Neural collaborative filtering (NCF) and recurrent recommender systems (RRN) have been successful in modeling user-item relational data. However, they are also limited in their assumption of static or sequential modeling of relational data as they do not account for evolving users' preference over time as well as changes in the underlying factors that drive the change in user-item relationship over time. We address these limitations by proposing a Neural Tensor Factorization (NTF) model for predictive tasks on dynamic relational data. The NTF model generalizes conventional tensor factorization from two perspectives: First, it leverages the long short-term memory architecture to characterize the multi-dimensional temporal interactions on relational data. Second, it incorporates the multi-layer perceptron structure for learning the non-linearities between different latent factors. Our extensive experiments demonstrate the significant improvement in rating prediction and link prediction on dynamic relational data by our NTF model over both neural network based factorization models and other traditional methods.
What is the Relationship between Tensor Factorizations and Circuits (and How Can We Exploit it)?
School of Informatics, University of Edinburgh（爱丁堡大学信息学院）；École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；Eindhoven University of Technology（埃因霍温理工大学）；Graz University of Technology（格拉茨工业大学）；University of Bari Aldo Moro（巴里大学 Aldo Moro）
University of Science and Technology of China（中国科学技术大学）
Tensor factorization based models have shown great power in knowledge graph completion (KGC). However, their performance usually suffers from the overfitting problem seriously. This motivates various regularizers -- such as the squared Frobenius norm and tensor nuclear norm regularizers -- while the limited applicability significantly limits their practical usage. To address this challenge, we propose a novel regularizer -- namely, DUality-induced RegulArizer (DURA) -- which is not only effective in improving the performance of existing models but widely applicable to various methods. The majo…
Georgia Institute of Technology（佐治亚理工学院）；Hong Kong Baptist University（香港浸会大学）；Sutter Health（萨特健康医疗集团）；IQVIA（艾昆纬公司）；Emory University（埃默里大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Existing tensor factorization methods assume that the input tensor follows some specific distribution (i.e. Poisson, Bernoulli, and Gaussian), and solve the factorization by minimizing some empirical loss functions defined based on the corresponding distribution. However, it suffers from several drawbacks: 1) In reality, the underlying distributions are complicated and unknown, making it infeasible to be approximated by a simple distribution. 2) The correlation across dimensions of the input tensor is not well utilized, leading to sub-optimal performance. Although heuristics were proposed to i…
Tensor factorization arises in many machine learning applications, such knowledge base modeling and parameter estimation in latent variable models. However, numerical methods for tensor factorization have not reached the level of maturity of matrix factorization methods. In this paper, we propose a new method for CP tensor factorization that uses random projections to reduce the problem to simultaneous matrix diagonalization. Our method is conceptually simple and also applies to non-orthogonal and asymmetric tensors of arbitrary order. We prove that a small number random projections essentiall…
Microsoft（微软）；Xidian University（西安电子科技大学）；Emory University（埃默里大学）；Health Science Center of University of Texas（德克萨斯大学健康科学中心）；Emory School of Medicine（埃默里医学院）
Tensor factorization has received increasing interest due to its intrinsic ability to capture latent factors in multi-dimensional data with many applications such as recommender systems and Electronic Health Records (EHR) mining. PARAFAC2 and its variants have been proposed to address irregular tensors where one of the tensor modes is not aligned, e.g., different users in recommender systems or patients in EHRs may have different length of records. PARAFAC2 has been successfully applied on EHRs for extracting meaningful medical concepts (phenotypes). Despite recent advancements, current models…
In this paper, we present our work on clustering and prediction of temporal dynamics of global congestion configurations in large-scale road networks. Instead of looking into temporal traffic state variation of individual links, or of small areas, we focus on spatial congestion configurations of the whole network. In our work, we aim at describing the typical temporal dynamic patterns of this network-level traffic state and achieving long-term prediction of the large-scale traffic dynamics, in a unified data-mining framework. To this end, we formulate this joint task using Non-negative Tensor …
