Tensor decomposition

<p>In <a href="/facts/Multilinear_algebra/LrwpUFsM">multilinear algebra</a>, a tensor decomposition is any scheme for expressing a <a href="/facts/Tensor_(machine_learning)/hsdCknKW">"data tensor"</a> (M-way array) as a sequence of elementary operations acting on other, often simpler tensors. Many tensor decompositions generalize some <a href="/facts/Matrix_decomposition/xVBnAg0x">matrix decompositions</a>.
</p><p><a href="/facts/Tensors/pNjFo5tV">Tensors</a> are generalizations of matrices to higher dimensions (or rather to higher orders, i.e. the higher number of dimensions) and can consequently be treated as multidimensional fields.
The main tensor decompositions are:
</p>
<ul><li><a href="/facts/Tensor_rank_decomposition/sL3JMvYx">Tensor rank decomposition</a>;</li>
<li><a href="/facts/Higher-order_singular_value_decomposition/JTtTDy39">Higher-order singular value decomposition</a>;</li>
<li><a href="/facts/Tucker_decomposition/qkef5Dst">Tucker decomposition</a>;</li>
<li><a href="/facts/Matrix_product_state/amohgody">matrix product states</a>, and operators or tensor trains;</li>
<li>Online Tensor Decompositions</li>
<li>hierarchical Tucker decomposition;</li>
<li>block term decomposition</li></ul>

Tensor decomposition open-in-new

Tensor decomposition