Learning Predictors from Multidimensional Data with Tensor Factorizations

Statistical machine learning algorithms often involve learning a linear relationship between dependent and independent variables. This relationship is modeled as a vector of numerical values, commonly referred to as weights or predictors. These weights allow us to make predictions, and the quality of these weights influence the accuracy of our predictions. However, when the dependent variable inherently possesses a more complex, multidimensional structure, it becomes increasingly difficult to model the relationship with a vector. In this paper, we address this issue by investigating machine learning classification algorithms with multidimensional (tensor) structure. By imposing tensor factorizations on the predictors, we can better model the relationship, as the predictors would take the form of the data in question. We empirically show that our approach works more efficiently than the traditional machine learning method when the data possesses both an exact and an approximate tensor structure. Additionally, we show that estimating predictors with these factorizations also allow us to solve for fewer parameters, making computation more feasible for multidimensional data.

Expressway Traffic Flow Missing Data Repair Method Based on Coupled Matrix-Tensor Factorizations

Traffic flow data is the basis of traffic management, planning, control, and other forms of implementation. Once missing, it will directly affect the monitoring and prediction of expressway traffic status. Regarding this, this paper proposes a repair method for the traffic flow missing data of expressway, combined with the idea of coupled matrix-tensor factorizations (CMTF), to couple the auxiliary traffic flow data into the main traffic flow data and to construct the coupling matrix-tensor expression of traffic flow data, and the alternating direction multiplier algorithm is used to realize the repair of missing traffic flow data. Combined with the measured data of expressway traffic flow, the experimental results show that, under different missing data types and missing rates, the proposed method outperforms the methods lacking auxiliary traffic flow data and achieves a good repair effect, especially for high miss data rates.

Neural Tensor Model for Learning Multi-Aspect Factors in Recommender Systems

Recommender systems often involve multi-aspect factors. For example, when shopping for shoes online, consumers usually look through their images, ratings, and product's reviews before making their decisions. To learn multi-aspect factors, many context-aware models have been developed based on tensor factorizations. However, existing models assume multilinear structures in the tensor data, thus failing to capture nonlinear feature interactions. To fill this gap, we propose a novel nonlinear tensor machine, which combines deep neural networks and tensor algebra to capture nonlinear interactions among multi-aspect factors. We further consider adversarial learning to assist the training of our model. Extensive experiments demonstrate the effectiveness of the proposed model.

Improved Coupled Tensor Factorization with Its Applications in Health Data Analysis

Coupled matrix and tensor factorizations have been successfully used in many data fusion scenarios where datasets are assumed to be exactly coupled. However, in the real world, not all the datasets share the same factor matrices, which makes joint analysis of multiple heterogeneous sources challenging. For this reason, approximate coupling or partial coupling is widely used in real-world data fusion, with exact coupling as a special case of these techniques. However, to fully address the challenge of tensor factorization, in this paper, we propose two improved coupled tensor factorization methods: one for approximately coupled datasets and the other for partially coupled datasets. A series of experiments using both simulated data and three real-world datasets demonstrate the improved accuracy of these approaches over existing baselines. In particular, when experiments on MRI data is conducted, the performance of our method is improved even by 12.47% in terms of accuracy compared with traditional methods.

Mining Multimodal Big Data

The last decade has witnessed exponential growth of data particularly in the fields of biomedicine, unstructured text processing and signal processing. There exist instances of data depicting simultaneous interactions amongst more than two types of entities. Such data are not readily amenable to matrix representation as matrices can show interactions between only two types of entities at a time. Tensors are multimodal extensions of matrices (a matrix can be thought of as 2-mode tensor), and tensor factorizations (decompositions) are multiway generalizations of matrix factorizations. This chapter provides an overview of tensor factorization methods as well as a literature review of selected applications in areas that are currently experiencing exponential data growth and likely of interest to a broad audience.

tensorBF: an R package for Bayesian tensor factorization

With recent advancements in measurement technologies, many multi-way and tensor datasets have started to emerge. Exploiting the natural tensor structure in the data has been shown to be advantageous for both explorative and predictive studies in several application areas of bioinformatics and computational biology. Therefore, there has subsequently arisen a need for robust and flexible tools for effectively analyzing tensor data sets. We present the R package tensorBF, which is the first R package providing Bayesian factorization of a tensor. Our package implements a generative model that automatically identifies the number of factors needed to explain the tensor, overcoming a key limitation of traditional tensor factorizations. We also recommend best practices when using tensor factorizations for both, explorative and predictive analysis with an example application on drug response dataset. The package also implements tools related to the normalization of data, informative noise priors and visualization. Availability: The package is available at https://cran.r-project.org/package=tensorBF.