New Jersey Institute of Technology（新泽西理工学院）；Central Michigan University（中密歇根大学）
Firms earning prediction plays a vital role in investment decisions, dividends expectation, and share price. It often involves multiple tensor-compatible datasets with non-linear multi-way relationships, spatiotemporal structures, and different levels of sparsity. Current non-linear tensor completion algorithms tend to learn noisy embedding and incur overfitting. This paper focuses on the embedding learning aspect of the tensor completion problem and proposes a new multi-layer neural network architecture for tensor factorization and completion (MLCTR). The network architecture entails multiple…
Northwestern University Feinberg School of Medicine（西北大学范伯格医学院）
Background: The increasing adoption of electronic health records (EHR) across the US has created troves of computable data, to which machine learning methods have been applied to extract useful insights. EHR data, represented as a three-dimensional analogue of a matrix (tensor), is decomposed into two-dimensional factors that can be interpreted as computational phenotypes. Methods: We apply constrained tensor factorization to derive computational phenotypes and predict mortality in cohorts of patients with breast, prostate, colorectal, or lung cancer in the Northwestern Medicine Enterprise Dat…
Xidian University（西安电子科技大学）；Chongqing University of Posts and Telecommunications（重庆邮电大学）
Multi-view clustering (MVC) based on non-negative matrix factorization (NMF) and its variants have received a huge amount of attention in recent years due to their advantages in clustering interpretability. However, existing NMF-based multi-view clustering methods perform NMF on each view data respectively and ignore the impact of between-view. Thus, they can't well exploit the within-view spatial structure and between-view complementary information. To resolve this issue, we present semi-non-negative tensor factorization (Semi-NTF) and develop a novel multi-view clustering based on Semi-NTF w…
Representation learning on static graph-structured data has shown a significant impact on many real-world applications. However, less attention has been paid to the evolving nature of temporal networks, in which the edges are often changing over time. The embeddings of such temporal networks should encode both graph-structured information and the temporally evolving pattern. Existing approaches in learning temporally evolving network representations fail to capture the temporal interdependence. In this paper, we propose Toffee, a novel approach for temporal network representation learning base…
Ludwig Maximilian University（路德维希-马克西米利安大学）；Siemens AG（西门子股份公司）
Tensor factorizations have become increasingly popular approaches for various learning tasks on structured data. In this work, we extend the RESCAL tensor factorization, which has shown state-of-the-art results for multi-relational learning, to account for the binary nature of adjacency tensors. We study the improvements that can be gained via this approach on various benchmark datasets and show that the logistic extension can improve the prediction results significantly.
IBM Research（IBM研究院）；University of Texas at Austin（德克萨斯大学奥斯汀分校）；University of Rochester（罗切斯特大学）
Identifying significant location categories visited by mobile users is the key to a variety of applications. This is an extremely challenging task due to the possible deviation between the estimated location coordinate and the actual location, which could be on the order of kilometers. To estimate the actual location category more precisely, we propose a novel tensor factorization framework, through several key observations including the intrinsic correlations between users, to infer the most likely location categories within the location uncertainty circle. In addition, the proposed algorithm…
Tensor factorization has been proved as an efficient unsupervised learning approach for health data analysis, especially for computational phenotyping, where the high-dimensional Electronic Health Records (EHRs) with patients' history of medical procedures, medications, diagnosis, lab tests, etc., are converted to meaningful and interpretable medical concepts. Federated tensor factorization distributes the tensor computation to multiple workers under the coordination of a central server, which enables jointly learning the phenotypes across multiple hospitals while preserving the privacy of the…
