:2108.00071 tab. 6]. |
| Oversampling as one stage of a feature-selection pipeline | Oversample the training rows only, and state the order in your write-up | The SECOM paper oversamples before selection but does not state its split order or DBSMOTE settings [arxiv:2008.12987 §3] [arxiv:2008.12987 §3.2]. |
| Hybrid of oversampling and cleaning | Not supported by this card | The chapter names SMOTE+ENN and SMOTE+Tomek but does not evaluate them [arxiv:2108.00071 §4.3]. |
| Deciding whether resampling helps at all | Run your own comparison with and without it | The chapter reports no run beyond one seed per method, and its split order is not stated [arxiv:2108.00071 §4] [arxiv:2108.00071 §5]. |

## Implementation sketch

The chapter's experiment uses a 30 percent test split with seed 0 and
logistic regression with C = 1.0 [arxiv:2108.00071 p. 6]. The split-first order
below is this page's design choice, because the chapter does not state its
order [arxiv:2108.00071 §4].

```pseudocode
# Split first, then resample only the training part
# Split settings as in the chapter  [arxiv:2108.00071 p. 6]
def fit_with_resampling(X, y, sampler):
    X_tr, X_te, y_tr, y_te = split(X, y, test_size=0.3, seed=0)

    # Undersampler [arxiv:2108.00071 §4.1] or oversampler [§4.2]
    # SMOTE and ADASYN interpolation details: not stated here [§4.2.2]
    X_res, y_res = sampler.fit_resample(X_tr, y_tr)

    # Logistic regression settings as printed  [arxiv:2108.00071 p. 6]
    model = LogisticRegression(C=1.0, penalty="l2", solver="liblinear")
    model.fit(X_res, y_res)

    # Report counts and derived scores, not accuracy alone  [§3.1] [§3.2]
    return confusion_matrix(y_te, model.predict(X_te))
```

## Contradictions

- **Precision and recall appear swapped.** Applying the definitions in
  [arxiv:2108.00071 §3.2] to the matrix in [arxiv:2108.00071 tab. 4] (TN 4115,
  FP 2402, FN 2878, TP 3622) gives precision 0.60 and recall 0.56. The table
  prints precision 0.56 and recall 0.60 [arxiv:2108.00071 tab. 5]. The same
  pattern appears in [arxiv:2108.00071 tab. 9], and the chapter's code appears
  to pass its arguments in reverse order [arxiv:2108.00071 p. 6]. The table
  values are shown above as printed.
- **G-mean has two definitions that disagree with the table.** The text defines
  G as the square root of precision times recall, which gives 0.58 for
  [arxiv:2108.00071 tab. 4]. The table prints 0.59, which matches the square
  root of recall times specificity [arxiv:2108.00071 §3.3] [arxiv:2108.00071 tab. 5].
- **F1 and G-mean in tab. 9 do not match its matrix.** The matrix gives an F1 of
  about 0.57 and a G-mean of about 0.59, while the table prints 0.59 and 0.57
  [arxiv:2108.00071 tab. 9].
- **Possible resampling before the split.** The test totals in
  [arxiv:2108.00071 tab. 4] and [arxiv:2108.00071 tab. 8] are about 30 percent
  of the resampled row counts in the text [arxiv:2108.00071 p. 8]
  [arxiv:2108.00071 p. 13]. That suggests the test sets may include copies or
  synthetic points of training rows. This is an inference from the totals, not
  something the chapter states, and it would make those scores not comparable
  with a split-first run.
- **Zero precision is reported, not explained.** Where a method predicts no
  positives, precision is undefined. The chapter reports 0 and does not say how
  it handled that case [arxiv:2108.00071 tab. 2] [arxiv:2108.00071 tab. 6].

## Papers

- [Foundations of data imbalance and solutions for a data democracy](/papers/2108.00071): a tutorial chapter that defines the imbalance ratio and metrics, then compares five resampling methods with a no-resampling baseline on Porto Seguro data; single run, author-reported.
- [AI-based Modeling and Data-driven Evaluation for Smart Manufacturing Processes](/papers/2008.12987): a GA feature-selection pipeline on SECOM sensor data, where density-based SMOTE oversamples the failure class; author-reported, with no resampling-only comparison.