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However, the tensor operation of long-term filter banks f2 is much more intractable.
In this case, long-term filter banks can be represented as a simple form of tensor operation, which can be easily implemented by a Toeplitz motivated network layer.
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The core data is extracted out of the gathered data by using tensor operations such as-matricization, vectorization and tensorization with the help of higher-order singular value decomposition.
We first introduce definitions of tensor operations to fix the notations.
Even if they do have formal training, big-O notation, Turing machines, NP-completeness, etc., are one thing; tensor operations and stochastic gradient descent algorithms are quite another.
The library provides a wide range of multi-index tensor operations that are normally used in scientific numerical computations.
The resulting low-rank tensor representation reduces dramatically the storage needs and the computational complexity of the consequent tensor operations on the electron density.
Moreover the Khatri-Rao product (columnwise Kronecker product) is denoted by A ◊ B. The tensor operations we use are consistent with [6]: The r -mode product of a tensor and a matrix along the r th mode is denoted as.
The two other models replace the tensor product operation with a novel self-organizing neural network, the Tensor-Multiple Peak Self-Organizing Map (T-MPSOM).
A generalization to two dimensional higher order mass matrix is further realized by the tensor product operation on the one dimensional reduced bandwidth and consistent mass matrices.
In case of a tensor, the vec operation is defined in (6).
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