Probabilistic Temporal Tensor Factorization (PTTF) is an effective algorithm to model the temporal tensor data. It leverages a time constraint to capture the evolving properties of tensor data. Nowadays the exploding dataset demands a large scale PTTF analysis, and a parallel solution is critical to accommodate the trend. Whereas, the parallelization of PTTF still remains unexplored. In this paper, we propose a simple yet efficient Parallel Probabilistic Temporal Tensor Factorization, referred to as P$^2$T$^2$F, to provide a scalable PTTF solution. P$^2$T$^2$F is fundamentally disparate from e…
Queensland University of Technology（昆士兰科技大学）；Singapore University of Technology and Design（新加坡科技设计大学）
Coupled Matrix Tensor Factorization (CMTF) facilitates the integration and analysis of multiple data sources and helps discover meaningful information. Nonnegative CMTF (N-CMTF) has been employed in many applications for identifying latent patterns, prediction, and recommendation. However, due to the added complexity with coupling between tensor and matrix data, existing N-CMTF algorithms exhibit poor computation efficiency. In this paper, a computationally efficient N-CMTF factorization algorithm is presented based on the column-wise element selection, preventing frequent gradient updates. Th…
Department of Mathematics, UC Santa Barbara（加州大学圣巴巴拉分校数学系）；Department of ECE, UC Santa Barbara（加州大学圣巴巴拉分校电气工程与计算机科学系）
Streaming tensor factorization is a powerful tool for processing high-volume and multi-way temporal data in Internet networks, recommender systems and image/video data analysis. Existing streaming tensor factorization algorithms rely on least-squares data fitting and they do not possess a mechanism for tensor rank determination. This leaves them susceptible to outliers and vulnerable to over-fitting. This paper presents a Bayesian robust streaming tensor factorization model to identify sparse outliers, automatically determine the underlying tensor rank and accurately fit low-rank structure. We…
We augment the nonnegative matrix factorization method for audio source separation with cues about directionality of sound propagation. This improves separation quality greatly and removes the need for training data, with only a twofold increase in run time. This is the first method which can exploit directional information from microphone arrays much smaller than the wavelength of sound, working both in simulation and in practice on millimeter-scale microphone arrays.
Despite the success of existing tensor factorization methods, most of them conduct a multilinear decomposition, and rarely exploit powerful modeling frameworks, like deep neural networks, to capture a variety of complicated interactions in data. More important, for highly expressive, deep factorization, we lack an effective approach to handle streaming data, which are ubiquitous in real-world applications. To address these issues, we propose SPIDER, a Streaming ProbabilistIc Deep tEnsoR factorization method. We first use Bayesian neural networks (NNs) to construct a deep tensor factorization m…
North Carolina State University（北卡罗来纳州立大学）；Fudan University（复旦大学）
With the proliferation of knowledge graphs, modeling data with complex multirelational structure has gained increasing attention in the area of statistical relational learning. One of the most important goals of statistical relational learning is link prediction, i.e., predicting whether certain relations exist in the knowledge graph. A large number of models and algorithms have been proposed to perform link prediction, among which tensor factorization method has proven to achieve state-of-the-art performance in terms of computation efficiency and prediction accuracy. However, a common drawbac…
Most popular word embedding techniques involve implicit or explicit factorization of a word co-occurrence based matrix into low rank factors. In this paper, we aim to generalize this trend by using numerical methods to factor higher-order word co-occurrence based arrays, or \textit{tensors}. We present four word embeddings using tensor factorization and analyze their advantages and disadvantages. One of our main contributions is a novel joint symmetric tensor factorization technique related to the idea of coupled tensor factorization. We show that embeddings based on tensor factorization can b…
University of Texas, Austin（得克萨斯大学奥斯汀分校）；Vanderbilt University（范德堡大学）；Emory University（埃默里大学）
It has been recently shown that sparse, nonnegative tensor factorization of multi-modal electronic health record data is a promising approach to high-throughput computational phenotyping. However, such approaches typically do not leverage available domain knowledge while extracting the phenotypes; hence, some of the suggested phenotypes may not map well to clinical concepts or may be very similar to other suggested phenotypes. To address these issues, we present a novel, automatic approach called PIVETed-Granite that mines existing biomedical literature (PubMed) to obtain cannot-link constrain…
