t-distributed Stochastic Neighborhood Embedding (t-SNE) is a method for dimensionality reduction and visualization that has become widely popular in recent years. Efficient implementations of t-SNE are available, but they scale poorly to datasets with hundreds of thousands to millions of high dimensional data-points. We present Fast Fourier Transform-accelerated Interpolation-based t-SNE (FIt-SNE), which dramatically accelerates the computation of t-SNE. The most time-consuming step of t-SNE is a convolution that we accelerate by interpolating onto an equispaced grid and subsequently using the fast Fourier transform to perform the convolution. We also optimize the computation of input similarities in high dimensions using multi-threaded approximate nearest neighbors. We further present a modification to t-SNE called "late exaggeration," which allows for easier identification of clusters in t-SNE embeddings. Finally, for datasets that cannot be loaded into the memory, we present out-of-core randomized principal component analysis (oocPCA), so that the top principal components of a dataset can be computed without ever fully loading the matrix, hence allowing for t-SNE of large datasets to be computed on resource-limited machines.
Local graph neighborhood sampling is a fundamental computational problem that is at the heart of algorithms for node representation learning. Several works have presented algorithms for learning discrete node embeddings where graph nodes are represented by discrete features such as attributes of neighborhood nodes. Discrete embeddings offer several advantages compared to continuous word2vec-like node embeddings: ease of computation, scalability, and interpretability. We present LoNe Sampler, a suite of algorithms for generating discrete node embeddings by Local Neighborhood Sampling, and addre…
Network embedding is an effective method to learn low-dimensional representations of nodes, which can be applied to various real-life applications such as visualization, node classification, and link prediction. Although significant progress has been made on this problem in recent years, several important challenges remain, such as how to properly capture temporal information in evolving networks. In practice, most networks are continually evolving. Some networks only add new edges or nodes such as authorship networks, while others support removal of nodes or edges such as internet data routin…
We consider the problem of learning latent features (aka embedding) for users and items in a recommendation setting. Given only a user-item interaction graph, the goal is to recommend items for each user. Traditional approaches employ matrix factorization-based collaborative filtering methods. Recent methods using graph convolutional networks (e.g., LightGCN) achieve state-of-the-art performance. They learn both user and item embedding. One major drawback of most existing methods is that they are not inductive; they do not generalize for users and items unseen during training. Besides, existin…
This is a tutorial and survey paper for Locally Linear Embedding (LLE) and its variants. The idea of LLE is fitting the local structure of manifold in the embedding space. In this paper, we first cover LLE, kernel LLE, inverse LLE, and feature fusion with LLE. Then, we cover out-of-sample embedding using linear reconstruction, eigenfunctions, and kernel mapping. Incremental LLE is explained for embedding streaming data. Landmark LLE methods using the Nystrom approximation and locally linear landmarks are explained for big data embedding. We introduce the methods for parameter selection of numb…
Conventional representation learning algorithms for knowledge graphs (KG) map each entity to a unique embedding vector, ignoring the rich information contained in the neighborhood. We propose a method named StarGraph, which gives a novel way to utilize the neighborhood information for large-scale knowledge graphs to obtain entity representations. An incomplete two-hop neighborhood subgraph for each target node is at first generated, then processed by a modified self-attention network to obtain the entity representation, which is used to replace the entity embedding in conventional methods. We …
Numerous dimensionality reduction problems in data analysis involve the recovery of low-dimensional models or the learning of manifolds underlying sets of data. Many manifold learning methods require the estimation of the tangent space of the manifold at a point from locally available data samples. Local sampling conditions such as (i) the size of the neighborhood (sampling width) and (ii) the number of samples in the neighborhood (sampling density) affect the performance of learning algorithms. In this work, we propose a theoretical analysis of local sampling conditions for the estimation of …
Stanford University（斯坦福大学）；Renmin University of China（中国人民大学）
