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We address the computational barrier of deploying advanced deep learning segmentation models in clinical settings by studying the efficacy of network compression through tensor decomposition. We propose a post-training Tucker factorization…
In structure from motion, quadrifocal tensors capture more information than their pairwise counterparts (essential matrices), yet they have often been thought of as impractical and only of theoretical interest. In this work, we challenge…
In this paper we study the problem of decomposing a given tensor into a tensor train such that the tensors at the vertices are orthogonally decomposable. When the tensor train has length two, and the orthogonally decomposable tensors at the…
This work studies the problem of high-dimensional data (referred to as tensors) completion from partially observed samplings. We consider that a tensor is a superposition of multiple low-rank components. In particular, each component can be…
Modeling inverse dynamics is crucial for accurate feedforward robot control. The model computes the necessary joint torques, to perform a desired movement. The highly non-linear inverse function of the dynamical system can be approximated…
We propose a sampling-based method for computing the tensor ring (TR) decomposition of a data tensor. The method uses leverage score sampled alternating least squares to fit the TR cores in an iterative fashion. By taking advantage of the…
This paper introduces matrix product state (MPS) decomposition as a new and systematic method to compress multidimensional data represented by higher-order tensors. It solves two major bottlenecks in tensor compression: computation and…
In the era of big data, effectively compressing large datasets while performing complex mathematical operations is crucial. Tensor-based decomposition methods have shown superior compression capabilities with minimal loss of accuracy…
This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks…
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…
The Tucker decomposition, an extension of singular value decomposition for higher-order tensors, is a useful tool in analysis and compression of large-scale scientific data. While it has been studied extensively for static datasets, there…
Reducing parameter redundancies in neural network architectures is crucial for achieving feasible computational and memory requirements during training and inference phases. Given its easy implementation and flexibility, one promising…
Tensor ring (TR) decomposition has been successfully used to obtain the state-of-the-art performance in the visual data completion problem. However, the existing TR-based completion methods are severely non-convex and computationally…
There is an emerging interest in tensor factorization applications in big-data analytics and machine learning. To speed up the factorization of extra-large datasets, organized in multidimensional arrays (aka tensors), easy to compute…
The Canonical Polyadic decomposition (CPD) is a convenient and intuitive tool for tensor factorization; however, for higher-order tensors, it often exhibits high computational cost and permutation of tensor entries, these undesirable…
A tensor is a multi-way array that can represent, in addition to a data set, the expression of a joint law or a multivariate function. As such it contains the description of the interactions between the variables corresponding to each of…
In this paper, we suggest a new method for a given tensor to find CP decompositions using a less number of rank $1$ tensors. The main ingredient is the Least Absolute Shrinkage and Selection Operator (LASSO) by considering the decomposition…
Tensors play a central role in many modern machine learning and signal processing applications. In such applications, the target tensor is usually of low rank, i.e., can be expressed as a sum of a small number of rank one tensors. This…
Tensor decomposition on big data has attracted significant attention recently. Among the most popular methods is a class of algorithms that leverages compression in order to reduce the size of the tensor and potentially parallelize…
How can we accurately complete tensors by learning relationships of dimensions along each mode? Tensor completion, a widely studied problem, is to predict missing entries in incomplete tensors. Tensor decomposition methods, fundamental…