Consider multiple seasonal time series being collected in real-time, in the form of a tensor stream. Real-world tensor streams often include missing entries (e.g., due to network disconnection) and at the same time unexpected outliers (e.g., due to system errors). Given such a real-world tensor stream, how can we estimate missing entries and predict future evolution accurately in real-time? In this work, we answer this question by introducing SOFIA, a robust factorization method for real-world tensor streams. In a nutshell, SOFIA smoothly and tightly integrates tensor factorization, outlier re…
The goal of tensor completion is to recover a tensor from a subset of its entries, often by exploiting its low-rank property. Among several useful definitions of tensor rank, the low-tubal-rank was shown to give a valuable characterization of the inherent low-rank structure of a tensor. While some low-tubal-rank tensor completion algorithms with favorable performance have been recently proposed, these algorithms utilize second-order statistics to measure the error residual, which may not work well when the observed entries contain large outliers. In this paper, we propose a new objective funct…
Rutgers, The State University of New Jersey（罗格斯新泽西州立大学）
In many signal processing and machine learning applications, datasets containing private information are held at different locations, requiring the development of distributed privacy-preserving algorithms. Tensor and matrix factorizations are key components of many processing pipelines. In the distributed setting, differentially private algorithms suffer because they introduce noise to guarantee privacy. This paper designs new and improved distributed and differentially private algorithms for two popular matrix and tensor factorization methods: principal component analysis (PCA) and orthogonal…
In recent years, the rapid growth in technology has increased the opportunity for longitudinal human behavioral studies. Rich multimodal data, from wearables like Fitbit, online social networks, mobile phones etc. can be collected in natural environments. Uncovering the underlying low-dimensional structure of noisy multi-way data in an unsupervised setting is a challenging problem. Tensor factorization has been successful in extracting the interconnected low-dimensional descriptions of multi-way data. In this paper, we apply non-negative tensor factorization on a real-word wearable sensor data…
University of Michigan（密歇根大学）；University of Florida（佛罗里达大学）；University of Florida Informatics Institute（佛罗里达大学信息学研究所）
We introduce a general tensor model suitable for data analytic tasks for {\em heterogeneous} datasets, wherein there are joint low-rank structures within groups of observations, but also discriminative structures across different groups. To capture such complex structures, a double core tensor (DCOT) factorization model is introduced together with a family of smoothing loss functions. By leveraging the proposed smoothing function, the model accurately estimates the model factors, even in the presence of missing entries. A linearized ADMM method is employed to solve regularized versions of DCOT…
Pohang University of Science and Technology（浦项科技大学）；Georgia Institute of Technology（佐治亚理工学院）；University of California, San Diego（加利福尼亚大学圣迭戈分校）
Tensor factorization models offer an effective approach to convert massive electronic health records into meaningful clinical concepts (phenotypes) for data analysis. These models need a large amount of diverse samples to avoid population bias. An open challenge is how to derive phenotypes jointly across multiple hospitals, in which direct patient-level data sharing is not possible (e.g., due to institutional policies). In this paper, we developed a novel solution to enable federated tensor factorization for computational phenotyping without sharing patient-level data. We developed secure data…
We present a scalable Bayesian model for low-rank factorization of massive tensors with binary observations. The proposed model has the following key properties: (1) in contrast to the models based on the logistic or probit likelihood, using a zero-truncated Poisson likelihood for binary data allows our model to scale up in the number of \emph{ones} in the tensor, which is especially appealing for massive but sparse binary tensors; (2) side-information in form of binary pairwise relationships (e.g., an adjacency network) between objects in any tensor mode can also be leveraged, which can be es…
National Engineering School of Tunis, University of Tunis El Manar（突尼斯埃尔马纳尔大学突尼斯国立工程学院）；Aix Marseille University（艾克斯-马赛大学）；CNRS（法国国家科学研究中心）；Ecole Centrale de Marseille（马赛中央理工学院）
