Domain adaptation is an essential task in transfer learning to leverage data in one domain to bolster learning in another domain. In this paper, we present a new semi-supervised manifold alignment technique based on a two-step approach of projecting and filtering the source and target domains to low dimensional spaces followed by joining the two spaces. Our proposed approach, filtered manifold alignment (FMA), reduces the computational complexity of previous manifold alignment techniques, is flexible enough to align domains with completely disparate sets of feature and demonstrates state-of-the-art classification accuracy on multiple benchmark domain adaptation tasks composed of classifying real world image datasets.
Due to widespread interest in machine translation and transfer learning, there are numerous algorithms for mapping multiple embeddings to a shared representation space. Recently, these algorithms have been studied in the setting of bilingual dictionary induction where one seeks to align the embeddings of a source and a target language such that translated word pairs lie close to one another in a common representation space. In this paper, we propose a method, Filtered Inner Product Projection (FIPP), for mapping embeddings to a common representation space and evaluate FIPP in the context of bi…
Utah State University（犹他州立大学）；Université de Montréal（蒙特利尔大学）
Multi-domain data is becoming increasingly common and presents both challenges and opportunities in the data science community. The integration of distinct data-views can be used for exploratory data analysis, and benefit downstream analysis including machine learning related tasks. With this in mind, we present a novel manifold alignment method called MALI (Manifold alignment with label information) that learns a correspondence between two distinct domains. MALI can be considered as belonging to a middle ground between the more commonly addressed semi-supervised manifold alignment problem wit…
University of Zurich（苏黎世大学）；Universitat de València（瓦伦西亚大学）
We introduce a kernel method for manifold alignment (KEMA) and domain adaptation that can match an arbitrary number of data sources without needing corresponding pairs, just few labeled examples in all domains. KEMA has interesting properties: 1) it generalizes other manifold alignment methods, 2) it can align manifolds of very different complexities, performing a sort of manifold unfolding plus alignment, 3) it can define a domain-specific metric to cope with multimodal specificities, 4) it can align data spaces of different dimensionality, 5) it is robust to strong nonlinear feature deformat…
Prognostics and Health Management (PHM) is an emerging field which has received much attention from the manufacturing industry because of the benefits and efficiencies it brings to the table. And Remaining Useful Life (RUL) prediction is at the heart of any PHM system. Most recent data-driven research demand substantial volumes of labelled training data before a performant model can be trained under the supervised learning paradigm. This is where Transfer Learning (TL) and Domain Adaptation (DA) methods step in and make it possible for us to generalize a supervised model to other domains with …
Institute of Computing Technology, CAS（中国科学院计算技术研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Tsinghua University（清华大学）
Visual domain adaptation aims to learn robust classifiers for the target domain by leveraging knowledge from a source domain. Existing methods either attempt to align the cross-domain distributions, or perform manifold subspace learning. However, there are two significant challenges: (1) degenerated feature transformation, which means that distribution alignment is often performed in the original feature space, where feature distortions are hard to overcome. On the other hand, subspace learning is not sufficient to reduce the distribution divergence. (2) unevaluated distribution alignment, whi…
National University of Singapore（新加坡国立大学）；Nanyang Technological University（南洋理工大学）
Reducing domain divergence is a key step in transfer learning problems. Existing works focus on the minimization of global domain divergence. However, two domains may consist of several shared subdomains, and differ from each other in each subdomain. In this paper, we take the local divergence of subdomains into account in transfer. Specifically, we propose to use low-dimensional manifold to represent subdomain, and align the local data distribution discrepancy in each manifold across domains. A Manifold Maximum Mean Discrepancy (M3D) is developed to measure the local distribution discrepancy …
