ORDinal Adaptive Correction (ORDAC)

• The paper introduces ORDAC, a method that dynamically updates Gaussian label distributions to correct noisy or ambiguous ordinal labels.
• It leverages Label Distribution Learning by representing each label as a Gaussian, allowing per-sample adjustment of both the mean and uncertainty.
• Empirical results show that ORDAC reduces MAE and enhances recall on benchmarks like Adience and Diabetic Retinopathy compared to existing methods.

ORDinal Adaptive Correction (ORDAC) is a data-centric method for ordinal image classification with noisy labels that was introduced to detect and correct label noise in settings where class boundaries are intrinsically ambiguous, such as age estimation and disease severity grading. The method leverages Label Distribution Learning (LDL) to represent each ordinal target as a Gaussian label distribution and then dynamically updates, for each sample, both the distribution mean and standard deviation during training. Its central premise is that noisy or ambiguous samples should be corrected and retained rather than discarded, so that the entire training dataset remains usable while uncertainty is explicitly modeled (Moghaddam et al., 2 Sep 2025).

1. Problem setting and motivation

Ordinal image classification differs from nominal classification in that labels possess an inherent order. In tasks such as age estimation or disease severity grading, adjacent classes are semantically closer than distant classes, and human annotators often make errors near class boundaries. The resulting annotations are therefore not merely noisy in the conventional sense; they are also ambiguous. This combination of ordinal structure and annotation uncertainty motivates methods that can encode proximity between classes and adapt to instance-level noise (Moghaddam et al., 2 Sep 2025).

The motivation for ORDAC is framed against three classes of existing approaches. Model-centric methods based on robust loss functions can improve robustness to noisy supervision, but they do not fix label errors. Data-centric sample selection methods such as CASSOR and ICDF filter out suspected noisy samples, but this discards part of the data and can therefore remove useful information. Direct label correction is comparatively rare, especially for ordinal tasks. ORDAC is designed around the alternative objective of correcting ambiguous or noisy labels while leveraging all the data and representing uncertainty.

A key implication is that the method treats label noise as a property that can often be revised rather than a reason to exclude observations outright. This suggests a training regime in which difficult samples continue to contribute, but with adapted targets and uncertainty estimates that better reflect the evidence available during optimization.

2. Label Distribution Learning formulation

ORDAC is built on Label Distribution Learning. In ordinal tasks, LDL replaces a single hard target with a probability distribution over all classes, typically with a unimodal shape such as a Gaussian. This formulation is naturally suited to ordinal ambiguity because it can assign nonzero mass to adjacent classes rather than forcing all supervision onto a single class index (Moghaddam et al., 2 Sep 2025).

For each sample $i$, ORDAC models the label as a Gaussian

$\mathcal{N}(\mu_i, \sigma_i^2),$

where $\mu_i$ is the label mean and $\sigma_i$ is the uncertainty. Initialization follows the noisy annotation: $\mu_i = \tilde{y}_i,$ while $\sigma_i$ is initially fixed for all samples, representing uniform uncertainty.

The distinctive feature of the method is that both parameters are subsequently updated per sample during training. The mean reflects the current estimate of the ordinal target, and the standard deviation reflects the instance-level ambiguity or noise. In this formulation, a sample does not merely have a corrected class; it has an adaptively corrected distribution whose spread modulates how strongly the sample influences the model. The method therefore encodes both correction and confidence in the same target representation.

3. Training framework and adaptive correction mechanism

ORDAC is organized as a training framework in which label distributions are dynamically corrected per sample over training epochs using reliable model predictions without discarding data (Moghaddam et al., 2 Sep 2025). The framework has two main structural components: K-fold cross-training and iterative correction.

In K-fold cross-training, the dataset is split into $K$ folds. For each of the $K$ runs, a separate model trains on $K-1$ folds and validates on one fold. The purpose is that, when a sample is corrected, the prediction used for that correction comes from a model that has not seen that sample. This is intended to prevent bias and overfitting in the correction signal.

Training proceeds through a warm-up phase followed by a correction phase. During warm-up, all models train for a few epochs on the original noisy label distributions. Starting after warm-up, each epoch includes prediction on the held-out fold, adaptive updates of $\mu_i$ and $\mathcal{N}(\mu_i, \sigma_i^2),$0 based on out-of-sample prediction, and propagation of the updated distributions into the next epoch’s training sets across all models.

The core innovation is the sample-specific update step. Because ordinal models may underfit rare classes and predict middle ranks, ORDAC first debiases predictions. For each class $\mathcal{N}(\mu_i, \sigma_i^2),$1,

$\mathcal{N}(\mu_i, \sigma_i^2),$2

and the debiased prediction for sample $\mathcal{N}(\mu_i, \sigma_i^2),$3 is

$\mathcal{N}(\mu_i, \sigma_i^2),$4

The correction coefficient is then defined as

$\mathcal{N}(\mu_i, \sigma_i^2),$5

where $\mathcal{N}(\mu_i, \sigma_i^2),$6 is model confidence and $\mathcal{N}(\mu_i, \sigma_i^2),$7 is the class frequency term. This coefficient modulates the update rates

$\mathcal{N}(\mu_i, \sigma_i^2),$8

Using the prediction error

$\mathcal{N}(\mu_i, \sigma_i^2),$9

the standard deviation is updated by

$\mu_i$0

and the mean is updated by

$\mu_i$1

These equations encode two coupled effects. If the model’s prediction differs strongly from the current mean, uncertainty increases; if the discrepancy is small, uncertainty decreases. Simultaneously, the mean moves toward the debiased prediction. The resulting correction is soft and iterative rather than a one-shot relabeling. A plausible implication is that this coupling reduces the risk of overcommitting to early prediction errors, because samples can become both shifted and downweighted through increased $\mu_i$2.

