PMAL: Open Set Recognition via Robust Prototype Mining

Jing LuYunlu XuHao LiZhanzhan ChengYi Niu

article2022AAAI84 citations

Proposes a prototype mining and learning framework that improves open set recognition by selecting high-quality, diverse training samples as explicit class prototypes based on data uncertainty and feature topology.

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Real-world machine learning systems must operate in open environments where they encounter novel or unseen categories during deployment. Standard visual recognition models assume a closed-world setting and will incorrectly classify unknown objects into predefined known classes. Open Set Recognition addresses this challenge by requiring systems to accurately classify known categories while simultaneously detecting and rejecting unknown samples. While prototype-based learning methods have shown promise by grouping similar samples together in feature space, existing techniques learn prototypes implicitly alongside model parameters. This often leaves systems vulnerable to low-quality, noisy data such as blur or occlusion, and leads to redundant prototype representations that fail to capture the diverse visual appearances within a category.

The article introduces and evaluates a two-stage framework called Prototype Mining And Learning (PMAL). The objective is to demonstrate that explicitly selecting high-quality, diverse visual prototypes from training data before optimizing the feature space significantly improves both known-class classification accuracy and unknown-class detection.

The evaluated approach divides the recognition pipeline into two distinct phases. First, in the prototype mining phase, high-quality image candidates are selected by measuring how robustly sample relationships are preserved across different initial model training runs, which filters out inherent data noise. A diversity-based selection algorithm then chooses a diverse set of final prototype images per category to capture multifarious visual appearances without redundancy. Second, in the embedding learning phase, these mined images serve as fixed anchors to optimize a discriminative feature space using an attention-based distance metric. The authors evaluated this framework across six standard small-scale benchmarks (such as MNIST, SVHN, CIFAR variants, and TinyImageNet) and three challenging large-scale datasets (ImageNet-100, ImageNet-200, and the long-tailed ImageNet-LT dataset) using both compact and standard neural network architectures.

The evaluation yielded several key findings. First, on large-scale and complex benchmarks, the proposed framework achieved dramatic improvements in detecting unknown classes, increasing area-under-the-curve performance by 12.6% to 16.5% over previous state-of-the-art methods. Second, the framework maintained superior known-class accuracy across all small and large benchmarks, achieving gains of 2% to 3.2% in closed-set accuracy on datasets like ImageNet-LT and CIFAR. Third, unlike prior prototype-based models that add millions of learnable parameters as the number of classes grows, the proposed method introduces zero additional parameters during inference, ensuring consistent scalability and efficiency. Finally, using multiple diverse prototypes per category (such as ten prototypes) substantially outperformed single-prototype baselines, effectively easing model optimization and creating wider safety margins between known and unknown categories.

These findings indicate that decoupling prototype selection from feature optimization provides a more robust and scalable path for deploying computer vision systems in unconstrained environments. By eliminating extra prototype parameters and avoiding noise interference, the approach reduces computational overhead during inference and lowers operational risk in safety-critical applications where unseen inputs must be rejected reliably. Furthermore, its strong performance on long-tailed data indicates high resilience when dealing with real-world category imbalances where sample counts vary widely.

Organizations developing computer vision systems for open-world deployments should adopt explicit sample-filtering pipelines to anchor category representations before training feature embeddings. Implementing a multi-prototype strategy per class is strongly advised over single-prototype approaches to capture real-world visual diversity. Teams can safely adopt compact neural architectures paired with this mining strategy to achieve competitive accuracy with minimal hardware resources.

The primary limitation noted in the article is that the framework was evaluated exclusively on image recognition tasks, and prototype candidate mining depends on an initial filtering threshold that balances sample quality against visual diversity. Nonetheless, the experimental evidence across multiple diverse benchmarks and model backbones provides high confidence in the framework's reliability and practical advantages.