ETH Zürich（苏黎世联邦理工学院）；SIB, Swiss Institute of Bioinformatics（瑞士生物信息学研究所）
We introduce Joint Multidimensional Scaling, a novel approach for unsupervised manifold alignment, which maps datasets from two different domains, without any known correspondences between data instances across the datasets, to a common low-dimensional Euclidean space. Our approach integrates Multidimensional Scaling (MDS) and Wasserstein Procrustes analysis into a joint optimization problem to simultaneously generate isometric embeddings of data and learn correspondences between instances from two different datasets, while only requiring intra-dataset pairwise dissimilarities as input. This u…
Sun Yat-Sen University（中山大学）；JiaYing University（嘉应学院）；Guangzhou University（广州大学）
Unsupervised domain adaptation is effective in leveraging the rich information from the source domain to the unsupervised target domain. Though deep learning and adversarial strategy make an important breakthrough in the adaptability of features, there are two issues to be further explored. First, the hard-assigned pseudo labels on the target domain are risky to the intrinsic data structure. Second, the batch-wise training manner in deep learning limits the description of the global structure. In this paper, a Riemannian manifold learning framework is proposed to achieve transferability and di…
We propose a novel manifold based geometric approach for learning unsupervised alignment of word embeddings between the source and the target languages. Our approach formulates the alignment learning problem as a domain adaptation problem over the manifold of doubly stochastic matrices. This viewpoint arises from the aim to align the second order information of the two language spaces. The rich geometry of the doubly stochastic manifold allows to employ efficient Riemannian conjugate gradient algorithm for the proposed formulation. Empirically, the proposed approach outperforms state-of-the-ar…
Utah State University（犹他州立大学）；Université de Montréal（蒙特利尔大学）
The integration of multimodal data presents a challenge in cases when the study of a given phenomena by different instruments or conditions generates distinct but related domains. Many existing data integration methods assume a known one-to-one correspondence between domains of the entire dataset, which may be unrealistic. Furthermore, existing manifold alignment methods are not suited for cases where the data contains domain-specific regions, i.e., there is not a counterpart for a certain portion of the data in the other domain. We propose Diffusion Transport Alignment (DTA), a semi-supervise…
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；Max Planck Institute for Mathematics in the Sciences（马克斯·普朗克数学研究所）；University of New South Wales（新南威尔士大学）
Learning mappings of data on manifolds is an important topic in contemporary machine learning, with applications in astrophysics, geophysics, statistical physics, medical diagnosis, biochemistry, 3D object analysis. This paper studies the problem of learning real-valued functions on manifolds through filtered hyperinterpolation of input-output data pairs where the inputs may be sampled deterministically or at random and the outputs may be clean or noisy. Motivated by the problem of handling large data sets, it presents a parallel data processing approach which distributes the data-fitting task…
Beyond Rigid Alignment: Graph Federated Learning via Dual Manifold Calibration
School of Computer Science and Engineering（计算机科学与工程学院）；Nanjing University of Science and Technology（南京理工大学）；Department of Computer Science（计算机科学系）；Hong Kong Baptist University（香港 Baptist 大学）；School of Automation and Intelligent Sensing（自动化与智能感知学院）
Forest-Guided Semantic Transport for Label-Supervised Manifold Alignment
Department of Mathematics and Statistics, Université de Montréal, Montreal, Canada（蒙特利尔大学数学与统计学系）；Mila - Quebec AI Institute, Montreal, Canada（魁北克人工智能研究所）；Department of Mathematics and Statistics, Utah State University, Logan, Utah, USA（犹他州立大学数学与统计学系）；Department of Statistics, Brigham Young University, Provo, Utah, USA（Brigham Young 大学统计学系）
This work presents the application of a recently developed parametric, non-intrusive, and multi-fidelity reduced-order modeling method on high-dimensional displacement and stress fields arising from the structural analysis of geometries that differ in the size of discretization and structural topology.The proposed approach leverages manifold alignment to fuse inconsistent field outputs from high- and low-fidelity simulations by individually projecting their solution onto a common subspace. The effectiveness of the method is demonstrated on two multi-fidelity scenarios involving the structural …
