Hong Kong University of Science and Technology（香港科技大学）；Alibaba Group（阿里巴巴集团）；University of Science and Technology of China（中国科学技术大学）；ByteDance Inc.（字节跳动有限公司）
The latent space of a Generative Adversarial Network (GAN) has been shown to encode rich semantics within some subspaces. To identify these subspaces, researchers typically analyze the statistical information from a collection of synthesized data, and the identified subspaces tend to control image attributes globally (i.e., manipulating an attribute causes the change of an entire image). By contrast, this work introduces low-rank subspaces that enable more precise control of GAN generation. Concretely, given an arbitrary image and a region of interest (e.g., eyes of face images), we manage to relate the latent space to the image region with the Jacobian matrix and then use low-rank factorization to discover steerable latent subspaces. There are three distinguishable strengths of our approach that can be aptly called LowRankGAN. First, compared to analytic algorithms in prior work, our low-rank factorization of Jacobians is able to find the low-dimensional representation of attribute manifold, making image editing more precise and controllable. Second, low-rank factorization naturally yields a null space of attributes such that moving the latent code within it only affects the outer region of interest. Therefore, local image editing can be simply achieved by projecting an attribute vector into the null space without relying on a spatial mask as existing methods do. Third, our method can robustly work with a local region from one image for analysis yet well generalize to other images, making it much easy to use in practice. Extensive experiments on state-of-the-art GAN models (including StyleGAN2 and BigGAN) trained on various datasets demonstrate the effectiveness of our LowRankGAN.
Although Generative Adversarial Networks (GANs) have made significant progress in face synthesis, there lacks enough understanding of what GANs have learned in the latent representation to map a random code to a photo-realistic image. In this work, we propose a framework called InterFaceGAN to interpret the disentangled face representation learned by the state-of-the-art GAN models and study the properties of the facial semantics encoded in the latent space. We first find that GANs learn various semantics in some linear subspaces of the latent space. After identifying these subspaces, we can r…
Key Laboratory of Intelligent Information Processing, ICT, CAS（中国科学院计算技术研究所智能信息处理重点实验室）；University of Chinese Academy of Sciences（中国科学院大学）；Peng Cheng Laboratory（鹏城实验室）
Recent studies on Generative Adversarial Network (GAN) reveal that different layers of a generative CNN hold different semantics of the synthesized images. However, few GAN models have explicit dimensions to control the semantic attributes represented in a specific layer. This paper proposes EigenGAN which is able to unsupervisedly mine interpretable and controllable dimensions from different generator layers. Specifically, EigenGAN embeds one linear subspace with orthogonal basis into each generator layer. Via generative adversarial training to learn a target distribution, these layer-wise su…
Carnegie Mellon University（卡内基梅隆大学）；Michigan State University（密歇根州立大学）
Traditional generative adversarial networks (GAN) and many of its variants are trained by minimizing the KL or JS-divergence loss that measures how close the generated data distribution is from the true data distribution. A recent advance called the WGAN based on Wasserstein distance can improve on the KL and JS-divergence based GANs, and alleviate the gradient vanishing, instability, and mode collapse issues that are common in the GAN training. In this work, we aim at improving on the WGAN by first generalizing its discriminator loss to a margin-based one, which leads to a better discriminato…
The Chinese University of Hong Kong（香港中文大学）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））
Despite the recent advance of Generative Adversarial Networks (GANs) in high-fidelity image synthesis, there lacks enough understanding of how GANs are able to map a latent code sampled from a random distribution to a photo-realistic image. Previous work assumes the latent space learned by GANs follows a distributed representation but observes the vector arithmetic phenomenon. In this work, we propose a novel framework, called InterFaceGAN, for semantic face editing by interpreting the latent semantics learned by GANs. In this framework, we conduct a detailed study on how different semantics a…
Google Research（谷歌研究院）；The Australian National University（澳大利亚国立大学）；Data61/CSIRO（澳大利亚联邦科学与工业研究组织数据61所）
