In this article, we derive a Bayesian model to learning the sparse and low rank PARAFAC decomposition for the observed tensor with missing values via the elastic net, with property to find the true rank and sparse factor matrix which is robust to the noise. We formulate efficient block coordinate descent algorithm and …
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48 results for “PARAFAC”
The PARAFAC tensor decomposition has enjoyed an increasing success in exploratory multi-aspect data mining scenarios. A major challenge remains the estimation of the number of latent factors (i.e., the rank) of the decomposition, which yields high-quality, interpretable results. Previously, we have proposed an automate…
Nonnegative CANDECOMP/PARAFAC (NCP) decomposition is an important tool to process nonnegative tensor. Sometimes, additional sparse regularization is needed to extract meaningful nonnegative and sparse components. Thus, an optimization method for NCP that can impose sparsity efficiently is required. In this paper, we co…
Motivated by large-scale Collaborative-Filtering applications, we present a Non-Commuting Latent Factor (NCLF) tensor-completion approach for modeling three-way arrays, which is diagonal like the standard PARAFAC, but wherein different terms distinguish different kinds of three-way relations of co-clusters, as determin…
The paper improves density estimation in high dimensions using tensor decompositions.
problem Density estimation struggles in high-dimensional data due to the curse of dimensionality.
method The paper uses nonnegative tensor decompositions to simplify dependence assumptions and estimate marginal distributions.
result Theoretical results show that restricting estimation to low-rank nonnegative PARAFAC or Tucker decompositions removes the dimensionality exponent on bin width rates.
Paper identifies tensor ranks via prior predictive matching, solving system of equations.
problem Determining the latent dimensions (ranks) in tensor factorization models.
method Prior predictive moment matching to transform moment matching conditions into a log-linear system of equations.
result Identifies which tensor models have identifiable ranks and derives rank estimators.
Tensor Decompositions for Identifying Directed Graph Topologies and Tracking Dynamic Networksstat.ML
Directed networks are pervasive both in nature and engineered systems, often underlying the complex behavior observed in biological systems, microblogs and social interactions over the web, as well as global financial markets. Since their structures are often unobservable, in order to facilitate network analytics, one …
Portfolio allocation and risk management make use of correlation matrices and heavily rely on the choice of a proper correlation matrix to be used. In this regard, one important question is related to the choice of the proper sample period to be used to estimate a stable correlation matrix. This paper addresses this qu…
We present an algorithm, AROFAC2, which detects the (CP-)rank of a degree 3 tensor and calculates its factorization into rank-one components. We provide generative conditions for the algorithm to work and demonstrate on both synthetic and real world data that AROFAC2 is a potentially outperforming alternative to the go…
In this paper we study the problem of noisy tensor completion for tensors that admit a canonical polyadic or CANDECOMP/PARAFAC (CP) decomposition with one of the factors being sparse. We present general theoretical error bounds for an estimate obtained by using a complexity-regularized maximum likelihood principle and …
New algorithm learns interpretable CP-basis from streaming tensor data under Markovian constraints.
problem Learning interpretable CP-basis from streaming tensor data under Markovian constraints.
method Online Tensor Factorization (OTF) with CANDECOMP/PARAFAC (CP) decomposition, proving convergence to stationary points.
result Algorithm converges almost surely to stationary points of the objective function under Markovian data generation.
In this work, we consider Corporate Governance (CG) ties among companies from a multiple network perspective. Such a structure naturally arises from the close interrelation between the Shareholding Network (SH) and the Board of Directors network (BD). In order to capture the simultaneous effects of both networks on CG,…
A new algorithm speeds up CP decomposition for large tensors.
problem Efficiently processing large-scale tensors in real-time.
method Randomized online CP decomposition (ROCP) algorithm.
result ROCP reduces computing time and memory usage significantly.
CP degeneracy affects tensor regression solutions, especially in high dimensions.
problem CP degeneracy in tensor regression.
method Analysis of CP degeneracy and development of a penalized strategy.
result A general penalized strategy to overcome CP degeneracy in tensor regression.