This study presents the results of a series of simulation experiments that evaluate and compare four different manifold alignment methods under the influence of noise. The data was created by simulating the dynamics of two slightly different double pendulums in three-dimensional space. The method of semi-supervised feature-level manifold alignment using global distance resulted in the most convincing visualisations. However, the semi-supervised feature-level local alignment methods resulted in smaller alignment errors. These local alignment methods were also more robust to noise and faster tha…
University of Sheffield（谢菲尔德大学）；University of Bristol（布里斯托大学）
We present Manifold Alignment Determination (MAD), an algorithm for learning alignments between data points from multiple views or modalities. The approach is capable of learning correspondences between views as well as correspondences between individual data-points. The proposed method requires only a few aligned examples from which it is capable to recover a global alignment through a probabilistic model. The strong, yet flexible regularization provided by the generative model is sufficient to align the views. We provide experiments on both synthetic and real data to highlight the benefit of…
Zero-shot learning (ZSL) aims at recognizing unseen classes with knowledge transferred from seen classes. This is typically achieved by exploiting a semantic feature space (FS) shared by both seen and unseen classes, i.e., attributes or word vectors, as the bridge. However, due to the mutually disjoint of training (seen) and testing (unseen) data, existing ZSL methods easily and commonly suffer from the domain shift problem. To address this issue, we propose a novel model called AMS-SFE. It considers the Alignment of Manifold Structures by Semantic Feature Expansion. Specifically, we build up …
Modality Alignment across Trees on Heterogeneous Hyperbolic Manifolds
Beijing Key Laboratory of Intelligent Information Technology, School of Computer Science & Technology, Beijing Institute of Technology（北京智能信息科技重点实验室，计算机科学与技术学院，北京理工大学）；Guangdong Laboratory of Machine Perception and Intelligent Computing, Shenzhen MSU-BIT University（广东机器感知与智能计算实验室，深圳MSU-BIT大学）；Department of Electrical and Computer System Engineering, Monash University（电子与计算机系统工程系，墨尔本大学）
In this paper, we introduce a neighbor embedding framework for manifold alignment. We demonstrate the efficacy of the framework using a manifold-aligned version of the uniform manifold approximation and projection algorithm. We show that our algorithm can learn an aligned manifold that is visually competitive to embedding of the whole dataset.
Nonlinear manifold learning from unorganized data points is a very challenging unsupervised learning and data visualization problem with a great variety of applications. In this paper we present a new algorithm for manifold learning and nonlinear dimension reduction. Based on a set of unorganized data points sampled with noise from the manifold, we represent the local geometry of the manifold using tangent spaces learned by fitting an affine subspace in a neighborhood of each data point. Those tangent spaces are aligned to give the internal global coordinates of the data points with respect to…
University Of Maryland Baltimore County (UMBC)（马里兰大学巴尔的摩郡分校）
We propose a Bi-Directional Manifold Alignment (BDMA) that learns a non-linear mapping between two manifolds by explicitly training it to be bijective. We demonstrate BDMA by training a model for a pair of languages rather than individual, directed source and target combinations, reducing the number of models by 50%. We show that models trained with BDMA in the "forward" (source to target) direction can successfully map words in the "reverse" (target to source) direction, yielding equivalent (or better) performance to standard unidirectional translation models where the source and target langu…
Generative Model Inversion Through the Lens of the Manifold Hypothesis
TMLR Group, Department of Computer Science, Hong Kong Baptist University（香港 Baptist 大学计算机科学系）；Sydney AI Centre, The University of Sydney（悉尼大学人工智能中心）；School of Computing and Information Systems, The University of Melbourne（墨尔本大学计算与信息系）；McCombs School of Business, The University of Texas at Austin（德克萨斯大学奥斯汀分校麦科姆斯商学院）
Guided Manifold Alignment with Geometry-Regularized Twin Autoencoders
Department of Statistics（统计学系）；Department of Computer Science（计算机科学系）；Neuroscience Center（神经科学中心）；Neuroscience Center and Department of Psychology（神经科学中心和心理学系）；Department of Psychology（心理学系）