In this paper, we improve Generative Adversarial Networks by incorporating a manifold learning step into the discriminator. We consider locality-constrained linear and subspace-based manifolds, and locality-constrained non-linear manifolds. In our design, the manifold learning and coding steps are intertwined with layers of the discriminator, with the goal of attracting intermediate feature representations onto manifolds. We adaptively balance the discrepancy between feature representations and their manifold view, which is a trade-off between denoising on the manifold and refining the manifol…
Exploring Attribute Variations in Style-based GANs using Diffusion Models
Indian Institute of Science（印度科学学院）；Indian Institute of Technology, Dharwad（印度理工学院达瓦德分校）；UCLA（加州大学洛杉矶分校）；Avataar AI（Avataar人工智能公司）；Stability AI（Stability人工智能公司）
TCS Research（塔塔咨询服务研究部）；Flytxt Mobile Solutions（Flytxt 移动解决方案公司）；Indian Institute of Space Science and Technology（印度空间科学技术研究所）
Several methods for discovering interpretable directions in the latent space of pre-trained GANs have been proposed. Latent semantics discovered by unsupervised methods are relatively less disentangled than supervised methods since they do not use pre-trained attribute classifiers. We propose Scale Ranking Estimator (SRE), which is trained using self-supervision. SRE enhances the disentanglement in directions obtained by existing unsupervised disentanglement techniques. These directions are updated to preserve the ordering of variation within each direction in latent space. Qualitative and qua…
Clarkson University（克拉克森大学）；University of Ljubljana（卢布尔雅那大学）
We present GlassesGAN, a novel image editing framework for custom design of glasses, that sets a new standard in terms of image quality, edit realism, and continuous multi-style edit capability. To facilitate the editing process with GlassesGAN, we propose a Targeted Subspace Modelling (TSM) procedure that, based on a novel mechanism for (synthetic) appearance discovery in the latent space of a pre-trained GAN generator, constructs an eyeglasses-specific (latent) subspace that the editing framework can utilize. Additionally, we also introduce an appearance-constrained subspace initialization (…
We propose a new approach to Generative Adversarial Networks (GANs) to achieve an improved performance with additional robustness to its so-called and well recognized mode collapse. We first proceed by mapping the desired data onto a frame-based space for a sparse representation to lift any limitation of small support features prior to learning the structure. To that end we start by dividing an image into multiple patches and modifying the role of the generative network from producing an entire image, at once, to creating a sparse representation vector for each image patch. We synthesize an en…
We propose a symmetric low-rank representation (SLRR) method for subspace clustering, which assumes that a data set is approximately drawn from the union of multiple subspaces. The proposed technique can reveal the membership of multiple subspaces through the self-expressiveness property of the data. In particular, the SLRR method considers a collaborative representation combined with low-rank matrix recovery techniques as a low-rank representation to learn a symmetric low-rank representation, which preserves the subspace structures of high-dimensional data. In contrast to performing iterative…
University of Adelaide（阿德莱德大学）；Australian National University（澳大利亚国立大学）；EPFL（洛桑联邦理工学院）
In this paper, we present a kernel subspace clustering method that can handle non-linear models. In contrast to recent kernel subspace clustering methods which use predefined kernels, we propose to learn a low-rank kernel matrix, with which mapped data in feature space are not only low-rank but also self-expressive. In this manner, the low-dimensional subspace structures of the (implicitly) mapped data are retained and manifested in the high-dimensional feature space. We evaluate the proposed method extensively on both motion segmentation and image clustering benchmarks, and obtain superior re…
Charles Sturt University（查尔斯特大学）；Western Sydney University（西悉尼大学）；The University of Sydney（悉尼大学）
In this paper we present Collaborative Low-Rank Subspace Clustering. Given multiple observations of a phenomenon we learn a unified representation matrix. This unified matrix incorporates the features from all the observations, thus increasing the discriminative power compared with learning the representation matrix on each observation separately. Experimental evaluation shows that our method outperforms subspace clustering on separate observations and the state of the art collaborative learning algorithm.