Methods based on vector embeddings of knowledge graphs have been actively pursued as a promising approach to knowledge graph completion.However, embedding models generate storage-inefficient representations, particularly when the number of entities and relations, and the dimensionality of the real-valued embedding vect…
A novel regularizer of the PARAFAC decomposition factors capturing the tensor's rank is proposed in this paper, as the key enabler for completion of three-way data arrays with missing entries. Set in a Bayesian framework, the tensor completion method incorporates prior information to enhance its smoothing and predictio…
Because tensor data appear more and more frequently in various scientific researches and real-world applications, analyzing the relationship between tensor features and the univariate outcome becomes an elementary task in many fields. To solve this task, we propose \underline{Fa}st \underline{S}parse \underline{T}ensor…
Recovery of low-rank matrices from a small number of linear measurements is now well-known to be possible under various model assumptions on the measurements. Such results demonstrate robustness and are backed with provable theoretical guarantees. However, extensions to tensor recovery have only recently began to be st…
Low-rank tensor decomposition and completion have attracted significant interest from academia given the ubiquity of tensor data. However, the low-rank structure is a global property, which will not be fulfilled when the data presents complex and weak dependencies given specific graph structures. One particular applica…
In this paper, we provide local and global convergence guarantees for recovering CP (Candecomp/Parafac) tensor decomposition. The main step of the proposed algorithm is a simple alternating rank- update which is the alternating version of the tensor power iteration adapted for asymmetric tensors. Local convergence g…
Tensor CANDECOMP/PARAFAC (CP) decomposition has wide applications in statistical learning of latent variable models and in data mining. In this paper, we propose fast and randomized tensor CP decomposition algorithms based on sketching. We build on the idea of count sketches, but introduce many novel ideas which are un…
We consider the problem of online subspace tracking of a partially observed high-dimensional data stream corrupted by noise, where we assume that the data lie in a low-dimensional linear subspace. This problem is cast as an online low-rank tensor completion problem. We propose a novel online tensor subspace tracking al…
High-dimensional tensors or multi-way data are becoming prevalent in areas such as biomedical imaging, chemometrics, networking and bibliometrics. Traditional approaches to finding lower dimensional representations of tensor data include flattening the data and applying matrix factorizations such as principal component…
New ADMM method for PARAFAC2 tensor decomposition with flexible regularization.
problem Challenges in applying regularisation to the evolving mode of PARAFAC2.
method Alternating Direction Method of Multipliers (AO-ADMM) for PARAFAC2 tensor fitting.
result The proposed ADMM-based approach accurately recovers underlying components from simulated data.
Hankel Matrix Nuclear Norm Regularized Tensor Completion for -dimensional Exponential Signalsstat.ML
Signals are generally modeled as a superposition of exponential functions in spectroscopy of chemistry, biology and medical imaging. For fast data acquisition or other inevitable reasons, however, only a small amount of samples may be acquired and thus how to recover the full signal becomes an active research topic. Bu…
Paper proposes an algorithm for PARAFAC2-based CMTF models with various constraints.
problem Jointly analyze matrices and tensors with irregular/ragged data.
method Alternating Optimization (AO) and ADMM for fitting PARAFAC2-based CMTF models with various constraints.
result Accurately recovers underlying patterns using various constraints and linear couplings.
Tensor decomposition is an important technique for capturing the high-order interactions among multiway data. Multi-linear tensor composition methods, such as the Tucker decomposition and the CANDECOMP/PARAFAC (CP), assume that the complex interactions among objects are multi-linear, and are thus insufficient to repres…
We describe a probabilistic PARAFAC/CANDECOMP (CP) factorization for multiway (i.e., tensor) data that incorporates auxiliary covariates, SupCP. SupCP generalizes the supervised singular value decomposition (SupSVD) for vector-valued observations, to allow for observations that have the form of a matrix or higher-order…
SimTensor is a multi-platform, open-source software for generating artificial tensor data (either with CP/PARAFAC or Tucker structure) for reproducible research on tensor factorization algorithms. SimTensor is a stand-alone application based on MATALB. It provides a wide range of facilities for generating tensor data w…
Tensor factorization has become an increasingly popular approach to knowledge graph completion(KGC), which is the task of automatically predicting missing facts in a knowledge graph. However, even with a simple model like CANDECOMP/PARAFAC(CP) tensor decomposition, KGC on existing knowledge graphs is impractical in res…
This paper addresses network anomography, that is, the problem of inferring network-level anomalies from indirect link measurements. This problem is cast as a low-rank subspace tracking problem for normal flows under incomplete observations, and an outlier detection problem for abnormal flows. Since traffic data is lar…
DinTucker: Scaling up Gaussian process models on multidimensional arrays with billions of elementscs.LG
Infinite Tucker Decomposition (InfTucker) and random function prior models, as nonparametric Bayesian models on infinite exchangeable arrays, are more powerful models than widely-used multilinear factorization methods including Tucker and PARAFAC decomposition, (partly) due to their capability of modeling nonlinear rel…
New algorithm for online tensor factorization with provable guarantees.
problem Factorizing structured tensors with unknown factors and non-convex optimization.
method Online CP/PARAFAC decomposition via dictionary learning with incoherence and sparsity constraints.
result Exact recovery of tensor factors at a linear rate under mild conditions.
