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Nonnegative matrix factorization (NMF) has an established reputation as a useful data analysis technique in numerous applications. However, its usage in practical situations is undergoing challenges in recent years. The fundamental factor…

Many real-world clustering problems are plagued by incomplete data characterized by missing or absent features for some or all of the data instances. Traditional clustering methods cannot be directly applied to such data without…

The recent low-rank prior based models solve the tensor completion problem efficiently. However, these models fail to exploit the local patterns of tensors, which compromises the performance of tensor completion. In this paper, we propose a…

By filling in missing values in datasets, imputation allows these datasets to be used with algorithms that cannot handle missing values by themselves. However, missing values may in principle contribute useful information that is lost…

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,…

Missing values are unavoidable in many applications of machine learning and present challenges both during training and at test time. When variables are missing in recurring patterns, fitting separate pattern submodels have been proposed as…

This study aims to solve the over-reliance on the rank estimation strategy in the standard tensor factorization-based tensor recovery and the problem of a large computational cost in the standard t-SVD-based tensor recovery. To this end, we…

We consider the tensor completion problem of predicting the missing entries of a tensor. The commonly used CP model has a triple product form, but an alternate family of quadratic models, which are the sum of pairwise products instead of a…

This paper proposes a novel formulation of the tensor completion problem to impute missing entries of data represented by tensors. The formulation is introduced in terms of tensor train (TT) rank which can effectively capture global…

Tensor classification is gaining importance across fields, yet handling partially observed data remains challenging. In this paper, we introduce a novel approach to tensor classification with incomplete data, framed within high-dimensional…

Tensor factorization is a powerful tool to analyse multi-way data. Compared with traditional multi-linear methods, nonlinear tensor factorization models are capable of capturing more complex relationships in the data. However, they are…

We present new algorithms to detect and correct errors in the lower-upper factorization of a matrix, or the triangular linear system solution, over an arbitrary field. Our main algorithms do not require any additional information or…

Squared tensor networks (TNs) and their extension as computational graphs--squared circuits--have been used as expressive distribution estimators, yet supporting closed-form marginalization. However, the squaring operation introduces…

Moving beyond evaluations that collapse performance across heterogeneous prompts toward fine-grained evaluation at the prompt level, or within relatively homogeneous subsets, is necessary to diagnose generative models' strengths and…

Recent approaches to the tensor completion problem have often overlooked the nonnegative structure of the data. We consider the problem of learning a nonnegative low-rank tensor, and using duality theory, we propose a novel factorization of…

Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…

Given sparse multi-dimensional data (e.g., (user, movie, time; rating) for movie recommendations), how can we discover latent concepts/relations and predict missing values? Tucker factorization has been widely used to solve such problems…

We consider tensor factorizations based on sparse measurements of the components of relatively high rank tensors. The measurements are designed in a way that the underlying graph of interactions is a random graph. The setup will be useful…

In this paper, we aim at the completion problem of high order tensor data with missing entries. The existing tensor factorization and completion methods suffer from the curse of dimensionality when the order of tensor N>>3. To overcome this…

The Nonnegative Matrix Factorization (NMF) of the rating matrix has shown to be an effective method to tackle the recommendation problem. In this paper we propose new methods based on the NMF of the rating matrix and we compare them with…