Tensor Factorization Method Research Articles

Rubik: Knowledge Guided Tensor Factorization and Completion for Health Data Analytics.

Computational phenotyping is the process of converting heterogeneous electronic health records (EHRs) into meaningful clinical concepts. Unsupervised phenotyping methods have the potential to leverage a vast amount of labeled EHR data for phenotype discovery. However, existing unsupervised phenotyping methods do not incorporate current medical knowledge and cannot directly handle missing, or noisy data. We propose Rubik, a constrained non-negative tensor factorization and completion method for phenotyping. Rubik incorporates 1) guidance constraints to align with existing medical knowledge, and 2) pairwise constraints for obtaining distinct, non-overlapping phenotypes. Rubik also has built-in tensor completion that can significantly alleviate the impact of noisy and missing data. We utilize the Alternating Direction Method of Multipliers (ADMM) framework to tensor factorization and completion, which can be easily scaled through parallel computing. We evaluate Rubik on two EHR datasets, one of which contains 647,118 records for 7,744 patients from an outpatient clinic, the other of which is a public dataset containing 1,018,614 CMS claims records for 472,645 patients. Our results show that Rubik can discover more meaningful and distinct phenotypes than the baselines. In particular, by using knowledge guidance constraints, Rubik can also discover sub-phenotypes for several major diseases. Rubik also runs around seven times faster than current state-of-the-art tensor methods. Finally, Rubik is scalable to large datasets containing millions of EHR records.

Multimodal approach to estimate the ocular movements during EEG recordings: A coupled tensor factorization method.

This paper deals with coupled tensor factorization. A relaxed criterion derived from the advanced coupled matrix-tensor factorization (ACMTF) proposed by Acar et al. is described. The proposed relaxed ACMTF (RACMTF) criterion is based on weaker assumptions that are thus more often satisfied when dealing with actual data. Numerical simulations show the benefit of using jointly two data sets when the underlying factors are highly correlated, especially if one of the modality is less noisy than the other one. The proposed method is finally applied on actual Gaze&EEG data to estimate the ocular artifacts into the EEG recordings.

Identifying regional service function from PM2.5 mass concentration throughout a city with non-negative tensor factorization approach.

This paper examines the holistic viewpoint on pollution pattern from time, day, and region dimensions based on the public data of fine particle concentrations, which cover 35 ambient monitoring stations in Beijing firstly. According to data driven, non-negative tensor factorization (NTF) method is introduced to distinguish pollution patterns which could identify the area service function. Results show that five patterns are obtained and annotated as traffic, industrial, residential, commercial, and steady ones. Each type owns special characteristics on time basis or day basis. Furthermore, calculating the reconstruction correlation of tensors with respect to sites, time, and days approximately approaches to 0.95-0.96, and it can be employed with high evaluation values of the model. Comparing with the original classifications drew by land use, this method corresponds with the reality well for considering the changes of surrounding sources. Some commendations on public travel and controlling measures based on local pollution presented in this study can be provided for further decrease of fine particle and improvement of air quality.

Non-negative tensor factorization models for Bayesian audio processing

We provide an overview of matrix and tensor factorization methods from a Bayesian perspective, giving emphasis on both the inference methods and modeling techniques. Factorization based models and their many extensions such as tensor factorizations have proved useful in a broad range of applications, supporting a practical and computationally tractable framework for modeling. Especially in audio processing, tensor models help in a unified manner the use of prior knowledge about signals, the data generation processes as well as available data from different modalities. After a general review of tensor models, we describe the general statistical framework, give examples of several audio applications and describe modeling strategies for key problems such as deconvolution, source separation, and transcription.

A Survey of Tensor Factorization Frameworks on Audio Modelling

This survey is about Tensor Factorization methods for audio modeling, which focuses on probabilistic latent tensor factorization and generalized coupled tensor factorization by expectation maximization method while using several linear and nonlinear distance measure methods