In this paper, we propose a low-rank representation with symmetric constraint (LRRSC) method for robust subspace clustering. Given a collection of data points approximately drawn from multiple subspaces, the proposed technique can simultaneously recover the dimension and members of each subspace. LRRSC extends the original low-rank representation algorithm by integrating a symmetric constraint into the low-rankness property of high-dimensional data representation. The symmetric low-rank representation, which preserves the subspace structures of high-dimensional data, guarantees weight consiste…
Institute for Systems and Robotics (ISR/IST), Instituto Superior Técnico, Universidade de Lisboa（里斯本大学高等技术学院系统与机器人研究所）
We propose a method to reconstruct and cluster incomplete high-dimensional data lying in a union of low-dimensional subspaces. Exploring the sparse representation model, we jointly estimate the missing data while imposing the intrinsic subspace structure. Since we have a non-convex problem, we propose an iterative method to reconstruct the data and provide a sparse similarity affinity matrix. This method is robust to initialization and achieves greater reconstruction accuracy than current methods, which dramatically improves clustering performance. Extensive experiments with synthetic and real…
Nanjing University of Aeronautics and Astronautics（南京航空航天大学）；Nanjing Hydraulic Research Institute（南京水利科学研究院）；State Key Laboratory of Urban Water Resource and Environment（城市水资源与水环境国家重点实验室）；The Key Laboratory of Rivers and Lakes Governance and Flood Protection of Yangtse River Water Conservancy Committee（长江水利委员会江湖治理与防洪重点实验室）
Subspace clustering refers to the problem of segmenting a set of data points approximately drawn from a union of multiple linear subspaces. Aiming at the subspace clustering problem, various subspace clustering algorithms have been proposed and low rank representation based subspace clustering is a very promising and efficient subspace clustering algorithm. Low rank representation method seeks the lowest rank representation among all the candidates that can represent the data points as linear combinations of the bases in a given dictionary. Nuclear norm minimization is adopted to minimize the …
Nanjing University of Aeronautics and Astronautics（南京航空航天大学）；Key Laboratory of Port, Waterway and Sedimentation Engineering of the Ministry of Transport, Nanjing Hydraulic Research Institute（南京水利科学研究院港口航道泥沙工程交通行业重点实验室）；State Key Laboratory of Urban Water Resource and Environment（城市水资源与水环境国家重点实验室）；The Key Laboratory of Rivers and Lakes Governance and Flood Protection of Yangtse River Water Conservancy Committee（长江水利委员会河湖治理与洪水防护重点实验室）
The problem of fitting a union of subspaces to a collection of data points drawn from multiple subspaces is considered in this paper. In the traditional low rank representation model, the dictionary used to represent the data points is chosen as the data points themselves and thus the dictionary is corrupted with noise. This problem is solved in the low rank subspace clustering model which decomposes the corrupted data matrix as the sum of a clean and self-expressive dictionary plus a matrix of noise and gross errors. Also, the clustering results of the low rank representation model can be enh…
We propose a low-rank transformation-learning framework to robustify subspace clustering. Many high-dimensional data, such as face images and motion sequences, lie in a union of low-dimensional subspaces. The subspace clustering problem has been extensively studied in the literature to partition such high-dimensional data into clusters corresponding to their underlying low-dimensional subspaces. However, low-dimensional intrinsic structures are often violated for real-world observations, as they can be corrupted by errors or deviate from ideal models. We propose to address this by learning a l…
School of Computer Science and Technology, Soochow University（苏州大学计算机科学与技术学院）；Nanjing University of Information Science and Technology（南京信息工程大学）
For subspace recovery, most existing low-rank representation (LRR) models performs in the original space in single-layer mode. As such, the deep hierarchical information cannot be learned, which may result in inaccurate recoveries for complex real data. In this paper, we explore the deep multi-subspace recovery problem by designing a multilayer architecture for latent LRR. Technically, we propose a new Multilayer Collabora-tive Low-Rank Representation Network model termed DeepLRR to discover deep features and deep subspaces. In each layer (>2), DeepLRR bilinearly reconstructs the data matrix b…
Low-rank Orthogonal Subspace Intervention for Generalizable Face Forgery Detection
Engineering Research Center of Digital Forensics, Ministry of Education, Nanjing University of Information Science and Technology（数字取证工程研究中心，教育部，南京信息科技大学）
Beijing University of Technology（北京工业大学）；Charles Sturt University（查尔斯特大学）
Low rank representation (LRR) has recently attracted great interest due to its pleasing efficacy in exploring low-dimensional subspace structures embedded in data. One of its successful applications is subspace clustering which means data are clustered according to the subspaces they belong to. In this paper, at a higher level, we intend to cluster subspaces into classes of subspaces. This is naturally described as a clustering problem on Grassmann manifold. The novelty of this paper is to generalize LRR on Euclidean space onto an LRR model on Grassmann manifold in a uniform kernelized framewo…