Hikvision Research Institute Zhejiang University association rules open set recognition robust prototype mining prototype learning

arXiv: 2203.08569

Paper: Toward Open Set Recognition, W. Scheirer et al. (2013). This seminal paper mathematically formalizes open set recognition and the minimization of open space risk, providing the foundational problem formulation that PMAL builds upon.
Paper: Towards Open Set Deep Networks, Abhijit Bendale et al. (2015). This work establishes the foundational OpenMax architecture for deep open set recognition, introducing the standard benchmark protocol and activation-space rejection mechanisms that PMAL seeks to improve.
Paper: Prototypical Networks for Few-shot Learning, Jake Snell et al. (2017). This paper introduces metric-based prototypical learning using class centroid anchors, which forms the underlying representation paradigm PMAL adapts through robust prototype mining.
Paper: Large-Scale Long-Tailed Recognition in an Open World, Ziwei Liu et al. (2019). This paper establishes the open long-tailed recognition framework and the ImageNet-LT benchmark, which PMAL directly uses to demonstrate robustness against class imbalance and open-world shift.
Paper: Generalized Out-of-Distribution Detection: A Survey, Jingkang Yang et al. (2021). This comprehensive survey categorizes open set and out-of-distribution detection benchmarks and evaluation methodologies, contextualizing the experimental landscape evaluated in PMAL.
Paper: A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks, Kimin Lee et al. (2018). This foundational chapter establishes distance-based anomaly detection using feature-space class distributions, motivating PMAL's metric-distance approach to unknown rejection.
Paper: Deep Anomaly Detection with Outlier Exposure, Dan Hendrycks et al. (2019). This work establishes standard outlier evaluation protocols and loss formulations for detecting unknown inputs, offering essential background for evaluating open set discriminative spaces.

Paper: Generalized Category Discovery with Decoupled Prototypical Network, Wenbin An et al. (2023). This paper extends prototype-based open-world recognition by decoupling known and novel category representations to discover unannotated classes in generalized category discovery.
Paper: PROB: Probabilistic Objectness for Open World Object Detection, Orr Zohar et al. (2023). This work extends open-world classification principles into transformer-based object detection, replacing heuristic visual mining with probabilistic objectness modeling to identify unknown instances.
Paper: SPTNet: An Efficient Alternative Framework for Generalized Category Discovery with Spatial Prompt Tuning, Hongjun Wang et al. (2024). This research builds on open category discovery by applying parameter-efficient spatial prompt tuning to categorize novel classes without extensive model retraining.
Paper: Revisiting Prototypical Network for Cross Domain Few-Shot Learning, Fei Zhou et al. (2023). This paper continues the exploration of robust prototype representations by enforcing local-global distillation to overcome visual shortcut biases across diverse target domains.
Paper: Scaling for Training Time and Post-hoc Out-of-distribution Detection Enhancement, Kai Xu et al. (2024). This work advances open-set and out-of-distribution detection by analyzing post-hoc feature activations and scaling mechanisms to maximize unknown sample separation.
Paper: Prototypical Residual Networks for Anomaly Detection and Localization, Hui Zhang et al. (2023). This paper adapts multi-scale prototype modeling to visual anomaly detection by learning residual feature differences between normal anchors and anomalous patterns.

Cover for PMAL: Open Set Recognition via Robust Prototype Mining

Abstract

Open Set Recognition (OSR) has been an emerging topic. Besides recognizing predefined classes, the system needs to reject the unknowns. Prototype learning is a potential manner to handle the problem, as its ability to improve intra-class compactness of representations is much needed in discrimination between the known and the unknowns. In this work, we propose a novel Prototype Mining And Learning (PMAL) framework. It has a prototype mining mechanism before the phase of optimizing embedding space, explicitly considering two crucial properties, namely high-quality and diversity of the prototype set. Concretely, a set of high-quality candidates are firstly extracted from training samples based on data uncertainty learning, avoiding the interference from unexpected noise. Considering the multifarious appearance of objects even in a single category, a diversity-based strategy for prototype set filtering is proposed. Accordingly, the embedding space can be better optimized to discriminate therein the predefined classes and between known and unknowns. Extensive experiments verify the two good characteristics (i.e., high-quality and diversity) embraced in prototype mining, and show the remarkable performance of the proposed framework compared to state-of-the-arts.

