In this work, we connect two distinct concepts for unsupervised domain adaptation: feature distribution alignment between domains by utilizing the task-specific decision boundary and the Wasserstein metric. Our proposed sliced Wasserstein discrepancy (SWD) is designed to capture the natural notion of dissimilarity between the outputs of task-specific classifiers. It provides a geometrically meaningful guidance to detect target samples that are far from the support of the source and enables efficient distribution alignment in an end-to-end trainable fashion. In the experiments, we validate the effectiveness and genericness of our method on digit and sign recognition, image classification, semantic segmentation, and object detection.
Learning from set-structured data is an essential problem with many applications in machine learning and computer vision. This paper focuses on non-parametric and data-independent learning from set-structured data using approximate nearest neighbor (ANN) solutions, particularly locality-sensitive hashing. We consider the problem of set retrieval from an input set query. Such retrieval problem requires: 1) an efficient mechanism to calculate the distances/dissimilarities between sets, and 2) an appropriate data structure for fast nearest neighbor search. To that end, we propose Sliced-Wasserste…
Sliced-Wasserstein on Symmetric Positive Definite Matrices for M/EEG Signals
Université Bretagne Sud（布列塔尼南部大学）；Université Paris-Saclay（巴黎萨克雷大学）；Inria（法国国家信息与自动化研究所）；CEA（法国原子能和替代能源委员会）；Criteo AI Lab（Criteo人工智能实验室）；Université de Rouen（鲁昂大学）；IMT Atlantique（大西洋国立高等矿业电信学校）；CNRS（法国国家科学研究中心）
The conventional sliced Wasserstein is defined between two probability measures that have realizations as vectors. When comparing two probability measures over images, practitioners first need to vectorize images and then project them to one-dimensional space by using matrix multiplication between the sample matrix and the projection matrix. After that, the sliced Wasserstein is evaluated by averaging the two corresponding one-dimensional projected probability measures. However, this approach has two limitations. The first limitation is that the spatial structure of images is not captured effi…
HRL Laboratories, LLC（HRL实验室有限责任公司）；University of Virginia（弗吉尼亚大学）
Gaussian mixture models (GMM) are powerful parametric tools with many applications in machine learning and computer vision. Expectation maximization (EM) is the most popular algorithm for estimating the GMM parameters. However, EM guarantees only convergence to a stationary point of the log-likelihood function, which could be arbitrarily worse than the optimal solution. Inspired by the relationship between the negative log-likelihood function and the Kullback-Leibler (KL) divergence, we propose an alternative formulation for estimating the GMM parameters using the sliced Wasserstein distance, …
Gatsby Computational Neuroscience Unit, University College London（伦敦大学学院盖茨比计算神经科学单元）；Department of Mathematics and Center for Scientific Computation and Mathematical Modeling, University of Maryland College Park（马里兰大学帕克分校数学系与科学计算与数学建模中心）
While variational autoencoders have been successful in several tasks, the use of conventional priors are limited in their ability to encode the underlying structure of input data. We introduce an Encoded Prior Sliced Wasserstein AutoEncoder wherein an additional prior-encoder network learns an embedding of the data manifold which preserves topological and geometric properties of the data, thus improving the structure of latent space. The autoencoder and prior-encoder networks are iteratively trained using the Sliced Wasserstein distance. The effectiveness of the learned manifold encoding is ex…
Min Generalized Sliced Gromov Wasserstein: A Scalable Path to Gromov Wasserstein
Department of Computer Science, College of Connected Computing, Vanderbilt University（计算机科学系，连接计算学院，范德比尔特大学）；Department of Electrical and Computer Engineering, Vanderbilt University（电气与计算机工程系，范德比尔特大学）
Automatic text recognition from ancient handwritten record images is an important problem in the genealogy domain. However, critical challenges such as varying noise conditions, vanishing texts, and variations in handwriting make the recognition task difficult. We tackle this problem by developing a handwritten-to-machine-print conditional Generative Adversarial network (HW2MP-GAN) model that formulates handwritten recognition as a text-Image-to-text-Image translation problem where a given image, typically in an illegible form, is converted into another image, close to its machine-print form. …
We address the problem of computing a textural loss based on the statistics extracted from the feature activations of a convolutional neural network optimized for object recognition (e.g. VGG-19). The underlying mathematical problem is the measure of the distance between two distributions in feature space. The Gram-matrix loss is the ubiquitous approximation for this problem but it is subject to several shortcomings. Our goal is to promote the Sliced Wasserstein Distance as a replacement for it. It is theoretically proven,practical, simple to implement, and achieves results that are visually s…
In generative modeling, the Wasserstein distance (WD) has emerged as a useful metric to measure the discrepancy between generated and real data distributions. Unfortunately, it is challenging to approximate the WD of high-dimensional distributions. In contrast, the sliced Wasserstein distance (SWD) factorizes high-dimensional distributions into their multiple one-dimensional marginal distributions and is thus easier to approximate. In this paper, we introduce novel approximations of the primal and dual SWD. Instead of using a large number of random projections, as it is done by conventional SW…
Deep convolutional neural networks (CNNs) are broadly considered to be state-of-the-art generic end-to-end image classification systems. However, they are known to underperform when training data are limited and thus require data augmentation strategies that render the method computationally expensive and not always effective. Rather than using a data augmentation strategy to encode invariances as typically done in machine learning, here we propose to mathematically augment a nearest subspace classification model in sliced-Wasserstein space by exploiting certain mathematical properties of the …
Fast rigid alignment of heterogeneous images in sliced Wasserstein distance