We study the implicit regularization effects of deep learning in tensor factorization. While implicit regularization in deep matrix and 'shallow' tensor factorization via linear and certain type of non-linear neural networks promotes low-rank solutions with at most quadratic growth, we show that its effect in deep tensor factorization grows polynomially with the depth of the network. This provides a remarkably faithful description of the observed experimental behaviour. Using numerical experiments, we demonstrate the benefits of this implicit regularization in yielding a more accurate estimati…
We present a Bayesian non-negative tensor factorization model for count-valued tensor data, and develop scalable inference algorithms (both batch and online) for dealing with massive tensors. Our generative model can handle overdispersed counts as well as infer the rank of the decomposition. Moreover, leveraging a reparameterization of the Poisson distribution as a multinomial facilitates conjugacy in the model and enables simple and efficient Gibbs sampling and variational Bayes (VB) inference updates, with a computational cost that only depends on the number of nonzeros in the tensor. The mo…
Aix Marseille Univ（艾克斯-马赛大学）；Université de Toulon（土伦大学）；CNRS（法国国家科学研究中心）；LIS（信息与系统实验室）；Ecole Centrale de Marseille（马赛中央理工学院）
Attempts of studying implicit regularization associated to gradient descent (GD) have identified matrix completion as a suitable test-bed. Late findings suggest that this phenomenon cannot be phrased as a minimization-norm problem, implying that a paradigm shift is required and that dynamics has to be taken into account. In the present work we address the more general setup of tensor completion by leveraging two popularized tensor factorization, namely Tucker and TensorTrain (TT). We track relevant quantities such as tensor nuclear norm, effective rank, generalized singular values and we intro…
University of Minnesota（明尼苏达大学）；IQVIA（艾昆纬）；University of Virginia（弗吉尼亚大学）；Temple University（天普大学）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Accurate prediction of the transmission of epidemic diseases such as COVID-19 is crucial for implementing effective mitigation measures. In this work, we develop a tensor method to predict the evolution of epidemic trends for many regions simultaneously. We construct a 3-way spatio-temporal tensor (location, attribute, time) of case counts and propose a nonnegative tensor factorization with latent epidemiological model regularization named STELAR. Unlike standard tensor factorization methods which cannot predict slabs ahead, STELAR enables long-term prediction by incorporating latent temporal …
This paper proposes a method to guide tensor factorization, using class labels. Furthermore, it shows the advantages of using the proposed method in identifying nodes that play a special role in multi-relational networks, e.g. spammers. Most complex systems involve multiple types of relationships and interactions among entities. Combining information from different relationships may be crucial for various prediction tasks. Instead of creating distinct prediction models for each type of relationship, in this paper we present a tensor factorization approach based on RESCAL, which collectively ex…
Emory University（埃默里大学）；UT Health Science Center at Houston（德克萨斯大学休斯顿健康科学中心）
Tensor factorization has been demonstrated as an efficient approach for computational phenotyping, where massive electronic health records (EHRs) are converted to concise and meaningful clinical concepts. While distributing the tensor factorization tasks to local sites can avoid direct data sharing, it still requires the exchange of intermediary results which could reveal sensitive patient information. Therefore, the challenge is how to jointly decompose the tensor under rigorous and principled privacy constraints, while still support the model's interpretability. We propose DPFact, a privacy-…
Given a time-evolving tensor with missing entries, how can we effectively factorize it for precisely predicting the missing entries? Tensor factorization has been extensively utilized for analyzing various multi-dimensional real-world data. However, existing models for tensor factorization have disregarded the temporal property for tensor factorization while most real-world data are closely related to time. Moreover, they do not address accuracy degradation due to the sparsity of time slices. The essential problems of how to exploit the temporal property for tensor decomposition and consider t…
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；IQVIA（艾昆纬）