Topics

association rules

Keywords

open set recognition robust prototype mining prototype learning Convolutional Prototype Network discriminative reciprocal points topology robustness diversity-based filtering few-shot learning Deep Ensembles unseen classes

Introduction
Related Work
Notation and Preliminaries
Notations
Preliminaries of Uncertainty
Prototype Mining
High-Quality Candidate Selection
Diverse Prototype-Set Filtering
Embedding Optimization
Prototype-based Space Optimization
Rejecting Unknowns
Experiments
Experiments on Small-Scale Benchmarks
Experiments on Larger-Scale Benchmarks
Detailed Analysis
Conclusion
References

Knowls

Knowl 1 — Prototype Mining And Learning framework
model/method
Prototype Mining And Learning (PMAL) is an open-set recognition framework that treats prototypes as selected training samples rather than independently learned feature vectors. It separates training into two ordered phases: (1) prototype mining, which selects class-specific samples that are both high-quality and diverse, and (2) embedding optimization, which uses the mined samples as fixed prototype anchors while learning a feature space that compactly represents known classes and separates them from unknowns. Because prototypes are mined before embedding optimization and introduce no trainable prototype parameters, the embedding model can focus on learning sample representations without jointly optimizing unstable prototype vectors.
Knowl 2 — Embedding topology robustness for measuring sample quality
definition
For an input sample $x_i$ , the paper models its embedding as

$z_i=\phi_i+n_i,\qquad n_i\sim\mathcal{N}(0,\sigma_i),$

where $z_i\in\mathbb{R}^{D}$ is the observed embedding, $\phi_i\in\mathbb{R}^{D}$ is the ideal class-relevant feature, and $\sigma_i$ represents data uncertainty caused by image-quality factors such as occlusion, blur, or background interference. Lower uncertainty implies a more reliable sample.

Two independently trained classifiers produce embeddings $Z^1$ and $Z^2$ . For an embedding $z_i$ , define its embedding topology as the vector of Mahalanobis distances to all $N$ training samples:

$t(z_i)=\bigl(d_M(z_i,z_1),\ldots,d_M(z_i,z_N)\bigr),\qquad d_M(a,b)=\sqrt{(a-b)\Sigma^{-1}(a-b)^\top},$

where $\Sigma$ is the embedding-space covariance matrix and $a,b\in\mathbb{R}^{D}$ are row-vector embeddings. Embedding topology robustness is