Understanding intrinsic patterns and predicting spatiotemporal characteristics of cities require a comprehensive representation of urban neighborhoods. Existing works relied on either inter- or intra-region connectivities to generate neighborhood representations but failed to fully utilize the informative yet heterogeneous data within neighborhoods. In this work, we propose Urban2Vec, an unsupervised multi-modal framework which incorporates both street view imagery and point-of-interest (POI) data to learn neighborhood embeddings. Specifically, we use a convolutional neural network to extract …
In this paper, we propose a Tensor Train Neighborhood Preserving Embedding (TTNPE) to embed multi-dimensional tensor data into low dimensional tensor subspace. Novel approaches to solve the optimization problem in TTNPE are proposed. For this embedding, we evaluate novel trade-off gain among classification, computation, and dimensionality reduction (storage) for supervised learning. It is shown that compared to the state-of-the-arts tensor embedding methods, TTNPE achieves superior trade-off in classification, computation, and dimensionality reduction in MNIST handwritten digits and Weizmann f…
Topic models are frequently used in machine learning owing to their high interpretability and modular structure. However, extending a topic model to include a supervisory signal, to incorporate pre-trained word embedding vectors and to include a nonlinear output function is not an easy task because one has to resort to a highly intricate approximate inference procedure. The present paper shows that topic modeling with pre-trained word embedding vectors can be viewed as implementing a neighborhood aggregation algorithm where messages are passed through a network defined over words. From the net…
Entity alignment aims at integrating heterogeneous knowledge from different knowledge graphs. Recent studies employ embedding-based methods by first learning the representation of Knowledge Graphs and then performing entity alignment via measuring the similarity between entity embeddings. However, they failed to make good use of the relation semantic information due to the trade-off problem caused by the different objectives of learning knowledge embedding and neighborhood consensus. To address this problem, we propose Relational Knowledge Distillation for Entity Alignment (RKDEA), a Graph Con…
Graph Neural Networks (GNNs) learn low dimensional representations of nodes by aggregating information from their neighborhood in graphs. However, traditional GNNs suffer from two fundamental shortcomings due to their local ($l$-hop neighborhood) aggregation scheme. First, not all nodes in the neighborhood carry relevant information for the target node. Since GNNs do not exclude noisy nodes in their neighborhood, irrelevant information gets aggregated, which reduces the quality of the representation. Second, traditional GNNs also fail to capture long-range non-local dependencies between nodes.…
Keyphrase extraction is the task of finding several interesting phrases in a text document, which provide a list of the main topics within the document. Most existing graph-based models use co-occurrence links as cohesion indicators to model the relationship of syntactic elements. However, a word may have different forms of expression within the document, and may have several synonyms as well. Simply using co-occurrence information cannot capture this information. In this paper, we enhance the graph-based ranking model by leveraging word embeddings as background knowledge to add semantic infor…
Embeddings mapping high-dimensional discrete input to lower-dimensional continuous vector spaces have been widely adopted in machine learning applications as a way to capture domain semantics. Interviewing 13 embedding users across disciplines, we find comparing embeddings is a key task for deployment or downstream analysis but unfolds in a tedious fashion that poorly supports systematic exploration. In response, we present the Embedding Comparator, an interactive system that presents a global comparison of embedding spaces alongside fine-grained inspection of local neighborhoods. It systemati…
Neighborhood-Adaptive Generalized Linear Graph Embedding with Latent Pattern Mining
School of Computer and Information, Anhui Normal University（安徽师范大学计算机与信息学院）；Anhui Provincial Key Laboratory of Industrial Intelligent Data Security（安徽省工业智能数据安全重点实验室）；Institute of Automation, State Key Laboratory of Multimodal Artificial Intelligence Systems, Chinese Academy of Sciences（自动化研究所，多模态人工智能系统国家重点实验室，中国科学院）；School of Artificial Intelligence, University of Chinese Academy of Sciences（中国科学院大学人工智能学院）
For a large multi-hop wireless network, nodes are preferable to make distributed and localized link-scheduling decisions with only interactions among a small number of neighbors. However, for a slowly decaying channel and densely populated interferers, a small size neighborhood often results in nontrivial link outages and is thus insufficient for making optimal scheduling decisions. A question arises how to deal with the information outside a neighborhood in distributed link-scheduling. In this work, we develop joint approximation of information and distributed link scheduling. We first apply …
University of Passau（帕绍大学）；Technical University of Munich（慕尼黑工业大学）
