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Hermitian Tensor Decompositions
Hermitian tensors are generalizations of Hermitian matrices, but they ha...
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Tensor Decomposition for Signal Processing and Machine Learning
Tensors or multi-way arrays are functions of three or more indices (i,j...
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Tensor Decompositions in Deep Learning
The paper surveys the topic of tensor decompositions in modern machine l...
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Efficient Orthogonal Tensor Decomposition, with an Application to Latent Variable Model Learning
Decomposing tensors into orthogonal factors is a well-known task in stat...
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Named Tensor Notation
We propose a notation for tensors with named axes, which relieves the au...
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Tensor Decompositions for Modeling Inverse Dynamics
Modeling inverse dynamics is crucial for accurate feedforward robot cont...
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Tensor-variate Mixture of Experts
When data are organized in matrices or arrays of higher dimensions (tens...
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Introduction to Tensor Decompositions and their Applications in Machine Learning
Tensors are multidimensional arrays of numerical values and therefore generalize matrices to multiple dimensions. While tensors first emerged in the psychometrics community in the 20^th century, they have since then spread to numerous other disciplines, including machine learning. Tensors and their decompositions are especially beneficial in unsupervised learning settings, but are gaining popularity in other sub-disciplines like temporal and multi-relational data analysis, too. The scope of this paper is to give a broad overview of tensors, their decompositions, and how they are used in machine learning. As part of this, we are going to introduce basic tensor concepts, discuss why tensors can be considered more rigid than matrices with respect to the uniqueness of their decomposition, explain the most important factorization algorithms and their properties, provide concrete examples of tensor decomposition applications in machine learning, conduct a case study on tensor-based estimation of mixture models, talk about the current state of research, and provide references to available software libraries.
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