$r(x_i)=\exp\left(-\left\|t(z_i^1)-t(z_i^2)\right\|_2\right),$

where $z_i^1$ and $z_i^2$ are the embeddings of the same sample under the two classifiers. High-quality samples preserve their relative distances across the two embedding spaces, giving $r(x_i)$ close to $1$ ; noisy, low-quality samples have less stable relative positions and therefore smaller $r(x_i)$ .
Knowl 3 — High-quality candidate prototype selection
algorithm
The candidate-selection procedure takes a labeled training set of $K$ known classes and returns a high-quality candidate set for each class.
1. Train $U=2$ SoftMax classifiers on the known-class training data, repeating initialization and data shuffling so that the classifiers induce two different embedding spaces.
2. Embed every training sample with both classifiers and compute each sample's embedding topology robustness $r(x_i)$ .
3. For class $k$ , let $S_k$ be all training samples with label $k$ , and let $r_k^{\max}=\max_{x_i\in S_k}r(x_i)$ .
4. Retain the class samples satisfying $r(x_i)\geq\epsilon r_k^{\max}$ as the candidate set $C_k$ , using $\epsilon=0.7$ in the main experiments.
5. Return $C=\bigcup_{k=1}^{K}C_k$ .
The procedure explicitly removes low-quality samples before diversity selection. The two classifiers are needed only during prototype mining; the final embedding model uses one classifier and adds no prototype-specific inference parameters.
Knowl 4 — Diversity-based prototype-set filtering
algorithm
For each class $k$ , the diversity filter receives a candidate set $C_k$ of $N_k$ samples, their embeddings in either of the two independently trained spaces, a robustness score $r(x)$ for every candidate, and a target prototype count $T=10$ . It returns a prototype set $P_k$ of $T$ training samples.
Input: Candidate sets $C_k$ for $k=1,\ldots,K$ ; robustness scores $r(x)$ ; target count $T=10
Output: Prototype sets $P_k$
for each class k do
    Compute the pairwise Mahalanobis distance matrix $D_k$ among samples in $C_k$
    For every candidate $x_i$ in $C_k$ do
        Find the closest candidate $x_j$ satisfying $r(x_j)>r(x_i)$ , if such a candidate exists
        Set $E[i]$ to the distance $D_k[i,j]$ ; if no such candidate exists, initialize $E[i]$ to the maximum distance in $D_k$
    end for
    Sort candidate indices by decreasing $E[i]$
    Initialize $P_k$ with the candidate having the largest robustness score
    while $|P_k|<T$ do
        Append the remaining candidate with the largest $E[i]$ to $P_k$
        Remove that candidate from the sorted list
    end while
end for
return all $P_k$
The score $E[i]$ favors candidates that are far from a nearby candidate of higher quality, so the procedure retains local high-robustness representatives while covering separated regions of the class embedding distribution. It therefore removes redundant candidates without discarding distinct visual modes within a class. Because high-quality samples have stable Mahalanobis distances across the two spaces, either space can be used for the filtering distances.
Knowl 5 — Prototype-based embedding optimization with self-attentive point-to-set distance
model/method
Let $x_i$ be a known-class training sample with embedding $z_i\in\mathbb{R}^{d}$ and true class $m$ . Let $P_k=\{p_{k,1},\ldots,p_{k,T}\}$ be the mined samples for class $k$ , and let

$z(P_k)=\bigl[z(p_{k,1}),\ldots,z(p_{k,T})\bigr]\in\mathbb{R}^{d\times T}$

be their embeddings under the current feature extractor. The point-to-set distance uses the sample embedding as a query over all prototypes:

$z_i^{\mathrm{att}}(P_k)=\operatorname{SoftMax}\left(\frac{z_i^\top z(P_k)}{\sqrt d}\right)z(P_k),$

$d\bigl(z_i,z(P_k)\bigr)=1-\frac{z_i^\top z_i^{\mathrm{att}}(P_k)}{\lVert z_i\rVert_2\,\lVert z_i^{\mathrm{att}}(P_k)\rVert_2}.$

The loss compares the distance to the true class's prototype set with the closest competing prototype set:

$L_p=\frac{1}{N}\sum_{i=1}^{N}\left[d\bigl(z_i,z(P_m)\bigr)-d\bigl(z_i,z(P_u)\bigr)+\delta\right]_+,$

$P_u=\underset{P_k\in P,\,P_k\neq P_m}{\arg\min}\ d\bigl(z_i,z(P_k)\bigr),$

where $N$ is the training-set size, $[a]_+=\max(a,0)$ , and $\delta=0.5$ is the margin used in the experiments. The total training objective is

$L=L_{\mathrm{cls}}+\lambda_pL_p,$

where $L_{\mathrm{cls}}$ is the ordinary SoftMax classification loss and $\lambda_p=1$ . The mined samples remain fixed as sample identities, but their embeddings are recomputed by the current feature extractor; unlike implicit prototype methods, no separate prototype vectors are optimized.
Knowl 6 — Unknown rejection using probabilities or prototype-set distance
model/method
PMAL supports two unknown-rejection rules after embedding optimization. Probability-based rejection rejects a sample when its maximum SoftMax class probability is below a selected threshold. Distance-based rejection rejects a sample when its nearest prototype-set distance,

$\min_{P_k}d\bigl(z_i,z(P_k)\bigr),$

is above a selected threshold. The distance rule is motivated by the expected separation of unknown samples from every known-class prototype set. The paper reports distance-based results because the two rejection rules produced similar performance.
Knowl 7 — Experimental protocol and implementation settings
experimental setup
The evaluation measures both known-class recognition and unknown detection. Known-class performance is reported as classification accuracy (ACC), while open-set performance is reported as AUROC over known and unknown test samples; results on the small benchmarks are averaged over five random known/unknown splits.