Low-rank tensor factorization or completion is well-studied and applied in various online settings, such as online tensor factorization (where the temporal mode grows) and online tensor completion (where incomplete slices arrive gradually). However, in many real-world settings, tensors may have more complex evolving patterns: (i) one or more modes can grow; (ii) missing entries may be filled; (iii) existing tensor elements can change. Existing methods cannot support such complex scenarios. To fill the gap, this paper proposes a Generalized Online Canonical Polyadic (CP) Tensor factorization an…
Recent efforts to unravel the mystery of implicit regularization in deep learning have led to a theoretical focus on matrix factorization -- matrix completion via linear neural network. As a step further towards practical deep learning, we provide the first theoretical analysis of implicit regularization in tensor factorization -- tensor completion via certain type of non-linear neural network. We circumvent the notorious difficulty of tensor problems by adopting a dynamical systems perspective, and characterizing the evolution induced by gradient descent. The characterization suggests a form …
University of Edinburgh（爱丁堡大学）；Samsung AI Centre（三星人工智能中心）
Knowledge graphs are structured representations of real world facts. However, they typically contain only a small subset of all possible facts. Link prediction is a task of inferring missing facts based on existing ones. We propose TuckER, a relatively straightforward but powerful linear model based on Tucker decomposition of the binary tensor representation of knowledge graph triples. TuckER outperforms previous state-of-the-art models across standard link prediction datasets, acting as a strong baseline for more elaborate models. We show that TuckER is a fully expressive model, derive suffic…
University of Southern California（南加州大学）；Kobe University（神户大学）；CyberAgent, Inc.（CyberAgent 公司）；Information Sciences Institute, University of Southern California（南加州大学信息科学研究所）
Understanding consumer behavior is an important task, not only for developing marketing strategies but also for the management of economic policies. Detecting consumption patterns, however, is a high-dimensional problem in which various factors that would affect consumers' behavior need to be considered, such as consumers' demographics, circadian rhythm, seasonal cycles, etc. Here, we develop a method to extract multi-timescale expenditure patterns of consumers from a large dataset of scanned receipts. We use a non-negative tensor factorization (NTF) to detect intra- and inter-week consumption…
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…
CANDECOMP/PARAFAC (CP) tensor factorization of incomplete data is a powerful technique for tensor completion through explicitly capturing the multilinear latent factors. The existing CP algorithms require the tensor rank to be manually specified, however, the determination of tensor rank remains a challenging problem especially for CP rank. In addition, existing approaches do not take into account uncertainty information of latent factors, as well as missing entries. To address these issues, we formulate CP factorization using a hierarchical probabilistic model and employ a fully Bayesian trea…
Genetic pathways usually encode molecular mechanisms that can inform targeted interventions. It is often challenging for existing machine learning approaches to jointly model genetic pathways (higher-order features) and variants (atomic features), and present to clinicians interpretable models. In order to build more accurate and better interpretable machine learning models for genetic medicine, we introduce Pathway Augmented Nonnegative Tensor factorization for HighER-order feature learning (PANTHER). PANTHER selects informative genetic pathways that directly encode molecular mechanisms. We a…
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…
Social media platforms facilitate mankind a data-driven world by enabling billions of people to share their thoughts and activities ubiquitously. This huge collection of data, if analysed properly, can provide useful insights into people's behavior. More than ever, now is a crucial time under the Covid-19 pandemic to understand people's online behaviors detailing what topics are being discussed, and where (space) and when (time) they are discussed. Given the high complexity and poor quality of the huge social media data, an effective spatio-temporal topic detection method is needed. This paper…
Queensland University of Technology（昆士兰科技大学）；Singapore University of Technology and Design（新加坡科技设计大学）
With the advancements in computing technology and web-based applications, data is increasingly generated in multi-dimensional form. This data is usually sparse due to the presence of a large number of users and fewer user interactions. To deal with this, the Nonnegative Tensor Factorization (NTF) based methods have been widely used. However existing factorization algorithms are not suitable to process in all three conditions of size, density, and rank of the tensor. Consequently, their applicability becomes limited. In this paper, we propose a novel fast and efficient NTF algorithm using the e…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Adobe Research（奥多比研究中心）