Department of Mathematics, University of California at Davis（加州大学戴维斯分校数学系）；Princeton University（普林斯顿大学）；Program in Applied and Computational Mathematics, Princeton University（普林斯顿大学应用与计算数学项目）
Anomaly detection (AD) has been an active research area in various domains. Yet, the increasing data scale, complexity, and dimension turn the traditional methods into challenging. Recently, the deep generative model, such as the variational autoencoder (VAE), has sparked a renewed interest in the AD problem. However, the probability distribution divergence used as the regularization is too strong, which causes the model cannot capture the manifold of the true data. In this paper, we propose the Projected Sliced Wasserstein (PSW) autoencoder-based anomaly detection method. Rooted in the optima…
In generative modeling, the Wasserstein distance (WD) has emerged as a useful metric to measure the discrepancy between generated and real data distributions. Unfortunately, it is challenging to approximate the WD of high-dimensional distributions. In contrast, the sliced Wasserstein distance (SWD) factorizes high-dimensional distributions into their multiple one-dimensional marginal distributions and is thus easier to approximate. In this paper, we introduce novel approximations of the primal and dual SWD. Instead of using a large number of random projections, as it is done by conventional SW…
Lidar became an important component of the perception systems in autonomous driving. But challenges of training data acquisition and annotation made emphasized the role of the sensor to sensor domain adaptation. In this work, we address the problem of lidar upsampling. Learning on lidar point clouds is rather a challenging task due to their irregular and sparse structure. Here we propose a method for lidar point cloud upsampling which can reconstruct fine-grained lidar scan patterns. The key idea is to utilize edge-aware dense convolutions for both feature extraction and feature expansion. Add…
We present a new method for face recognition from digital images acquired under varying illumination conditions. The method is based on mathematical modeling of local gradient distributions using the Radon Cumulative Distribution Transform (R-CDT). We demonstrate that lighting variations cause certain types of deformations of local image gradient distributions which, when expressed in R-CDT domain, can be modeled as a subspace. Face recognition is then performed using a nearest subspace in R-CDT domain of local gradient distributions. Experiment results demonstrate the proposed method outperfo…
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Snap Inc.（Snap公司）
Generative Adversarial Nets (GANs) are very successful at modeling distributions from given samples, even in the high-dimensional case. However, their formulation is also known to be hard to optimize and often not stable. While this is particularly true for early GAN formulations, there has been significant empirically motivated and theoretically founded progress to improve stability, for instance, by using the Wasserstein distance rather than the Jenson-Shannon divergence. Here, we consider an alternative formulation for generative modeling based on random projections which, in its simplest f…
Department of Mathematics（数学系）；Computer Vision Laboratory（计算机视觉实验室）；Department of Information Technology and Electrical Engineering（信息技术与电气工程系）
The extension of image generation to video generation turns out to be a very difficult task, since the temporal dimension of videos introduces an extra challenge during the generation process. Besides, due to the limitation of memory and training stability, the generation becomes increasingly challenging with the increase of the resolution/duration of videos. In this work, we exploit the idea of progressive growing of Generative Adversarial Networks (GANs) for higher resolution video generation. In particular, we begin to produce video samples of low-resolution and short-duration, and then pro…
Multiscale Sliced Wasserstein Distances as Perceptual Color Difference Measures
City University of Hong Kong（香港城市大学）；Shenzhen Research Institute, City University of Hong Kong（香港城市大学深圳研究院）；Shenzhen MSU-BIT University（深圳北理莫斯科大学）；Guangdong OPPO Mobile Telecommunications Corp., Ltd.（广东欧珀移动通信有限公司）；Jiangxi University of Finance and Economics（江西财经大学）；The Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳））
There exist growing interests in intelligent systems for numerous medical imaging, image processing, and computer vision applications, such as face recognition, medical diagnosis, character recognition, and self-driving cars, among others. These applications usually require solving complex classification problems involving complex images with unknown data generative processes. In addition to recent successes of the current classification approaches relying on feature engineering and deep learning, several shortcomings of them, such as the lack of robustness, generalizability, and interpretabil…
VinAI Research（VinAI 研究院）；Woven Planet North America, Level 5（Woven Planet 北美公司 Level 5）；RIKEN AIP（理化学研究所革新智能综合研究中心）；University of Texas, Austin（德克萨斯大学奥斯汀分校）；VinUniversity（Vin大学）
Learning an effective representation of 3D point clouds requires a good metric to measure the discrepancy between two 3D point sets, which is non-trivial due to their irregularity. Most of the previous works resort to using the Chamfer discrepancy or Earth Mover's distance, but those metrics are either ineffective in measuring the differences between point clouds or computationally expensive. In this paper, we conduct a systematic study with extensive experiments on distance metrics for 3D point clouds. From this study, we propose to use sliced Wasserstein distance and its variants for learnin…
SGWIB:Sliced Gromov-Wasserstein Information Bottleneck for Video Highlight Detection
Key Laboratory of Agricultural Machinery Intelligent Control and Manufacturing of Fujian Province University, College of Mechanical and Electrical Engineering, Wuyi University（武夷大学机电工程学院福建省高校农业机械智能控制与制造重点实验室）；National Taiwan University of Science and Technology（国立台湾科技大学）
AdamFlow: Adam-based Wasserstein Gradient Flows for Surface Registration in Medical Imaging
Department of Brain Sciences, Imperial College London（帝国理工学院脑科学系）；Department of Computing, Imperial College London（帝国理工学院计算系）；School of Computer Science, University of Birmingham（伯明翰大学计算机科学学院）；Department of Computer Science, Columbia University（哥伦比亚大学计算机科学系）；Data Science Institute, Imperial College London（帝国理工学院数据科学研究所）