GPUTENSOR: Efficient tensor factorization for context-aware recommendations

Recommendation systems play an important role in many practical applications that help users manage information and provide personalized recommendations. The context in which a choice is made is an important factor for recommendation systems. Recently, researchers extended the classical matrix factorization to enable generic integration of contextual information by modeling the relevant data as a tensor. However, current tensor factorization methods have two important limitations: (1) computing costs can be very high in practice and (2) they can only be applied to static conditions. In this paper, we propose the GPUTENSOR, a parallel tensor factorization algorithm, to accelerate the tensor factorization of large datasets to support efficient context-aware recommendations. The basic idea of this algorithm is to partition a tensor into smaller blocks and then exploit the inherent parallelism and high memory bandwidth of Graphics Processing Units (GPU) to perform tensor related operations in parallel. Furthermore, based on the observation that contextual information changes dynamically and frequently, we present GPUTENSOR+, an effective incremental method that models the apparent changes of a tensor by adaptively updating its previously factorized components instead of recomputing them on the whole dataset every time data are changed. Experiments indicate that the proposed methods can achieve significant timesavings without a significant loss in accuracy. As an important data mining tool, these methods can be used a potential basis for many other interesting tensor applications, such as clustering, trend detection, social network analysis, and latent concept discovery.

Optimization Study of Personalized Information Recommendation Model Based on Tensor Decomposition

Based on the tensor decomposition especially pyramid decomposition method in matrix model, according to the high operation complexity of TD model, the author arises pairwise interaction tensor factorization (PITF) method to optimize it. And the tag recommendation, for example, this article simulate the interaction between all the labels on items a user tagging. The results show that on achieving expected quality test, PITF has obvious advantages than TD and CD at running time.

Limestone: High-throughput candidate phenotype generation via tensor factorization

The rapidly increasing availability of electronic health records (EHRs) from multiple heterogeneous sources has spearheaded the adoption of data-driven approaches for improved clinical research, decision making, prognosis, and patient management. Unfortunately, EHR data do not always directly and reliably map to medical concepts that clinical researchers need or use. Some recent studies have focused on EHR-derived phenotyping, which aims at mapping the EHR data to specific medical concepts; however, most of these approaches require labor intensive supervision from experienced clinical professionals. Furthermore, existing approaches are often disease-centric and specialized to the idiosyncrasies of the information technology and/or business practices of a single healthcare organization.In this paper, we propose Limestone, a nonnegative tensor factorization method to derive phenotype candidates with virtually no human supervision. Limestone represents the data source interactions naturally using tensors (a generalization of matrices). In particular, we investigate the interaction of diagnoses and medications among patients. The resulting tensor factors are reported as phenotype candidates that automatically reveal patient clusters on specific diagnoses and medications. Using the proposed method, multiple phenotypes can be identified simultaneously from data.We demonstrate the capability of Limestone on a cohort of 31,815 patient records from the Geisinger Health System. The dataset spans 7years of longitudinal patient records and was initially constructed for a heart failure onset prediction study. Our experiments demonstrate the robustness, stability, and the conciseness of Limestone-derived phenotypes. Our results show that using only 40 phenotypes, we can outperform the original 640 features (169 diagnosis categories and 471 medication types) to achieve an area under the receiver operator characteristic curve (AUC) of 0.720 (95% CI 0.715 to 0.725). Moreover, in consultation with a medical expert, we confirmed 82% of the top 50 candidates automatically extracted by Limestone are clinically meaningful.

Coupled Analysis of In Vitro and Histology Tissue Samples to Quantify Structure-Function Relationship

The structure/function relationship is fundamental to our understanding of biological systems at all levels, and drives most, if not all, techniques for detecting, diagnosing, and treating disease. However, at the tissue level of biological complexity we encounter a gap in the structure/function relationship: having accumulated an extraordinary amount of detailed information about biological tissues at the cellular and subcellular level, we cannot assemble it in a way that explains the correspondingly complex biological functions these structures perform. To help close this information gap we define here several quantitative temperospatial features that link tissue structure to its corresponding biological function. Both histological images of human tissue samples and fluorescence images of three-dimensional cultures of human cells are used to compare the accuracy of in vitro culture models with their corresponding human tissues. To the best of our knowledge, there is no prior work on a quantitative comparison of histology and in vitro samples. Features are calculated from graph theoretical representations of tissue structures and the data are analyzed in the form of matrices and higher-order tensors using matrix and tensor factorization methods, with a goal of differentiating between cancerous and healthy states of brain, breast, and bone tissues. We also show that our techniques can differentiate between the structural organization of native tissues and their corresponding in vitro engineered cell culture models.