Small-scale experiments use MNIST, SVHN, CIFAR-10, CIFAR+10, CIFAR+50, and TinyImageNet. Four classes are known for MNIST, SVHN, and CIFAR-10; four non-animal CIFAR-10 classes are known for CIFAR+10 and CIFAR+50; and 20 randomly selected TinyImageNet classes are known. The lightweight OSCRI backbone has fewer than 1M parameters, and Wide-ResNet has about 9M parameters. Training uses Adam for 600 epochs with batch size 128, initial learning rate $0.01$ , a $0.1$ learning-rate multiplier every 120 epochs, momentum $0.9$ , and weight decay $5\times10^{-4}$ . The default PMAL settings are $T=10$ , $\epsilon=0.7$ , $U=2$ , $\delta=0.5$ , and $\lambda_p=1$ .

Large-scale experiments use ImageNet-100, ImageNet-200, and long-tailed ImageNet-LT. ResNet-50 is trained with SGD at learning rate $0.2$ , reduced by a factor of $0.1$ every 30 epochs; other settings follow the small-scale protocol. ImageNet-LT contains 1,000 known ImageNet-2012 classes with additional ImageNet-2010 classes treated as unknown, and has between 5 and 1,280 images per class.
Knowl 8 — Small-scale open-set recognition results
data/table
The numerical benchmark results reported on page 6 compare close-set ACC and open-set AUROC across six small datasets. PMAL obtains the strongest or tied-strongest results throughout, with PMAL-WRN reaching AUROC values from $83.1$ to $99.7$ and PMAL-OSCRI remaining competitive despite its much smaller backbone. The results demonstrate that mined prototypes improve both known-class classification and unknown detection.
Could not parse LaTeX table
Here C10 denotes CIFAR-10, C+10 and C+50 denote CIFAR+10 and CIFAR+50, TINY denotes TinyImageNet, and $^*$ marks results implemented by the paper's authors. Compared with RPL-WRN, PMAL-WRN improves TinyImageNet AUROC from $80.9$ to $83.1$ ; compared with same-backbone alternatives, PMAL-OSCRI improves TinyImageNet AUROC from $70.2$ for RPL-OSCRI to $81.8$ .
Knowl 9 — Large-scale and long-tailed benchmark results
data/table
The large-scale results reported on page 7 show substantially larger gains for PMAL than those observed on the small datasets. PMAL improves close-set ACC by $3.2$ percentage points on ImageNet-LT relative to RPL++ and by $2.0$ points on ImageNet-200 relative to the strongest listed prior result. Its AUROC gains over the strongest prior listed method are $16.5$ , $12.6$ , and $13.7$ points on ImageNet-LT, ImageNet-100, and ImageNet-200, respectively. PMAL also uses no additional prototype parameters, whereas prior prototype methods add up to $4$ M parameters on ImageNet-LT.
Could not parse LaTeX table
IN-LT denotes ImageNet-LT, and IN-100 and IN-200 denote ImageNet-100 and ImageNet-200. The results support the paper's claim that directly mining reliable samples is particularly beneficial when the number of known classes is large or the class distribution is long-tailed, where jointly learned prototype parameters become difficult to optimize and unstable for few-sample classes.
Knowl 10 — Ablation and sensitivity evidence for quality, diversity, and point-to-set learning
empirical result
The component studies on TinyImageNet show that both prototype quality and prototype diversity contribute to PMAL, with high-quality selection being the more important factor. Combining both properties and the proposed point-to-set embedding objective gives the best ablation AUROC of $83.1$ ; replacing the point-to-set distance with the usual nearest-prototype distance reduces AUROC by about $1.2$ percentage points.

