We propose a novel approach to disentangle the generative factors of variation underlying a given set of observations. Our method builds upon the idea that the (unknown) low-dimensional manifold underlying the data space can be explicitly modeled as a product of submanifolds. This definition of disentanglement gives rise to a novel weakly-supervised algorithm for recovering the unknown explanatory factors behind the data. At training time, our algorithm only requires pairs of non i.i.d. data samples whose elements share at least one, possibly multidimensional, generative factor of variation. We require no knowledge on the nature of these transformations, and do not make any limiting assumption on the properties of each subspace. Our approach is easy to implement, and can be successfully applied to different kinds of data (from images to 3D surfaces) undergoing arbitrary transformations. In addition to standard synthetic benchmarks, we showcase our method in challenging real-world applications, where we compare favorably with the state of the art.
Reducing Class-wise Confusion for Incremental Learning with Disentangled Manifolds
College of Intelligence and Computing, Tianjin University（天津大学智能与计算学部）；Haihe Laboratory of Information Technology Application Innovation (Haihe Lab of ITAI)（海河信息技术应用创新实验室）
KU Leuven（鲁汶大学）；Université de Lille（里尔大学）；CNRS（法国国家科学研究中心）；Centrale Lille（里尔中央理工学院）
Disentanglement is a useful property in representation learning which increases the interpretability of generative models such as Variational autoencoders (VAE), Generative Adversarial Models, and their many variants. Typically in such models, an increase in disentanglement performance is traded-off with generation quality. In the context of latent space models, this work presents a representation learning framework that explicitly promotes disentanglement by encouraging orthogonal directions of variations. The proposed objective is the sum of an autoencoder error term along with a Principal C…
CLIP-PAE: Projection-Augmentation Embedding to Extract Relevant Features for a Disentangled, Interpretable, and Controllable Text-Guided Face Manipulation
Department of Biomedical Informatics and Data Science, Yale School of Medicine（耶鲁医学院生物医学信息学与数据科学部）；School of Information, University of Michigan（密歇根大学信息学院）
Bocconi University（博科尼大学）；Bocconi Institute for Data Science and Analytics（博科尼数据科学与分析研究所）；University of Verona（威尼斯大学）；HUMATICS - SYS-DAT Group（HUMATICS-SYS-DAT组）；University of Milano-Bicocca（米兰-比科卡大学）
Inner Mongolia University（内蒙古大学）；Hainan University（海南大学）；Zhijiang College, Zhejiang University of Technology（浙江工业大学之江学院）；China Agriculture University（中国农业大学）
Cross-manifold clustering is a hard topic and many traditional clustering methods fail because of the cross-manifold structures. In this paper, we propose a Multiple Flat Projections Clustering (MFPC) to deal with cross-manifold clustering problems. In our MFPC, the given samples are projected into multiple subspaces to discover the global structures of the implicit manifolds. Thus, the cross-manifold clusters are distinguished from the various projections. Further, our MFPC is extended to nonlinear manifold clustering via kernel tricks to deal with more complex cross-manifold clustering. A se…
University College London（伦敦大学学院）；Columbia University（哥伦比亚大学）；Flatiron Institute（弗莱提荣研究所）；Leiden University（莱顿大学）
Modern astronomical surveys are observing spectral data for millions of stars. These spectra contain chemical information that can be used to trace the Galaxy's formation and chemical enrichment history. However, extracting the information from spectra, and making precise and accurate chemical abundance measurements are challenging. Here, we present a data-driven method for isolating the chemical factors of variation in stellar spectra from those of other parameters (i.e. \teff, \logg, \feh). This enables us to build a spectral projection for each star with these parameters removed. We do this…
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…
We study stochastic projection-free methods for constrained optimization of smooth functions on Riemannian manifolds, i.e., with additional constraints beyond the parameter domain being a manifold. Specifically, we introduce stochastic Riemannian Frank-Wolfe methods for nonconvex and geodesically convex problems. We present algorithms for both purely stochastic optimization and finite-sum problems. For the latter, we develop variance-reduced methods, including a Riemannian adaptation of the recently proposed Spider technique. For all settings, we recover convergence rates that are comparable t…
Interesting data often concentrate on low dimensional smooth manifolds inside a high dimensional ambient space. Random projections are a simple, powerful tool for dimensionality reduction of such data. Previous works have studied bounds on how many projections are needed to accurately preserve the geometry of these manifolds, given their intrinsic dimensionality, volume and curvature. However, such works employ definitions of volume and curvature that are inherently difficult to compute. Therefore such theory cannot be easily tested against numerical simulations to understand the tightness of …
Tutte Institute for Mathematics and Computing（塔特数学与计算研究所）
UMAP (Uniform Manifold Approximation and Projection) is a novel manifold learning technique for dimension reduction. UMAP is constructed from a theoretical framework based in Riemannian geometry and algebraic topology. The result is a practical scalable algorithm that applies to real world data. The UMAP algorithm is competitive with t-SNE for visualization quality, and arguably preserves more of the global structure with superior run time performance. Furthermore, UMAP has no computational restrictions on embedding dimension, making it viable as a general purpose dimension reduction technique…