Tensor clustering via adaptive subspace iteration

Multi-way data or tensors are generalizations of matrices. Clustering multi-way data is a very important research topic due to the intrinsic rich structures in real-world datasets. Despite significant progress made on subspace clustering for two-way data, few attempts have been made to develop subspace clustering algorithms on multi-way data. In this paper, we propose the subspace clustering algorithm on multi-way data, called ASI-T Adaptive Subspace Iteration on Tensor. We show that ASI-T is a special version of High Order SVD HOSVD, a commonly used tensor factorization method. We show that ASI-T is simultaneously performing subspace identification using 2DSVD identifying the subspace structure of the tensor from the current data clusters and data clustering using K-Means clustering the data units on the current identified subspaces. By explicitly modeling subspace structures, ASI-T is also able to generate interpretable clustering results. The experimental results on both synthetic data and real-world data demonstrate the effectiveness of ASI-T.

Image representation using Laplacian regularized nonnegative tensor factorization

Tensor provides a better representation for image space by avoiding information loss in vectorization. Nonnegative tensor factorization (NTF), whose objective is to express an n-way tensor as a sum of k rank-1 tensors under nonnegative constraints, has recently attracted a lot of attentions for its efficient and meaningful representation. However, NTF only sees Euclidean structures in data space and is not optimized for image representation as image space is believed to be a sub-manifold embedded in high-dimensional ambient space. To avoid the limitation of NTF, we propose a novel Laplacian regularized nonnegative tensor factorization (LRNTF) method for image representation and clustering in this paper. In LRNTF, the image space is represented as a 3-way tensor and we explicitly consider the manifold structure of the image space in factorization. That is, two data points that are close to each other in the intrinsic geometry of image space shall also be close to each other under the factorized basis. To evaluate the performance of LRNTF in image representation and clustering, we compare our algorithm with NMF, NTF, NCut and GNMF methods on three standard image databases. Experimental results demonstrate that LRNTF achieves better image clustering performance, while being more insensitive to noise.

PARAFAC algorithms for large-scale problems

Parallel factor analysis (PARAFAC) is a tensor (multiway array) factorization method which allows to find hidden factors (component matrices) from a multidimensional data. Most of the existing algorithms for the PARAFAC, especially the alternating least squares (ALS) algorithm need to compute Khatri–Rao products of tall factors and multiplication of large matrices, and due to this require high computational cost and large memory and are not suitable for very large-scale-problems. Hence, PARAFAC for large-scale data tensors is still a challenging problem. In this paper, we propose a new approach based on a modified ALS algorithm which computes Hadamard products, instead Khatri–Rao products, and employs relatively small matrices. The new algorithms are able to process extremely large-scale tensors with billions of entries. Extensive experiments confirm the validity and high performance of the developed algorithm in comparison with other well-known algorithms.

A non-negative tensor factorization model for selectional preference induction

AbstractThe distributional similarity methods have proven to be a valuable tool for the induction of semantic similarity. Until now, most algorithms use two-way co-occurrence data to compute the meaning of words. Co-occurrence frequencies, however, need not be pairwise. One can easily imagine situations where it is desirable to investigate co-occurrence frequencies of three modes and beyond. This paper will investigate tensor factorization methods to build a model of three-way co-occurrences. The approach is applied to the problem of selectional preference induction, and automatically evaluated in a pseudo-disambiguation task. The results show that tensor factorization, and non-negative tensor factorization in particular, is a promising tool for Natural Language Processing (nlp).

Coupled segmentation and denoising/deblurring models for hyperspectral material identification

SUMMARYA crucial aspect of spectral image analysis is the identification of the materials present in the object or scene being imaged and to quantify their abundance in the mixture. An increasingly useful approach to extracting such underlying structure is to employ image classification and object identification techniques to compressively represent the original data cubes by a set of spatially orthogonal bases and a set of spectral signatures. Owing to the increasing quantity of data usually encountered in hyperspectral data sets, effective data compressive representation is an important consideration, and noise and blur can present data analysis problems. In this paper, we develop image segmentation methods for hyperspectral space object material identification. We also couple the segmentation with a hyperspectral image data denoising/deblurring model and propose this method as an alternative to a tensor factorization methods proposed recently for space object material identification. The model provides the segmentation result and the restored image simultaneously. Numerical results show the effectiveness of our proposed combined model in hyperspectral material identification. Copyright © 2010 John Wiley & Sons, Ltd.