4. Data correction rather than sample removal

A defining characteristic of ORDAC is that it corrects labels instead of removing samples. The method adapts the label distributions while retaining all data, thereby preserving feature information that might otherwise be lost through filtering (Moghaddam et al., 2 Sep 2025).

The mechanism supports this objective in two ways. First, increasing $\mu_i$3 downgrades the influence of suspected noisy labels, making the model less sensitive to them without excluding them from training. Second, repeated mean updates allow the label itself to move toward a more plausible ordinal position when sufficient evidence accumulates. The dataset is therefore treated as uncertain but salvageable rather than partitioned into clean and expendable subsets.

This design directly contrasts with sample selection methods such as CASSOR and ICDF. In those approaches, suspected noisy samples are filtered out. In ORDAC, even heavily noisy samples can continue to contribute, but with a label distribution that has been adapted to reflect uncertainty. This suggests a data-efficiency advantage in scenarios where ambiguous cases are common and where outright removal may discard informative visual structure.

5. Empirical evaluation

The empirical evaluation reported for ORDAC uses two benchmark datasets: Adience for age estimation, with 8 groups and real-world unfiltered faces exhibiting strong intrinsic label noise, and Diabetic Retinopathy (DR) for disease severity detection, with 5 levels (Moghaddam et al., 2 Sep 2025). Synthetic noise is injected using an asymmetric Gaussian distribution in which adjacent classes are confused more often, with corruption rates up to $\mu_i$4.

The baselines listed are CORAL, described as a SOTA ordinal regression method with simple hard labels; DLDL-v2, an LDL method with fixed standard deviation; and CASSOR, described as a SOTA sample selection method for noisy ordinal data. Evaluation uses macro-averaged Mean Absolute Error (MAE), where lower is better, and macro-averaged Recall, where higher is better and the metric is not dominated by majority classes.

Several reported results are central. On the Adience dataset with $\mu_i$5 noise, the abstract reports that ORDAC_R reduced the mean absolute error from $\mu_i$6 to $\mu_i$7 and increased the recall metric from $\mu_i$8 to $\mu_i$9 (Moghaddam et al., 2 Sep 2025). The detailed experimental highlights report, for the same setting, CORAL at MAE $\sigma_i$0, DLDL-v2 at $\sigma_i$1, and ORDAC_R at $\sigma_i$2, with recall improving from $\sigma_i$3 for DLDL-v2 to $\sigma_i$4 for ORDAC_R. On DR with $\sigma_i$5 noise, ORDAC_R achieves MAE $\sigma_i$6, compared with $\sigma_i$7 for CASSOR.

The reported findings also state that ORDAC improves performance even when no synthetic noise is injected, that is, at $\sigma_i$8. This is presented as evidence that the method can correct intrinsic annotation issues already present in the original datasets. The analysis of corrections indicates that most corrections are small, typically shifting by one class, and that the method rarely makes large changes. The paper further notes that some label changes may appear incorrect on visual inspection but can in fact correspond to hidden label errors in the original data, as supported by qualitative analysis.

6. Variants, hybrid strategies, and scope

The paper defines two extended versions of the method in addition to the base ORDAC procedure (Moghaddam et al., 2 Sep 2025).

Variant	Description	Training consequence
ORDAC_C	Runs full ORDAC to generate a static cleaned dataset using final per-sample $\sigma_i$9	A standard LDL model is trained from scratch on corrected data without further online corrections
ORDAC_R	Extends ORDAC_C by removing samples whose uncertainty $\mu_i = \tilde{y}_i,$0 did not decrease compared to initialization	A model is trained on the further filtered dataset

ORDAC_C is used to assess whether the cleaned labels themselves are of high quality. ORDAC_R combines correction with removal for samples that remain highly uncertain or outlying after correction. The reported findings indicate that hybrid strategies, including the application of CASSOR to the ORDAC-corrected dataset, can sometimes outperform either correction or selection alone, especially at very high noise levels.

This variant structure refines the interpretation of ORDAC. The base method is not simply an anti-filtering argument; rather, it proposes correction as the default mechanism and reserves removal for cases in which uncertainty remains unresolved. A plausible implication is that the framework supports multiple operating points, ranging from full retention with adaptive uncertainty to a correction-plus-selection pipeline suited to extremely noisy regimes.

7. Terminological usage and related ambiguity

Within the computer vision context addressed here, ORDAC refers specifically to “Ordinal Adaptive Correction: A Data-Centric Approach to Ordinal Image Classification with Noisy Labels” (Moghaddam et al., 2 Sep 2025). The acronym is tied to adaptive correction of per-sample Gaussian label distributions in ordinal image classification.

A separate summary associated with “Adaptive Hierarchical Clustering Using Ordinal Queries” describes an “ORDinal Adaptive Correction” mechanism in a different sense: adaptively querying so as to correct for noise during active learning of hierarchical clustering from ordinal triplet responses (1708.00149). That setting concerns rooted binary trees, ordinal queries over triplets, and noisy query responses, rather than image classification, LDL, or per-sample label distributions. The two usages therefore describe different methodological objects despite the shared phrase.

This distinction matters because one common misconception is to treat ORDAC as a generic label-noise correction acronym across ordinal learning problems. In the image-classification literature represented here, ORDAC denotes a particular data-centric LDL-based framework with dynamic updates of $\mu_i = \tilde{y}_i,$1 and $\mu_i = \tilde{y}_i,$2. In the hierarchical-clustering context, the phrase is descriptive of adaptive error correction in ordinal querying rather than the name of the same method. For implementation details of the image-classification method, the reported code repository is: https://github.com/AlirezaSM/ORDAC/.