Graph embedding has recently gained momentum in the research community, in particular after the introduction of random walk and neural network based approaches. However, most of the embedding approaches focus on representing the local neighborhood of nodes and fail to capture the global graph structure, i.e. to retain the relations to distant nodes. To counter that problem, we propose a novel extension to random walk based graph embedding, which removes a percentage of least frequent nodes from the walks at different levels. By this removal, we simulate farther distant nodes to reside in the c…
Point clouds have been widely adopted in 3D semantic scene understanding. However, point clouds for typical tasks such as 3D shape segmentation or indoor scenario parsing are much denser than outdoor LiDAR sweeps for the application of autonomous driving perception. Due to the spatial property disparity, many successful methods designed for dense point clouds behave depreciated effectiveness on the sparse data. In this paper, we focus on the semantic segmentation task of sparse outdoor point clouds. We propose a new method called MNEW, including multi-domain neighborhood embedding, and attenti…
We consider the question of embedding nodes with similar local neighborhoods together in embedding space, commonly referred to as "role embeddings." We propose RAE, an unsupervised framework that learns role embeddings. It combines a within-node loss function and a graph neural network (GNN) architecture to place nodes with similar local neighborhoods close in embedding space. We also propose a faster way of generating negative examples called neighbor shuffling, which quickly creates negative examples directly within batches. These techniques can be easily combined with existing GNN methods t…
Ferdowsi University of Mashhad（马什哈德费尔多西大学）；Center of Excellence in Soft Computing and Intelligent Information Processing, Ferdowsi University of Mashhad（马什哈德费尔多西大学软计算与智能信息处理卓越中心）
University of Rochester（罗切斯特大学）；KAUST, Saudi Arabia（沙特国王科技大学）；University of Michigan（密歇根大学）；Alibaba Group（阿里巴巴集团）；Tencent AI lab（腾讯AI实验室）
Graph embedding is a central problem in social network analysis and many other applications, aiming to learn the vector representation for each node. While most existing approaches need to specify the neighborhood and the dependence form to the neighborhood, which may significantly degrades the flexibility of representation, we propose a novel graph node embedding method (namely GESF) via the set function technique. Our method can 1) learn an arbitrary form of representation function from neighborhood, 2) automatically decide the significance of neighbors at different distances, and 3) be appl…
Recent urbanization has coincided with the enrichment of geotagged data, such as street view and point-of-interest (POI). Region embedding enhanced by the richer data modalities has enabled researchers and city administrators to understand the built environment, socioeconomics, and the dynamics of cities better. While some efforts have been made to simultaneously use multi-modal inputs, existing methods can be improved by incorporating different measures of 'proximity' in the same embedding space - leveraging not only the data that characterizes the regions (e.g., street view, local businesses…
In a traditional setting, classifiers are trained to approximate a target function $f:X \rightarrow Y$ where at least a sample for each $y \in Y$ is presented to the training algorithm. In a zero-shot setting we have a subset of the labels $\hat{Y} \subset Y$ for which we do not observe any corresponding training instance. Still, the function $f$ that we train must be able to correctly assign labels also on $\hat{Y}$. In practice, zero-shot problems are very important especially when the label set is large and the cost of editorially label samples for all possible values in the label set might…
Feinberg School of Medicine（Feinberg医学院）；Northwestern University（西北大学）
Graph Neural Network (GNN) aggregates the neighborhood of each node into the node embedding and shows its powerful capability for graph representation learning. However, most existing GNN variants aggregate the neighborhood information in a fixed non-injective fashion, which may map different graphs or nodes to the same embedding, reducing the model expressiveness. We present a theoretical framework to design a continuous injective set function for neighborhood aggregation in GNN. Using the framework, we propose expressive GNN that aggregates the neighborhood of each node with a continuous inj…
University of Michigan（密歇根大学）；The Hebrew University of Jerusalem（耶路撒冷希伯来大学）
We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance matrix, which can be computationally intensive in large dimensions. Approximate inference based on message-passing algorithms, on the other hand, can lead to unstable and biased estimation in loopy graphical models. In this paper, we propose a general framework for distributed estimation based on a maximum marginal likelihood (MML) approach. This approach compute…
Rethinking Pre-Training in Tabular Data: A Neighborhood Embedding Perspective
School of Artificial Intelligence, Nanjing University（南京大学人工智能学院）；The Ohio State University（俄亥俄州立大学）；China National Key Laboratory for Novel Software Technology（计算机软件新技术国家重点实验室）