For selecting high-quality samples, the reported ACC/AUROC pairs are: probability selection $(81.9,79.3)$ , deep ensembles $(82.3,80.5)$ , MC-dropout $(81.6,78.8)$ , and embedding topology robustness $(84.7,83.1)$ . For selecting multiple prototypes, randomization gives $(81.5,79.1)$ , clustering gives $(81.8,79.6)$ , and the proposed diversity filter gives $(84.7,83.1)$ , where each pair is $(\mathrm{ACC},\mathrm{AUROC})$ .

The reported AUROC sensitivity values are $79.9,81.1,83.1,82.6,83.1$ for prototype counts $T=1,5,10,20,30$ ; $73.6,78.1,82.6,83.1,81.2$ for quality thresholds $\epsilon=0.1,0.3,0.5,0.7,0.9$ ; $83.1,83.3,83.2,83.0,83.3$ for $U=2,3,4,5,6$ embedding models; and $80.9,82.8,83.1,82.1,80.5$ for margins $\delta=0.1,0.3,0.5,0.8,1.0$ . Varying $\lambda_p$ over $0.5,0.8,1$ produces AUROC values $82.6,82.8,82.9$ , respectively. These results motivate the default setting $T=10$ , $\epsilon=0.7$ , $U=2$ , $\delta=0.5$ , and $\lambda_p=1$ .

Coverage note — Qualitative t-SNE visualizations of learned embeddings and the small fluctuation of mined prototypes across three repetitions were omitted because they corroborate the quantitative quality, diversity, and stability results rather than add a separate load-bearing method or numerical conclusion.

References

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Citation

MLA

Lu, J., et al. “PMAL: Open Set Recognition via Robust Prototype Mining”. arXiv, 2022, http://arxiv.org/abs/2203.08569v1.

APA

Lu, J., Xu, Y., Li, H., Cheng, Z., & Niu, Y. (2022). PMAL: Open Set Recognition via Robust Prototype Mining. arXiv. http://arxiv.org/abs/2203.08569v1

Chicago

Lu, J., Y. Xu, H. Li, Z. Cheng, and Y. Niu. 2022. “PMAL: Open Set Recognition via Robust Prototype Mining”. arXiv. http://arxiv.org/abs/2203.08569v1.

Harvard

Lu, J. et al. (2022) “PMAL: Open Set Recognition via Robust Prototype Mining”, arXiv [Preprint]. Available at: http://arxiv.org/abs/2203.08569v1.

Vancouver

1. Lu J, Xu Y, Li H, Cheng Z, Niu Y (2022) PMAL: Open Set Recognition via Robust Prototype Mining. arXiv

BibTeX

@article{lu2022pmal,
  title = {PMAL: Open Set Recognition via Robust Prototype Mining},
  author = {Lu, Jing and Xu, Yunxu and Li, Hao and Cheng, Zhanzhan and Niu, Yi},
  year = {2022},
  journal = {arXiv},
  url = {http://arxiv.org/abs/2203.08569v1},
  eprint = {2203.08569}
}

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PMAL: Open Set Recognition via Robust Prototype Mining

Abstract

Topics

Keywords

Table of Contents

Knowls

Knowl 1 — Prototype Mining And Learning framework

Knowl 2 — Embedding topology robustness for measuring sample quality

Knowl 3 — High-quality candidate prototype selection

Knowl 4 — Diversity-based prototype-set filtering

Knowl 5 — Prototype-based embedding optimization with self-attentive point-to-set distance

Knowl 6 — Unknown rejection using probabilities or prototype-set distance

Knowl 7 — Experimental protocol and implementation settings

Knowl 8 — Small-scale open-set recognition results

Knowl 9 — Large-scale and long-tailed benchmark results

Knowl 10 — Ablation and sensitivity evidence for quality, diversity, and point-to-set learning

References

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