Bayesian method for imputing missing values in tensor data.
problem Missing data in multi-way arrays (tensors) in biomedical studies.
method Flexible Bayesian framework with conjugate priors for CP factorization.
result Accurately captures uncertainty in microbiome profiles at missing timepoints.
Overcomplete latent representations have been very popular for unsupervised feature learning in recent years. In this paper, we specify which overcomplete models can be identified given observable moments of a certain order. We consider probabilistic admixture or topic models in the overcomplete regime, where the numbe…
Shape Constrained Tensor Decompositions using Sparse Representations in Over-Complete Librariesstat.ML
We consider -way data arrays and low-rank tensor factorizations where the time mode is coded as a sparse linear combination of temporal elements from an over-complete library. Our method, Shape Constrained Tensor Decomposition (SCTD) is based upon the CANDECOMP/PARAFAC (CP) decomposition which produces -rank appr…
The data in many disciplines such as social networks, web analysis, etc. is link-based, and the link structure can be exploited for many different data mining tasks. In this paper, we consider the problem of temporal link prediction: Given link data for times 1 through T, can we predict the links at time T+1? If our da…
This paper reviews methods for discovering patient subgroups from EHR data.
problem Discovering subgroups of patients and co-occurring medical conditions from EHR data.
method Low-rank data approximation methods like matrix and tensor decompositions.
result These methods provide transparent and interpretable insights into patient phenotypes.
NeSGD efficiently updates tensor-based features for online model learning in multi-way data.
problem Incremental updates of tensor-based features and model coefficients for evolving data distributions.
method Online NeSGD for CP decomposition of tensor data.
result Proposed NeSGD method significantly improves classification accuracy and adapts to changing data distributions.
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 e…
Guaranteed Simultaneous Asymmetric Tensor Decomposition via Orthogonalized Alternating Least Squaresstat.ML
Tensor CANDECOMP/PARAFAC (CP) decomposition is an important tool that solves a wide class of machine learning problems. Existing popular approaches recover components one by one, not necessarily in the order of larger components first. Recently developed simultaneous power method obtains only a high probability recover…
How can we find patterns and anomalies in a tensor, or multi-dimensional array, in an efficient and directly interpretable way? How can we do this in an online environment, where a new tensor arrives each time step? Finding patterns and anomalies in a tensor is a crucial problem with many applications, including buildi…
NeCPD improves online tensor decomposition using SGD with Hessian analysis and NAG.
problem Efficiently decompose multi-way tensors in online data processing.
method NeCPD solver based on SGD with Hessian analysis and NAG.
result NeCPD provides more accurate results than existing methods.
A new method for analyzing multi-source, multi-way data reduces dimensionality and reveals shared and individual structures.
problem Analyzing multi-source, multi-way data from different high-throughput technologies.
method Multiple Linked Tensor Factorization (MULTIFAC) extending CP decomposition with L2 penalties and EM algorithm for incomplete data.
result MULTIFAC approximates underlying signal, identifies shared and unshared structures, and imputes missing data.
FRAPPE estimates tensor canonical rank without CPD computation.
problem Estimating the canonical rank of tensors efficiently.
method Generates synthetic data matching input tensor's size and sparsity, trains a regression model to estimate rank.
result 24 times faster than best baseline, 10% improvement in MAPE on synthetic dataset.
New tensor model reduces GLM estimation error and sample complexity.
problem Estimating GLM coefficients with reduced sample complexity.
method Developed LSR tensor model and block coordinate descent algorithm.
result Minimax lower bound on estimation error, suggesting lower sample complexity.
Deep Kronecker Networkstat.ML
DKN adapts to medical imaging data with limited samples and interpretable models.
problem Medical imaging data's unique nature makes general methods like CNN unsuitable.
method DKN uses a Kronecker product structure to adapt to low sample size and provide interpretable models.
result DKN achieves prediction power comparable to CNN and provides model interpretability.
TEC combines multiple RPSTMs to classify big tensors efficiently.
problem Tensor classification for big data applications.
method Tensor Ensemble Classifier (TEC) using Random Projection-based Support Tensor Machine (RPSTM).
result TEC provides statistically consistent predictions with reduced computational cost.