Deep neural networks often require copious amount of labeled-data to train their scads of parameters. Training larger and deeper networks is hard without appropriate regularization, particularly while using a small dataset. Laterally, collecting well-annotated data is expensive, time-consuming and often infeasible. A popular way to regularize these networks is to simply train the network with more data from an alternate representative dataset. This can lead to adverse effects if the statistics of the representative dataset are dissimilar to our target. This predicament is due to the problem of…
Representation learning for graphs enables the application of standard machine learning algorithms and data analysis tools to graph data. Replacing discrete unordered objects such as graph nodes by real-valued vectors is at the heart of many approaches to learning from graph data. Such vector representations, or embeddings, capture the discrete relationships in the original data by representing nodes as vectors in a high-dimensional space. In most applications graphs model the relationship between real-life objects and often nodes contain valuable meta-information about the original objects. W…
The University of Edinburgh（爱丁堡大学）；School of Informatics（信息学院）
We present network embedding algorithms that capture information about a node from the local distribution over node attributes around it, as observed over random walks following an approach similar to Skip-gram. Observations from neighborhoods of different sizes are either pooled (AE) or encoded distinctly in a multi-scale approach (MUSAE). Capturing attribute-neighborhood relationships over multiple scales is useful for a diverse range of applications, including latent feature identification across disconnected networks with similar attributes. We prove theoretically that matrices of node-fea…
In recent years it has become popular to study machine learning problems in a setting of ordinal distance information rather than numerical distance measurements. By ordinal distance information we refer to binary answers to distance comparisons such as $d(A,B)<d(C,D)$. For many problems in machine learning and statistics it is unclear how to solve them in such a scenario. Up to now, the main approach is to explicitly construct an ordinal embedding of the data points in the Euclidean space, an approach that has a number of drawbacks. In this paper, we propose algorithms for the problems of med…
Beckman Institute, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校贝克曼研究所）；Adobe Research（奥多比研究院）
Classifying large-scale image data into object categories is an important problem that has received increasing research attention. Given the huge amount of data, non-parametric approaches such as nearest neighbor classifiers have shown promising results, especially when they are underpinned by a learned distance or similarity measurement. Although metric learning has been well studied in the past decades, most existing algorithms are impractical to handle large-scale data sets. In this paper, we present an image similarity learning method that can scale well in both the number of images and th…
Network alignment, the process of finding correspondences between nodes in different graphs, has many scientific and industrial applications. Existing unsupervised network alignment methods find suboptimal alignments that break up node neighborhoods, i.e. do not preserve matched neighborhood consistency. To improve this, we propose CONE-Align, which models intra-network proximity with node embeddings and uses them to match nodes across networks after aligning the embedding subspaces. Experiments on diverse, challenging datasets show that CONE-Align is robust and obtains 19.25% greater accuracy…
Indian Institute of Technology Hyderabad（印度理工学院海得拉巴分校）
Several state-of-the-art neural graph embedding methods are based on short random walks (stochastic processes) because of their ease of computation, simplicity in capturing complex local graph properties, scalability, and interpretibility. In this work, we are interested in studying how much a probabilistic bias in this stochastic process affects the quality of the nodes picked by the process. In particular, our biased walk, with a certain probability, favors movement towards nodes whose neighborhoods bear a structural resemblance to the current node's neighborhood. We succinctly capture this …
Sun Yat-Sen University（中山大学）；University of Science and Technology of China（中国科学技术大学）；Pazhou Lab（琶洲实验室）
This paper aims to solve a distributed learning problem under Byzantine attacks. In the underlying distributed system, a number of unknown but malicious workers (termed as Byzantine workers) can send arbitrary messages to the master and bias the learning process, due to data corruptions, computation errors or malicious attacks. Prior work has considered a total variation (TV) norm-penalized approximation formulation to handle the Byzantine attacks, where the TV norm penalty forces the regular workers' local variables to be close, and meanwhile, tolerates the outliers sent by the Byzantine work…
