In recent years, substantial progress has been made on Graph Convolutional Networks (GCNs). However, the computing of GCN usually requires a large memory space for keeping the entire graph. In consequence, GCN is not flexible enough, especially for large scale graphs in complex real-world applications. Fortunately, methods based on Matrix Factorization (MF) naturally support constructing mini-batches, and thus are more friendly to distributed computing compared with GCN. Accordingly, in this paper, we analyze the connections between GCN and MF, and simplify GCN as matrix factorization with unitization and co-training. Furthermore, under the guidance of our analysis, we propose an alternative model to GCN named Unitized and Co-training Matrix Factorization (UCMF). Extensive experiments have been conducted on several real-world datasets. On the task of semi-supervised node classification, the experimental results illustrate that UCMF achieves similar or superior performances compared with GCN. Meanwhile, distributed UCMF significantly outperforms distributed GCN methods, which shows that UCMF can greatly benefit large scale and complex real-world applications. Moreover, we have also conducted experiments on a typical task of graph embedding, i.e., community detection, and the proposed UCMF model outperforms several representative graph embedding models.
The paper discusses a pooling mechanism to induce subsampling in graph structured data and introduces it as a component of a graph convolutional neural network. The pooling mechanism builds on the Non-Negative Matrix Factorization (NMF) of a matrix representing node adjacency and node similarity as adaptively obtained through the vertices embedding learned by the model. Such mechanism is applied to obtain an incrementally coarser graph where nodes are adaptively pooled into communities based on the outcomes of the non-negative factorization. The empirical analysis on graph classification bench…
In the pursuit of explaining implicit regularization in deep learning, prominent focus was given to matrix and tensor factorizations, which correspond to simplified neural networks. It was shown that these models exhibit an implicit tendency towards low matrix and tensor ranks, respectively. Drawing closer to practical deep learning, the current paper theoretically analyzes the implicit regularization in hierarchical tensor factorization, a model equivalent to certain deep convolutional neural networks. Through a dynamical systems lens, we overcome challenges associated with hierarchy, and est…
Toyota Technological Institute at Chicago（芝加哥丰田理工学院）；Microsoft Research（微软研究院）
We investigate the problem of factorizing a matrix into several sparse matrices and propose an algorithm for this under randomness and sparsity assumptions. This problem can be viewed as a simplification of the deep learning problem where finding a factorization corresponds to finding edges in different layers and values of hidden units. We prove that under certain assumptions for a sparse linear deep network with $n$ nodes in each layer, our algorithm is able to recover the structure of the network and values of top layer hidden units for depths up to $\tilde O(n^{1/6})$. We further discuss t…
Tensor methods have emerged as a powerful paradigm for consistent learning of many latent variable models such as topic models, independent component analysis and dictionary learning. Model parameters are estimated via CP decomposition of the observed higher order input moments. However, in many domains, additional invariances such as shift invariances exist, enforced via models such as convolutional dictionary learning. In this paper, we develop novel tensor decomposition algorithms for parameter estimation of convolutional models. Our algorithm is based on the popular alternating least squar…
University of Science and Technology（科学技术大学）；Electronics and Telecommunications Research Institute（电子通信研究院）
Convolutional Neural Networks (CNNs) is one of successful method in many areas such as image classification tasks. However, the amount of memory and computational cost needed for CNNs inference obstructs them to run efficiently in mobile devices because of memory and computational ability limitation. One of the method to compress CNNs is compressing the layers iteratively, i.e. by layer-by-layer compression and fine-tuning, with CP-decomposition in convolutional layers. To compress with CP-decomposition, rank selection is important. In the previous approach rank selection that is based on sens…
China University of Petroleum（中国石油大学）；East China Jiaotong University（华东交通大学）；Federation University Australia（澳大利亚联邦大学）
Sparsity of user-to-item rating data becomes one of challenging issues in the recommender systems, which severely deteriorates the recommendation performance. Fortunately, context-aware recommender systems can alleviate the sparsity problem by making use of some auxiliary information, such as the information of both the users and items. In particular, the visual information of items, such as the movie poster, can be considered as the supplement for item description documents, which helps to obtain more item features. In this paper, we focus on movie recommender system and propose a probabilist…
China University of Petroleum（中国石油大学）；Minjiang University（闽江学院）；Dalian University of Technology（大连理工大学）；Federation University Australia（澳大利亚联邦大学）
The rapid growth of edge data generated by mobile devices and applications deployed at the edge of the network has exacerbated the problem of information overload. As an effective way to alleviate information overload, recommender system can improve the quality of various services by adding application data generated by users on edge devices, such as visual and textual information, on the basis of sparse rating data. The visual information in the movie trailer is a significant part of the movie recommender system. However, due to the complexity of visual information extraction, data sparsity c…