Learning causal relationships in high-dimensional data (images, videos) is a hard task, as they are often defined on low dimensional manifolds and must be extracted from complex signals dominated by appearance, lighting, textures and also spurious correlations in the data. We present a method for learning counterfactual reasoning of physical processes in pixel space, which requires the prediction of the impact of interventions on initial conditions. Going beyond the identification of structural relationships, we deal with the challenging problem of forecasting raw video over long horizons. Our…
Zero-shot learning aims at recognizing unseen classes (no training example) with knowledge transferred from seen classes. This is typically achieved by exploiting a semantic feature space shared by both seen and unseen classes, i.e., attribute or word vector, as the bridge. One common practice in zero-shot learning is to train a projection between the visual and semantic feature spaces with labeled seen classes examples. When inferring, this learned projection is applied to unseen classes and recognizes the class labels by some metrics. However, the visual and semantic feature spaces are mutua…
University of Maryland, Baltimore County（马里兰大学巴尔的摩郡分校）；Booz Allen Hamilton（博思艾伦汉密尔顿公司）
We propose a cross-modality manifold alignment procedure that leverages triplet loss to jointly learn consistent, multi-modal embeddings of language-based concepts of real-world items. Our approach learns these embeddings by sampling triples of anchor, positive, and negative data points from RGB-depth images and their natural language descriptions. We show that our approach can benefit from, but does not require, post-processing steps such as Procrustes analysis, in contrast to some of our baselines which require it for reasonable performance. We demonstrate the effectiveness of our approach o…
This paper provides fascinating connections between several mathematical problems which lie on the intersection of several mathematics subjects, namely algebraic geometry, approximation theory, complex-harmonic analysis and high dimensional data science. Modern techniques in algebraic geometry, approximation theory, computational harmonic analysis and extensions develop the first of its kind, a unified framework which allows for a simultaneous study of labeled and unlabeled near alignment data problems in of $\mathbb R^D$ with the near isometry extension problem for discrete and non-discrete s…
We present Contrastive Neighborhood Alignment (CNA), a manifold learning approach to maintain the topology of learned features whereby data points that are mapped to nearby representations by the source (teacher) model are also mapped to neighbors by the target (student) model. The target model aims to mimic the local structure of the source representation space using a contrastive loss. CNA is an unsupervised learning algorithm that does not require ground-truth labels for the individual samples. CNA is illustrated in three scenarios: manifold learning, where the model maintains the local top…
Unsupervised domain mapping has attracted substantial attention in recent years due to the success of models based on the cycle-consistency assumption. These models map between two domains by fooling a probabilistic discriminator, thereby matching the probability distributions of the real and generated data. Instead of this probabilistic approach, we cast the problem in terms of aligning the geometry of the manifolds of the two domains. We introduce the Manifold Geometry Matching Generative Adversarial Network (MGM GAN), which adds two novel mechanisms to facilitate GANs sampling from the geom…
Riemannian Time Warping: Multiple Sequence Alignment in Curved Spaces
Technology and Innovation Center (TIC), KUKA Deutschland GmbH（技术与创新中心（TIC），KUKA德国公司）；Institute of Robotics and Process Control (IRP), Technische Universität Braunschweig（机器人与过程控制研究所（IRP），柏林工业大学）
University Of Maryland Baltimore County (UMBC)（马里兰大学巴尔的摩分校（UMBC））
We present a locality preserving loss (LPL) that improves the alignment between vector space embeddings while separating uncorrelated representations. Given two pretrained embedding manifolds, LPL optimizes a model to project an embedding and maintain its local neighborhood while aligning one manifold to another. This reduces the overall size of the dataset required to align the two in tasks such as cross-lingual word alignment. We show that the LPL-based alignment between input vector spaces acts as a regularizer, leading to better and consistent accuracy than the baseline, especially when th…