NEC Labs America（美国NEC实验室）；National Research Council Canada（加拿大国家研究委员会）；Duke University（杜克大学）
Parametric embedding methods such as parametric t-SNE (pt-SNE) have been widely adopted for data visualization and out-of-sample data embedding without further computationally expensive optimization or approximation. However, the performance of pt-SNE is highly sensitive to the hyper-parameter batch size due to conflicting optimization goals, and often produces dramatically different embeddings with different choices of user-defined perplexities. To effectively solve these issues, we present parametric t-distributed stochastic exemplar-centered embedding methods. Our strategy learns embedding …
Recent successes in word embedding and document embedding have motivated researchers to explore similar representations for networks and to use such representations for tasks such as edge prediction, node label prediction, and community detection. Such network embedding methods are largely focused on finding distributed representations for unsigned networks and are unable to discover embeddings that respect polarities inherent in edges. We propose SIGNet, a fast scalable embedding method suitable for signed networks. Our proposed objective function aims to carefully model the social structure …
On the Two Sides of Redundancy in Graph Neural Networks
Faculty of Computer Science, University of Vienna（维也纳大学计算机科学学院）；UniVie Doctoral School Computer Science, University of Vienna（维也纳大学UniVie计算机科学博士学院）；Simula Research Laboratory（Simula研究实验室）；Research Network Data Science, University of Vienna（维也纳大学数据科学研究网络）
The University of Texas at Austin（得克萨斯大学奥斯汀分校）；Microsoft Research（微软研究院）
Many applications today, such as NLP, network analysis, and code analysis, rely on semantically embedding objects into low-dimensional fixed-length vectors. Such embeddings naturally provide a way to perform useful downstream tasks, such as identifying relations among objects or predicting objects for a given context, etc. Unfortunately, the training necessary for accurate embeddings is usually computationally intensive and requires processing large amounts of data. Furthermore, distributing this training is challenging. Most embedding training uses stochastic gradient descent (SGD), an "inher…
Embedding models have been an effective learning paradigm for high-dimensional data. However, one open issue of embedding models is that their representations (latent factors) often result in large parameter space. We observe that existing distributed training frameworks face a scalability issue of embedding models since updating and retrieving the shared embedding parameters from servers usually dominates the training cycle. In this paper, we propose HET, a new system framework that significantly improves the scalability of huge embedding model training. We embrace skewed popularity distribut…
University of Virginia（弗吉尼亚大学）；Microsoft Research（微软研究院）；Microsoft Bing Ads（微软必应广告）
This paper examines the challenging problem of learning representations of entities and relations in a complex multi-relational knowledge graph. We propose HittER, a Hierarchical Transformer model to jointly learn Entity-relation composition and Relational contextualization based on a source entity's neighborhood. Our proposed model consists of two different Transformer blocks: the bottom block extracts features of each entity-relation pair in the local neighborhood of the source entity and the top block aggregates the relational information from outputs of the bottom block. We further design …
Distributed word representations (word embeddings) have recently contributed to competitive performance in language modeling and several NLP tasks. In this work, we train word embeddings for more than 100 languages using their corresponding Wikipedias. We quantitatively demonstrate the utility of our word embeddings by using them as the sole features for training a part of speech tagger for a subset of these languages. We find their performance to be competitive with near state-of-art methods in English, Danish and Swedish. Moreover, we investigate the semantic features captured by these embed…
University of Maryland Baltimore County（马里兰大学巴尔的摩县分校）；Atypon Systems（Atypon系统公司）
Word embedding models such as the skip-gram learn vector representations of words' semantic relationships, and document embedding models learn similar representations for documents. On the other hand, topic models provide latent representations of the documents' topical themes. To get the benefits of these representations simultaneously, we propose a unifying algorithm, called neural embedding allocation (NEA), which deconstructs topic models into interpretable vector-space embeddings of words, topics, documents, authors, and so on, by learning neural embeddings to mimic the topic models. We s…
Can GNNs Learn Link Heuristics? A Concise Review and Evaluation of Link Prediction Methods
Faculty of Engineering and Information Technology, University of Technology Sydney（工程与信息技术学院，悉尼大学）；Faculty of Engineering and Information Sciences, University of Wollongong（工程与信息科学学院，沃林戈大学）；College of Electrical Engineering, Zhejiang University（电气工程学院，浙江大学）