We propose a completely unsupervised method to understand audio scenes observed with random microphone arrangements by decomposing the scene into its constituent sources and their relative presence in each microphone. To this end, we formulate a neural network architecture that can be interpreted as a nonnegative tensor factorization of a multi-channel audio recording. By clustering on the learned network parameters corresponding to channel content, we can learn sources' individual spectral dictionaries and their activation patterns over time. Our method allows us to leverage deep learning adv…
Université de Mons（蒙斯大学）；Université de Rennes（雷恩大学）；INRIA（法国国家信息与自动化研究所）；CNRS（法国国家科学研究中心）；IRISA（雷恩第一大学计算机科学研究所）
This paper is concerned with improving the empirical convergence speed of block-coordinate descent algorithms for approximate nonnegative tensor factorization (NTF). We propose an extrapolation strategy in-between block updates, referred to as heuristic extrapolation with restarts (HER). HER significantly accelerates the empirical convergence speed of most existing block-coordinate algorithms for dense NTF, in particular for challenging computational scenarios, while requiring a negligible additional computational budget.
University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）；Columbia University（哥伦比亚大学）；Microsoft Research（微软研究院）
We present a Bayesian tensor factorization model for inferring latent group structures from dynamic pairwise interaction patterns. For decades, political scientists have collected and analyzed records of the form "country $i$ took action $a$ toward country $j$ at time $t$"---known as dyadic events---in order to form and test theories of international relations. We represent these event data as a tensor of counts and develop Bayesian Poisson tensor factorization to infer a low-dimensional, interpretable representation of their salient patterns. We demonstrate that our model's predictive perform…
We propose a nonparametric factorization approach for sparsely observed tensors. The sparsity does not mean zero-valued entries are massive or dominated. Rather, it implies the observed entries are very few, and even fewer with the growth of the tensor; this is ubiquitous in practice. Compared with the existent works, our model not only leverages the structural information underlying the observed entry indices, but also provides extra interpretability and flexibility -- it can simultaneously estimate a set of location factors about the intrinsic properties of the tensor nodes, and another set …
Georgia Institute of Technology（佐治亚理工学院）；Health at Scale；INOVA；Sutter Health（萨特医疗）；Emory University（埃默里大学）
Phenotyping electronic health records (EHR) focuses on defining meaningful patient groups (e.g., heart failure group and diabetes group) and identifying the temporal evolution of patients in those groups. Tensor factorization has been an effective tool for phenotyping. Most of the existing works assume either a static patient representation with aggregate data or only model temporal data. However, real EHR data contain both temporal (e.g., longitudinal clinical visits) and static information (e.g., patient demographics), which are difficult to model simultaneously. In this paper, we propose Te…
Southern University of Science and Technology（南方科技大学）；Sun Yat-sen University（中山大学）
Tensor decomposition is an effective tool for learning multi-way structures and heterogeneous features from high-dimensional data, such as the multi-view images and multichannel electroencephalography (EEG) signals, are often represented by tensors. However, most of tensor decomposition methods are the linear feature extraction techniques, which are unable to reveal the nonlinear structure within high-dimensional data. To address such problem, a lot of algorithms have been proposed for simultaneously performs linear and non-linear feature extraction. A representative algorithm is the Graph Reg…
We propose a general algorithmic framework for constrained matrix and tensor factorization, which is widely used in signal processing and machine learning. The new framework is a hybrid between alternating optimization (AO) and the alternating direction method of multipliers (ADMM): each matrix factor is updated in turn, using ADMM, hence the name AO-ADMM. This combination can naturally accommodate a great variety of constraints on the factor matrices, and almost all possible loss measures for the fitting. Computation caching and warm start strategies are used to ensure that each update is eva…