Moscow State University（莫斯科国立大学）；Yandex；National Research University Higher School of Economics（国家研究型大学高等经济学院）；Institute of Numerical Mathematics of the Russian Academy of Sciences（俄罗斯科学院数值数学研究所）
Convolutional neural networks excel in image recognition tasks, but this comes at the cost of high computational and memory complexity. To tackle this problem, [1] developed a tensor factorization framework to compress fully-connected layers. In this paper, we focus on compressing convolutional layers. We show that while the direct application of the tensor framework [1] to the 4-dimensional kernel of convolution does compress the layer, we can do better. We reshape the convolutional kernel into a tensor of higher order and factorize it. We combine the proposed approach with the previous work …
Machine Learning Department, Carnegie Mellon University（卡内基梅隆大学机器学习系）；Department of Computer Science, University of Texas at Austin（德克萨斯大学奥斯汀分校计算机科学系）
We propose a new algorithm to learn a one-hidden-layer convolutional neural network where both the convolutional weights and the outputs weights are parameters to be learned. Our algorithm works for a general class of (potentially overlapping) patches, including commonly used structures for computer vision tasks. Our algorithm draws ideas from (1) isotonic regression for learning neural networks and (2) landscape analysis of non-convex matrix factorization problems. We believe these findings may inspire further development in designing provable algorithms for learning neural networks and other…
We recover a video of the motion taking place in a hidden scene by observing changes in indirect illumination in a nearby uncalibrated visible region. We solve this problem by factoring the observed video into a matrix product between the unknown hidden scene video and an unknown light transport matrix. This task is extremely ill-posed, as any non-negative factorization will satisfy the data. Inspired by recent work on the Deep Image Prior, we parameterize the factor matrices using randomly initialized convolutional neural networks trained in a one-off manner, and show that this results in dec…
University of Science and Technology of China（中国科学技术大学）；Nanjing University of Science and Technology（南京理工大学）；University of Electronic Science and Technology of China（电子科技大学）；Hefei University of Technology（合肥工业大学）；Nanjing University（南京大学）；National University of Singapore（新加坡国立大学）
Matrix factorization (MF) has been widely used to discover the low-rank structure and to predict the missing entries of data matrix. In many real-world learning systems, the data matrix can be very high-dimensional but sparse. This poses an imbalanced learning problem, since the scale of missing entries is usually much larger than that of observed entries, but they cannot be ignored due to the valuable negative signal. For efficiency concern, existing work typically applies a uniform weight on missing entries to allow a fast learning algorithm. However, this simplification will decrease modeli…
Supervised Deep Multimodal Matrix Factorization for Interpretable Brain Network Analysis
Dept. of Mathematics & Operational Research University of Mons（数学与运筹学系蒙斯大学）；Dept. of Computer Science & Engineering Lehigh University（计算机科学与工程系莱斯大学）；Dept. of Industrial & Systems Engineering Lehigh University（工业与系统工程系莱斯大学）
Elasticities in depth, width, kernel size and resolution have been explored in compressing deep neural networks (DNNs). Recognizing that the kernels in a convolutional neural network (CNN) are 4-way tensors, we further exploit a new elasticity dimension along the input-output channels. Specifically, a novel nuclear-norm rank minimization factorization (NRMF) approach is proposed to dynamically and globally search for the reduced tensor ranks during training. Correlation between tensor ranks across multiple layers is revealed, and a graceful tradeoff between model size and accuracy is obtained.…
University of Sheffield（谢菲尔德大学）；University of Bristol（布里斯托大学）；Amazon Inc.（亚马逊公司）；Google Inc.（谷歌公司）
Cross-domain recommendation (CDR) can help customers find more satisfying items in different domains. Existing CDR models mainly use common users or mapping functions as bridges between domains but have very limited exploration in fully utilizing extra knowledge across domains. In this paper, we propose to incorporate the knowledge graph (KG) for CDR, which enables items in different domains to share knowledge. To this end, we first construct a new dataset AmazonKG4CDR from the Freebase KG and a subset (two domain pairs: movies-music, movie-book) of Amazon Review Data. This new dataset facilit…
Samsung Electronics（三星电子）；Seoul National University（首尔国立大学）
Although the latest high-end smartphone has powerful CPU and GPU, running deeper convolutional neural networks (CNNs) for complex tasks such as ImageNet classification on mobile devices is challenging. To deploy deep CNNs on mobile devices, we present a simple and effective scheme to compress the entire CNN, which we call one-shot whole network compression. The proposed scheme consists of three steps: (1) rank selection with variational Bayesian matrix factorization, (2) Tucker decomposition on kernel tensor, and (3) fine-tuning to recover accumulated loss of accuracy, and each step can be eas…
Deep convolutional neural networks (CNN) has become the most promising method for object recognition, repeatedly demonstrating record breaking results for image classification and object detection in recent years. However, a very deep CNN generally involves many layers with millions of parameters, making the storage of the network model to be extremely large. This prohibits the usage of deep CNNs on resource limited hardware, especially cell phones or other embedded devices. In this paper, we tackle this model storage issue by investigating information theoretical vector quantization methods f…
Qualcomm AI Research（高通人工智能研究院）；Qualcomm Technologies Netherlands B.V.（高通技术荷兰有限公司）；Qualcomm Technologies, Inc.（高通技术公司）
