Point-set Distances for Learning Representations of 3D Point Clouds

Nguyen, Trung; Pham, Quang-Hieu; Le, Tam; Pham, Tung; Ho, Nhat; Hua, Binh-Son

doi:10.48550/arxiv.2102.04014

Cited by 3 publications

(4 citation statements)

References 41 publications

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“…We note that our proposed SSD divergence is closely related to Chamfer distance/divergence (CD) (Fan et al, 2017;Nguyen et al, 2021) and Relaxed Word Mover's Distance (RWMD) (Kusner et al, 2015). While both CD and RWMD are stated for discrete points (see Section 6 for further comments), SSD divergence is a general difference measure between arbitrary (discrete or continuous) distributions.…”

Section: Difference Between Supportsmentioning

confidence: 94%

“…Balaji et al (2020) introduced relaxed distribution alignment with a different focus, aiming to be insensitive to outliers. Chamfer distance/divergence (CD) is used to compute similarity between images/3D point clouds (Fan et al, 2017;Nguyen et al, 2021). For text data, Kusner et al (2015) presented Relaxed Word Mover's Distance (RWMD) to prune candidates of similar documents.…”

Section: Related Workmentioning

confidence: 99%

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Adversarial Support Alignment

Tong¹,

Garipov²,

Zhang³

et al. 2022

Preprint

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We study the problem of aligning the supports of distributions. Compared to the existing work on distribution alignment, support alignment does not require the densities to be matched. We propose symmetric support difference as a divergence measure to quantify the mismatch between supports. We show that select discriminators (e.g. discriminator trained for Jensen-Shannon divergence) are able to map support differences as support differences in their one-dimensional output space. Following this result, our method aligns supports by minimizing a symmetrized relaxed optimal transport cost in the discriminator 1D space via an adversarial process. Furthermore, we show that our approach can be viewed as a limit of existing notions of alignment by increasing transportation assignment tolerance. We quantitatively evaluate the method across domain adaptation tasks with shifts in label distributions. Our experiments 1 show that the proposed method is more robust against these shifts than other alignment-based baselines.

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Section: Difference Between Supportsmentioning

confidence: 94%

Section: Related Workmentioning

confidence: 99%

Adversarial Support Alignment

Tong¹,

Garipov²,

Zhang³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…where N and Q are batch and inference sizes. A variation of the point-set distance, d(B(z), G), is the Chamfer distance [12]. In (3), µ and ν are hyperparameters.…”

Section: Our Proposed Omasgan Algorithmmentioning

confidence: 99%

OMASGAN: Out-of-distribution Minimum Anomaly Score GAN for Anomaly Detection

Dionelis

Tsaftaris

Yaghoobi

2022

2022 Sensor Signal Processing for Defence Conference (SSPD)

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Generative models trained in an unsupervised manner may set high likelihood and low reconstruction loss to Out-of-Distribution (OoD) samples. This leads to failures to detect anomalies, overall decreasing Anomaly Detection (AD) performance. In addition, AD models underperform due to the rarity of anomalies. To address these limitations, we develop the OoD Minimum Anomaly Score GAN (OMASGAN) which performs retraining by including the proposed minimum-anomalyscore OoD samples. These OoD samples are generated on the boundary of the support of the normal class data distribution in a proposed self-supervised learning manner. Our OMASGAN retraining algorithm leads to more accurate estimation of the underlying data distribution including multimodal supports and also disconnected modes. For inference, for AD, we devise a discriminator which is trained with negative and positive samples either generated (negative or positive) or real (only positive). The evaluation of OMASGAN on image data using the leave-one-out method shows that it achieves an improvement of at least 0.24 and 0.07 points in AUROC on average on the MNIST and CIFAR-10 datasets, respectively, over other benchmark models for AD.

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“…where the batch and inference sizes are denoted by N and Q, respectively. A variation of our point-set distance, d(B(z), G(z)), can be obtained by the Chamfer statistical divergence [33]. Good modeling is achieved by finding the boundary of a model of x rather than of x. OMASGAN finds the minimumanomaly score OoD samples, performs active sampling of negative examples, and generates strong and specifically adversarial anomalies.…”

Section: Our Proposed Omasgan Algorithmmentioning

confidence: 99%

OMASGAN: Out-of-Distribution Minimum Anomaly Score GAN for Sample Generation on the Boundary

Dionelis¹,

Yaghoobi²,

Tsaftaris³

2021

Preprint

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Generative models trained in an unsupervised manner may set high likelihood and low reconstruction loss to Out-of-Distribution (OoD) samples. This increases Type II errors and leads to missed anomalies, overall decreasing Anomaly Detection (AD) performance. In addition, AD models underperform due to the rarity of anomalies. To address these limitations, we propose the OoD Minimum Anomaly Score GAN (OMASGAN). OMASGAN generates, in a negative data augmentation manner, anomalous samples on the estimated distribution boundary. These samples are then used to refine an AD model, leading to more accurate estimation of the underlying data distribution including multimodal supports with disconnected modes. OMASGAN performs retraining by including the abnormal minimumanomaly-score OoD samples generated on the distribution boundary in a selfsupervised learning manner. For inference, for AD, we devise a discriminator which is trained with negative and positive samples either generated (negative or positive) or real (only positive). OMASGAN addresses the rarity of anomalies by generating strong and adversarial OoD samples on the distribution boundary using only normal class data, effectively addressing mode collapse. A key characteristic of our model is that it uses any f-divergence distribution metric in its variational representation, not requiring invertibility. OMASGAN does not use feature engineering and makes no assumptions about the data distribution. The evaluation of OMASGAN on image data using the leave-one-out methodology shows that it achieves an improvement of at least 0.24 and 0.07 points in AUROC on average on the MNIST and CIFAR-10 datasets, respectively, over other benchmark and state-of-the-art models for AD.

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Point-set Distances for Learning Representations of 3D Point Clouds

Cited by 3 publications

References 41 publications

Adversarial Support Alignment

Adversarial Support Alignment

OMASGAN: Out-of-distribution Minimum Anomaly Score GAN for Anomaly Detection

OMASGAN: Out-of-Distribution Minimum Anomaly Score GAN for Sample Generation on the Boundary

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