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the weighting functions are one variable functions of the parameter vector in an orthonormed system for each parameter (singular functions); the sub tensors of the core tensor are also in orthogonal positions; the core tensor and the weighting functions are ordered according to the higher-order singular values of the parameter vector;
Keras contains numerous implementations of commonly used neural-network building blocks such as layers, objectives, activation functions, optimizers, and a host of tools for working with image and text data to simplify programming in deep neural network area. [11]
MATLAB (an abbreviation of "MATrix LABoratory" [18]) is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks.MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages.
The concept of HOSVD was carried over to functions by Baranyi and Yam via the TP model transformation. [ 28 ] [ 29 ] This extension led to the definition of the HOSVD-based canonical form of tensor product functions and Linear Parameter Varying system models [ 30 ] and to convex hull manipulation based control optimization theory, see TP model ...
In MATLAB, the function kron (A, B) is used for this product. These often generalize to multi-dimensional arguments, and more than two arguments. In the Python library NumPy, the outer product can be computed with function np.outer(). [8] In contrast, np.kron results in a flat array.
NumPy (pronounced / ˈ n ʌ m p aɪ / NUM-py) is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays. [3]
The Hadamard product operates on identically shaped matrices and produces a third matrix of the same dimensions. In mathematics, the Hadamard product (also known as the element-wise product, entrywise product [1]: ch. 5 or Schur product [2]) is a binary operation that takes in two matrices of the same dimensions and returns a matrix of the multiplied corresponding elements.
A whitening transformation or sphering transformation is a linear transformation that transforms a vector of random variables with a known covariance matrix into a set of new variables whose covariance is the identity matrix, meaning that they are uncorrelated and each have variance 1. [1]