The success of deep neural networks in many real-world applications is leading to new challenges in building more efficient architectures. One effective way of making networks more efficient is neural network compression. We provide an overview of existing neural network compression methods that can be used to make neural networks more efficient by changing the architecture of the network. First, we introduce a new way to categorize all published compression methods, based on the amount of data and compute needed to make the methods work in practice. These are three 'levels of compression solu…
The University of Hong Kong（香港大学）；McGill University（麦吉尔大学）
Missing data is an inevitable and ubiquitous problem for traffic data collection in intelligent transportation systems. Despite extensive research regarding traffic data imputation, there still exist two limitations to be addressed: first, existing approaches fail to capture the complex spatiotemporal dependencies in traffic data, especially the dynamic spatial dependencies evolving with time; second, prior studies mainly focus on randomly missing patterns while other more complex missing scenarios are less discussed. To fill these research gaps, we propose a novel deep learning framework call…
Technion-Israel Institute of Technology（以色列理工学院）；Stanford University（斯坦福大学）
The recently proposed Multi-Layer Convolutional Sparse Coding (ML-CSC) model, consisting of a cascade of convolutional sparse layers, provides a new interpretation of Convolutional Neural Networks (CNNs). Under this framework, the computation of the forward pass in a CNN is equivalent to a pursuit algorithm aiming to estimate the nested sparse representation vectors -- or feature maps -- from a given input signal. Despite having served as a pivotal connection between CNNs and sparse modeling, a deeper understanding of the ML-CSC is still lacking: there are no pursuit algorithms that can serve …
Simula Metropolitan Center for Digital Engineering（Simula大都会数字工程中心）；UMBC（马里兰大学巴尔的摩郡分校）；Georgia State University（佐治亚州立大学）
Characterizing time-evolving networks is a challenging task, but it is crucial for understanding the dynamic behavior of complex systems such as the brain. For instance, how spatial networks of functional connectivity in the brain evolve during a task is not well-understood. A traditional approach in neuroimaging data analysis is to make simplifications through the assumption of static spatial networks. In this paper, without assuming static networks in time and/or space, we arrange the temporal data as a higher-order tensor and use a tensor factorization model called PARAFAC2 to capture under…
Beijing Institute of Technology（北京理工大学）；University of Technology Sydney（悉尼科技大学）
Network alignment is a critical task to a wide variety of fields. Many existing works leverage on representation learning to accomplish this task without eliminating domain representation bias induced by domain-dependent features, which yield inferior alignment performance. This paper proposes a unified deep architecture (DANA) to obtain a domain-invariant representation for network alignment via an adversarial domain classifier. Specifically, we employ the graph convolutional networks to perform network embedding under the domain adversarial principle, given a small set of observed anchors. T…
Faculty of Medicine and Health Technology, Tampere University（坦佩雷大学医学院与健康技术学院）
Twitter has been a prominent social media platform for mining population-level health data and accurate clustering of health-related tweets into topics is important for extracting relevant health insights. In this work, we propose deep convolutional autoencoders for learning compact representations of health-related tweets, further to be employed in clustering. We compare our method to several conventional tweet representation methods including bag-of-words, term frequency-inverse document frequency, Latent Dirichlet Allocation and Non-negative Matrix Factorization with 3 different clustering …
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…
IQIVA Inc.（艾昆纬公司）；University of Minnesota（明尼苏达大学）；University of Chicago（芝加哥大学）
Models have been proposed to extract temporal patterns from longitudinal electronic health records (EHR) for clinical predictive models. However, the common relations among patients (e.g., receiving the same medical treatments) were rarely considered. In this paper, we propose to learn patient similarity features as phenotypes from the aggregated patient-medical service matrix using non-negative matrix factorization. On real-world medical claim data, we show that the learned phenotypes are coherent within each group, and also explanatory and indicative of targeted diseases. We conducted experi…
In this paper, we consider the Click-Through-Rate (CTR) prediction problem. Factorization Machines and their variants consider pair-wise feature interactions, but normally we won't do high-order feature interactions using FM due to high time complexity. Given the success of deep neural networks (DNNs) in many fields, researchers have proposed several DNN-based models to learn high-order feature interactions. Multi-layer perceptrons (MLP) have been widely employed to learn reliable mappings from feature embeddings to final logits. In this paper, we aim to explore more about these high-order fea…
The network embedding problem that maps nodes in a graph to vectors in Euclidean space can be very useful for addressing several important tasks on a graph. Recently, graph neural networks (GNNs) have been proposed for solving such a problem. However, most embedding algorithms and GNNs are difficult to interpret and do not scale well to handle millions of nodes. In this paper, we tackle the problem from a new perspective based on the equivalence of three constrained optimization problems: the network embedding problem, the trace maximization problem of the modularity matrix in a sampled graph,…