Zhejiang University（浙江大学）；Microsoft Research Asia（微软亚洲研究院）
We analyze and improve low rank representation (LRR), the state-of-the-art algorithm for subspace segmentation of data. We prove that for the noiseless case, the optimization model of LRR has a unique solution, which is the shape interaction matrix (SIM) of the data matrix. So in essence LRR is equivalent to factorization methods. We also prove that the minimum value of the optimization model of LRR is equal to the rank of the data matrix. For the noisy case, we show that LRR can be approximated as a factorization method that combines noise removal by column sparse robust PCA. We further propo…
University of Bath（巴斯大学）；Technische Universität München（慕尼黑工业大学）；GE Healthcare（通用电气医疗集团）
Deep learning (DL) has recently emerged to address the heavy storage and computation requirements of the baseline dictionary-matching (DM) for Magnetic Resonance Fingerprinting (MRF) reconstruction. Fed with non-iterated back-projected images, the network is unable to fully resolve spatially-correlated corruptions caused from the undersampling artefacts. We propose an accelerated iterative reconstruction to minimize these artefacts before feeding into the network. This is done through a convex regularization that jointly promotes spatio-temporal regularities of the MRF time-series. Except for …
Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；University of Technology, Sydney（悉尼科技大学）；The Hong Kong Polytechnic University（香港理工大学）；Xiamen University（厦门大学）
In this paper, we address the multi-view subspace clustering problem. Our method utilizes the circulant algebra for tensor, which is constructed by stacking the subspace representation matrices of different views and then rotating, to capture the low rank tensor subspace so that the refinement of the view-specific subspaces can be achieved, as well as the high order correlations underlying multi-view data can be explored.} By introducing a recently proposed tensor factorization, namely tensor-Singular Value Decomposition (t-SVD) \cite{kilmer13}, we can impose a new type of low-rank tensor cons…
Guangdong University of Technology（广东工业大学）；The University of Sydney（悉尼大学）；Western Sydney University（西悉尼大学）
The plenty information from multiple views data as well as the complementary information among different views are usually beneficial to various tasks, e.g., clustering, classification, de-noising. Multi-view subspace clustering is based on the fact that the multi-view data are generated from a latent subspace. To recover the underlying subspace structure, the success of the sparse and/or low-rank subspace clustering has been witnessed recently. Despite some state-of-the-art subspace clustering approaches can numerically handle multi-view data, by simultaneously exploring all possible pairwise…
In this work, we address the following matrix recovery problem: suppose we are given a set of data points containing two parts, one part consists of samples drawn from a union of multiple subspaces and the other part consists of outliers. We do not know which data points are outliers, or how many outliers there are. The rank and number of the subspaces are unknown either. Can we detect the outliers and segment the samples into their right subspaces, efficiently and exactly? We utilize a so-called {\em Low-Rank Representation} (LRR) method to solve this problem, and prove that under mild techni…
Most existing approaches address multi-view subspace clustering problem by constructing the affinity matrix on each view separately and afterwards propose how to extend spectral clustering algorithm to handle multi-view data. This paper presents an approach to multi-view subspace clustering that learns a joint subspace representation by constructing affinity matrix shared among all views. Relying on the importance of both low-rank and sparsity constraints in the construction of the affinity matrix, we introduce the objective that balances between the agreement across different views, while at …
Southeast University（东南大学）；Caritas Institute of Higher Education（明爱专上学院）；City University of Hong Kong（香港城市大学）
In this letter, we propose a novel semi-supervised subspace clustering method, which is able to simultaneously augment the initial supervisory information and construct a discriminative affinity matrix. By representing the limited amount of supervisory information as a pairwise constraint matrix, we observe that the ideal affinity matrix for clustering shares the same low-rank structure as the ideal pairwise constraint matrix. Thus, we stack the two matrices into a 3-D tensor, where a global low-rank constraint is imposed to promote the affinity matrix construction and augment the initial pair…
Southern Illinois University（南伊利诺伊大学）；University of Hawaii at Hilo（夏威夷大学希洛分校）
Low-rank matrix is desired in many machine learning and computer vision problems. Most of the recent studies use the nuclear norm as a convex surrogate of the rank operator. However, all singular values are simply added together by the nuclear norm, and thus the rank may not be well approximated in practical problems. In this paper, we propose to use a log-determinant (LogDet) function as a smooth and closer, though non-convex, approximation to rank for obtaining a low-rank representation in subspace clustering. Augmented Lagrange multipliers strategy is applied to iteratively optimize the Log…