Weifang University（潍坊学院）；The University of Hong Kong（香港大学）；Southwestern University of Finance and Economics（西南财经大学）
In this paper, we develop a new alternating projection method to compute nonnegative low rank matrix approximation for nonnegative matrices. In the nonnegative low rank matrix approximation method, the projection onto the manifold of fixed rank matrices can be expensive as the singular value decomposition is required. We propose to use the tangent space of the point in the manifold to approximate the projection onto the manifold in order to reduce the computational cost. We show that the sequence generated by the alternating projections onto the tangent spaces of the fixed rank matrices manifo…
Learning from demonstration is an effective method for human users to instruct desired robot behaviour. However, for most non-trivial tasks of practical interest, efficient learning from demonstration depends crucially on inductive bias in the chosen structure for rewards/costs and policies. We address the case where this inductive bias comes from an exchange with a human user. We propose a method in which a learning agent utilizes the information bottleneck layer of a high-parameter variational neural model, with auxiliary loss terms, in order to ground abstract concepts such as spatial relat…
Uniform Manifold Approximation and Projection (UMAP) is one of the state-of-the-art methods for dimensionality reduction and data visualization. This is a tutorial and survey paper on UMAP and its variants. We start with UMAP algorithm where we explain probabilities of neighborhood in the input and embedding spaces, optimization of cost function, training algorithm, derivation of gradients, and supervised and semi-supervised embedding by UMAP. Then, we introduce the theory behind UMAP by algebraic topology and category theory. Then, we introduce UMAP as a neighbor embedding method and compare …
Technical University of Munich（慕尼黑工业大学）；Munich Center for Machine Learning（慕尼黑机器学习中心）；Huawei Noah’s Ark Lab（华为诺亚方舟实验室）；Google（谷歌）；Johns Hopkins University（约翰斯·霍普金斯大学）
Graph representation of objects and their relations in a scene, known as a scene graph, provides a precise and discernible interface to manipulate a scene by modifying the nodes or the edges in the graph. Although existing works have shown promising results in modifying the placement and pose of objects, scene manipulation often leads to losing some visual characteristics like the appearance or identity of objects. In this work, we propose DisPositioNet, a model that learns a disentangled representation for each object for the task of image manipulation using scene graphs in a self-supervised …
In order to avoid the curse of dimensionality, frequently encountered in Big Data analysis, there was a vast development in the field of linear and nonlinear dimension reduction techniques in recent years. These techniques (sometimes referred to as manifold learning) assume that the scattered input data is lying on a lower dimensional manifold, thus the high dimensionality problem can be overcome by learning the lower dimensionality behavior. However, in real life applications, data is often very noisy. In this work, we propose a method to approximate $\mathcal{M}$ a $d$-dimensional $C^{m+1}$ …
Cluster Exploration using Informative Manifold Projections
Department of Computer Science, University of Liverpool, Liverpool, UK（利物浦大学计算机科学系）；Department of Chemistry, University of Liverpool, Liverpool, UK（利物浦大学化学系）；Leverhulme Research Centre for Functional Materials Design, University of Liverpool, Liverpool, UK（利物浦大学功能性材料设计勒弗赫姆研究中心）
Federated Learning on Riemannian Manifolds: A Gradient-Free Projection-Based Approach
School of Information Management and Engineering, Shanghai University of Finance and Economics（上海金融学院信息管理与工程学院）；School of Information Management and Engineering, Shanghai University of Finance and Economics（上海金融学院信息管理与工程学院；明尼苏达大学工业与系统工程系）；Department of Industrial and System Engineering, University of Minnesota（明尼苏达大学电气与计算机工程系）；Department of Electrical and Computer Engineering, University of Minnesota
We present an encoder-powered generative adversarial network (EncGAN) that is able to learn both the multi-manifold structure and the abstract features of data. Unlike the conventional decoder-based GANs, EncGAN uses an encoder to model the manifold structure and invert the encoder to generate data. This unique scheme enables the proposed model to exclude discrete features from the smooth structure modeling and learn multi-manifold data without being hindered by the disconnections. Also, as EncGAN requires a single latent space to carry the information for all the manifolds, it builds abstract…
HUMAP: Hierarchical Uniform Manifold Approximation and Projection
São Paulo State University (UNESP) and Nomic AI（圣保罗州立大学（UNESP）和Nomic AI）；São Paulo State University (UNESP)（圣保罗州立大学（UNESP））；Eindhoven University of Technology（埃因霍温理工大学）；Linnaeus University（林纳大学）
United States Census Bureau, Center for Economic Studies（美国人口普查局经济研究中心）
The Whitney embedding theorem gives an upper bound on the smallest embedding dimension of a manifold. If a data set lies on a manifold, a random projection into this reduced dimension will retain the manifold structure. Here we present an algorithm to find a projection that distorts the data as little as possible.
Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）
In the past few years, Generative Adversarial Networks (GANs) have dramatically advanced our ability to represent and parameterize high-dimensional, non-linear image manifolds. As a result, they have been widely adopted across a variety of applications, ranging from challenging inverse problems like image completion, to problems such as anomaly detection and adversarial defense. A recurring theme in many of these applications is the notion of projecting an image observation onto the manifold that is inferred by the generator. In this context, Projected Gradient Descent (PGD) has been the most …
Swiss Federal Institute of Technology (ETH) Zürich（苏黎世联邦理工学院）；Johns Hopkins University（约翰斯·霍普金斯大学）；Johns Hopkins School of Medicine（约翰斯·霍普金斯大学医学院）；University of Maryland School of Medicine（马里兰大学医学院）
The thalamus is a subcortical gray matter structure that plays a key role in relaying sensory and motor signals within the brain. Its nuclei can atrophy or otherwise be affected by neurological disease and injuries including mild traumatic brain injury. Segmenting both the thalamus and its nuclei is challenging because of the relatively low contrast within and around the thalamus in conventional magnetic resonance (MR) images. This paper explores imaging features to determine key tissue signatures that naturally cluster, from which we can parcellate thalamic nuclei. Tissue contrasts include T1…
Learning disentangled representations is regarded as a fundamental task for improving the generalization, robustness, and interpretability of generative models. However, measuring disentanglement has been challenging and inconsistent, often dependent on an ad-hoc external model or specific to a certain dataset. To address this, we present a method for quantifying disentanglement that only uses the generative model, by measuring the topological similarity of conditional submanifolds in the learned representation. This method showcases both unsupervised and supervised variants. To illustrate the…
We analyze 14,651 HIV1 reverse transcriptase (HIV RT) sequences from the Stanford HIV Drug Resistance Database labeled with treatment regimen in order to study the evolution this enzyme under drug selection in the clinic. Our goal is to identify distinct sectors of HIV RT's sequence space that are undergoing evolution as a way to identify individual selections and/or evolutionary solutions. We utilize Uniform Manifold Approximation and Projection (UMAP), a graph-based dimensionality reduction technique uniquely suited for the detection of non-linear dependencies and visualize the results using…
Chalmers University of Technology（查尔姆斯理工大学）；ENS（巴黎高等师范学院）；CNRS（法国国家科学研究中心）；PSL University（巴黎文理研究大学）；Inria（法国国家信息与自动化研究所）；National University of Singapore（新加坡国立大学）
We propose a generic, Bayesian, information geometric approach to the exploration--exploitation trade-off in multi-armed bandit problems. Our approach, BelMan, uniformly supports pure exploration, exploration--exploitation, and two-phase bandit problems. The knowledge on bandit arms and their reward distributions is summarised by the barycentre of the joint distributions of beliefs and rewards of the arms, the \emph{pseudobelief-reward}, within the beliefs-rewards manifold. BelMan alternates \emph{information projection} and \emph{reverse information projection}, i.e., projection of the pseudo…
The impact of convolution neural networks (CNNs) in the supervised settings provided tremendous increment in performance. The representations learned from CNN's operated on hyperspherical manifold led to insightful outcomes in face recognition, face identification, and other supervised tasks. A broad range of activation functions were developed with hypersphere intuition which performs superior to softmax in euclidean space. The main motive of this research is to provide insights. First, the stereographic projection is implied to transform data from Euclidean space ($\mathbb{R}^{n}$) to hypers…
Accelerating Birkhoff Projection for Manifold-Constrained Hyper-Connections
School of Statistics（统计学系）；Renmin University of China（中国人民大学）；School of Statistics and Data Science（统计学与数据科学学院）；Institute of Big Data Research（大数据研究院）；Shanghai University of Finance and Economics（上海财经大学）
