相关论文: A Simple and Scalable Tensor Completion Algorithm …

We study a noisy tensor completion problem of broad practical interest, namely, the reconstruction of a low-rank tensor from highly incomplete and randomly corrupted observations of its entries. While a variety of prior work has been…

Recommender systems play a fundamental role in web applications in filtering massive information and matching user interests. While many efforts have been devoted to developing more effective models in various scenarios, the exploration on…

Recommender System (RS) is currently an effective way to solve information overload. To meet users' next click behavior, RS needs to collect users' personal information and behavior to achieve a comprehensive and profound user preference…

This paper studies the rank-1 tensor completion problem for cubic tensors when there are noises for observed tensor entries. First, we propose a robust biquadratic optimization model for obtaining rank-1 completing tensors. When the…

In this paper a new Riemannian rank adaptive method (RRAM) is proposed for the low-rank tensor completion problem (LRTCP) formulated as a least-squares optimization problem on the algebraic variety of tensors of bounded tensor-train (TT)…

This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models---including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation---which…

Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and…

Robust tensor CP decomposition involves decomposing a tensor into low rank and sparse components. We propose a novel non-convex iterative algorithm with guaranteed recovery. It alternates between low-rank CP decomposition through gradient…

This paper studies tensor eigenvalue complementarity problems. Basic properties of standard and complementarity tensor eigenvalues are discussed. We formulate tensor eigenvalue complementarity problems as constrained polynomial…

We propose a new numerical algorithm for computing the tensor rank decomposition or canonical polyadic decomposition of higher-order tensors subject to a rank and genericity constraint. Reformulating this computational problem as a system…

We study low rank matrix and tensor completion and propose novel algorithms that employ adaptive sampling schemes to obtain strong performance guarantees. Our algorithms exploit adaptivity to identify entries that are highly informative for…

Although a variety of methods have been proposed for sequential recommendation, it is still far from being well solved partly due to two challenges. First, the existing methods often lack the simultaneous consideration of the global…

Machine learning (ML) and tensor-based methods have been of significant interest for the scientific community for the last few decades. In a previous work we presented a novel tensor-based system identification framework to ease the…

In this paper, we analyze the fundamental conditions for low-rank tensor completion given the separation or tensor-train (TT) rank, i.e., ranks of unfoldings. We exploit the algebraic structure of the TT decomposition to obtain the…

Many problems in operations research require that constraints be specified in the model. Determining the right constraints is a hard and laborsome task. We propose an approach to automate this process using artificial intelligence and…

Chemically relevant compositions (CRCs) and atomic arrangements of inorganic compounds have been collected as inorganic crystal structure databases. Machine-learning is a unique approach to search for currently unknown CRCs from vast…

We propose an adaptive and provably accurate tensor completion approach based on combining matrix completion techniques (see, e.g., arXiv:0805.4471, arXiv:1407.3619, arXiv:1306.2979) for a small number of slices with a modified noise robust…

Learning a good representation of text is key to many recommendation applications. Examples include news recommendation where texts to be recommended are constantly published everyday. However, most existing recommendation techniques, such…

Higher-order low-rank tensor arises in many data processing applications and has attracted great interests. Inspired by low-rank approximation theory, researchers have proposed a series of effective tensor completion methods. However, most…

Recommender systems (RSs) have become an inseparable part of our everyday lives. They help us find our favorite items to purchase, our friends on social networks, and our favorite movies to watch. Traditionally, the recommendation problem…