Matrix rank minimization problem is in general NP-hard. The nuclear norm is used to substitute the rank function in many recent studies. Nevertheless, the nuclear norm approximation adds all singular values together and the approximation error may depend heavily on the magnitudes of singular values. This might restrict its capability in dealing with many practical problems. In this paper, an arctangent function is used as a tighter approximation to the rank function. We use it on the challenging subspace clustering problem. For this nonconvex minimization problem, we develop an effective optim…
Vision problems ranging from image clustering to motion segmentation to semi-supervised learning can naturally be framed as subspace segmentation problems, in which one aims to recover multiple low-dimensional subspaces from noisy and corrupted input data. Low-Rank Representation (LRR), a convex formulation of the subspace segmentation problem, is provably and empirically accurate on small problems but does not scale to the massive sizes of modern vision datasets. Moreover, past work aimed at scaling up low-rank matrix factorization is not applicable to LRR given its non-decomposable constrain…
University of Central Florida（中佛罗里达大学）；Sharif University of Technology（谢里夫理工大学）
The problem of signal detection using a flexible and general model is considered. Due to applicability and flexibility of sparse signal representation and approximation, it has attracted a lot of attention in many signal processing areas. In this paper, we propose a new detection method based on sparse decomposition in a union of subspaces (UoS) model. Our proposed detector uses a dictionary that can be interpreted as a bank of matched subspaces. This improves the performance of signal detection, as it is a generalization for detectors. Low-rank assumption for the desired signals implies that …
Recently, the low-rank property of different components extracted from the image has been considered in man hyperspectral image denoising methods. However, these methods usually unfold the 3D tensor to 2D matrix or 1D vector to exploit the prior information, such as nonlocal spatial self-similarity (NSS) and global spectral correlation (GSC), which break the intrinsic structure correlation of hyperspectral image (HSI) and thus lead to poor restoration quality. In addition, most of them suffer from heavy computational burden issues due to the involvement of singular value decomposition operatio…
A low-rank transformation learning framework for subspace clustering and classification is here proposed. Many high-dimensional data, such as face images and motion sequences, approximately lie in a union of low-dimensional subspaces. The corresponding subspace clustering problem has been extensively studied in the literature to partition such high-dimensional data into clusters corresponding to their underlying low-dimensional subspaces. However, low-dimensional intrinsic structures are often violated for real-world observations, as they can be corrupted by errors or deviate from ideal models…
Shanghai Jiao Tong University（上海交通大学）；Microsoft Research Asia（微软亚洲研究院）；Peking University（北京大学）；National University of Singapore（新加坡国立大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Columbia University（哥伦比亚大学）
In this work we address the subspace recovery problem. Given a set of data samples (vectors) approximately drawn from a union of multiple subspaces, our goal is to segment the samples into their respective subspaces and correct the possible errors as well. To this end, we propose a novel method termed Low-Rank Representation (LRR), which seeks the lowest-rank representation among all the candidates that can represent the data samples as linear combinations of the bases in a given dictionary. It is shown that LRR well solves the subspace recovery problem: when the data is clean, we prove that L…
In many applications, high-dimensional data points can be well represented by low-dimensional subspaces. To identify the subspaces, it is important to capture a global and local structure of the data which is achieved by imposing low-rank and sparseness constraints on the data representation matrix. In low-rank sparse subspace clustering (LRSSC), nuclear and $\ell_1$ norms are used to measure rank and sparsity. However, the use of nuclear and $\ell_1$ norms leads to an overpenalized problem and only approximates the original problem. In this paper, we propose two $\ell_0$ quasi-norm based regu…
Low-rank learning has attracted much attention recently due to its efficacy in a rich variety of real-world tasks, e.g., subspace segmentation and image categorization. Most low-rank methods are incapable of capturing low-dimensional subspace for supervised learning tasks, e.g., classification and regression. This paper aims to learn both the discriminant low-rank representation (LRR) and the robust projecting subspace in a supervised manner. To achieve this goal, we cast the problem into a constrained rank minimization framework by adopting the least squares regularization. Naturally, the dat…
Recently there is a line of research work proposing to employ Spectral Clustering (SC) to segment (group){Throughout the paper, we use segmentation, clustering, and grouping, and their verb forms, interchangeably.} high-dimensional structural data such as those (approximately) lying on subspaces {We follow {liu2010robust} and use the term "subspace" to denote both linear subspaces and affine subspaces. There is a trivial conversion between linear subspaces and affine subspaces as mentioned therein.} or low-dimensional manifolds. By learning the affinity matrix in the form of sparse reconstruct…
