Search results
Results from the WOW.Com Content Network
In machine learning, the term tensor informally refers to two different concepts (i) a way of organizing data and (ii) a multilinear (tensor) transformation. Data may be organized in a multidimensional array (M-way array), informally referred to as a "data tensor"; however, in the strict mathematical sense, a tensor is a multilinear mapping over a set of domain vector spaces to a range vector ...
This ensures that a two-dimensional convolution will be able to be performed by a one-dimensional convolution operator as the 2D filter has been unwound to a 1D filter with gaps of zeroes separating the filter coefficients. One-Dimensional Filtering Strip after being Unwound. Assuming that some-low pass two-dimensional filter was used, such as:
Often this envelope or structure is taken from another sound. The convolution of two signals is the filtering of one through the other. [39] In electrical engineering, the convolution of one function (the input signal) with a second function (the impulse response) gives the output of a linear time-invariant system (LTI). At any given moment ...
Fig 1: A sequence of four plots depicts one cycle of the overlap–save convolution algorithm. The 1st plot is a long sequence of data to be processed with a lowpass FIR filter. The 2nd plot is one segment of the data to be processed in piecewise fashion. The 3rd plot is the filtered segment, with the usable portion colored red.
Circular convolution, also known as cyclic convolution, is a special case of periodic convolution, which is the convolution of two periodic functions that have the same period. Periodic convolution arises, for example, in the context of the discrete-time Fourier transform (DTFT).
For a symmetric matrix A, the vector vec(A) contains more information than is strictly necessary, since the matrix is completely determined by the symmetry together with the lower triangular portion, that is, the n(n + 1)/2 entries on and below the main diagonal. For such matrices, the half-vectorization is
Some aspects can be traced as far back as F. L. Hitchcock in 1928, [1] but it was L. R. Tucker who developed for third-order tensors the general Tucker decomposition in the 1960s, [2] [3] [4] further advocated by L. De Lathauwer et al. [5] in their Multilinear SVD work that employs the power method, or advocated by Vasilescu and Terzopoulos ...
There is a similar notion of column equivalence, defined by elementary column operations; two matrices are column equivalent if and only if their transpose matrices are row equivalent. Two rectangular matrices that can be converted into one another allowing both elementary row and column operations are called simply equivalent .