The Experts below are selected from a list of 81627 Experts worldwide ranked by ideXlab platform
Roberts, Lucas R. - One of the best experts on this subject based on the ideXlab platform.
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QR and LQ Decomposition Matrix Backpropagation Algorithms for Square, Wide, and Deep Matrices and Their Software Implementation
2020Co-Authors: Roberts, Denisa A. O., Roberts, Lucas R.Abstract:This article presents Matrix backpropagation algorithms for the QR Decomposition of matrices $A_{m, n}$, that are either square (m = n), wide (m < n), or deep (m > n), with rank $k = min(m, n)$. Furthermore, we derive novel Matrix backpropagation results for the pivoted (full-rank) QR Decomposition and for the LQ Decomposition of deep input matrices. Differentiable QR Decomposition offers a numerically stable, computationally efficient method to solve least squares problems frequently encountered in machine learning and computer vision. Software implementation across popular deep learning frameworks (PyTorch, TensorFlow, MXNet) incorporate the methods for general use within the deep learning community. Furthermore, this article aids the practitioner in understanding the Matrix backpropagation methodology as part of larger computational graphs, and hopefully, leads to new lines of research
Lucas Roberts - One of the best experts on this subject based on the ideXlab platform.
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qr and lq Decomposition Matrix backpropagation algorithms for square wide and deep real or complex matrices and their software implementation
arXiv: Numerical Analysis, 2020Co-Authors: Denisa Roberts, Lucas RobertsAbstract:This article presents Matrix backpropagation algorithms for the QR Decomposition of matrices $A_{m, n}$, that are either square (m = n), wide (m n), with rank $k = min(m, n)$. Furthermore, we derive novel Matrix backpropagation results for the pivoted (full-rank) QR Decomposition and for the LQ Decomposition of deep input matrices. Differentiable QR Decomposition offers a numerically stable, computationally efficient method to solve least squares problems frequently encountered in machine learning and computer vision. Other use cases such as graph learning and network compression are listed in the article. Software implementation across popular deep learning frameworks (PyTorch, TensorFlow, MXNet) incorporate the methods for general use within the deep learning community. Furthermore, this article aids the practitioner in understanding the Matrix backpropagation methodology as part of larger computational graphs.
Zhang Changqin - One of the best experts on this subject based on the ideXlab platform.
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discrete cosine wavelet packet transform and compressed sensing for speech signal
Technical Acoustics, 2014Co-Authors: Zhang ChangqinAbstract:Concerning the compressed sensing of speech signal, the discrete cosine wavelet packet transform(DCWPT) for speech signal is proposed on basis of the properties of discrete cosine transform and wavelet packet transform. The coefficients of DCWPT can be obtained by wavelet packet transform(DWT) from the coefficients of discrete cosine transform(DCT), and the coefficients are sparser in DCWPT domain than in DCT domain. In order to apply this new efficient transform to the compressed sensing of speech signal successfully, the sparse Decomposition Matrix of DCWPT is constructed and its performance analyzed. Also the orthogonal matching pursuit reconstruction algorithm is optimized according to the sparse Decomposition Matrix, and a new framework of the compressed sensing of speech signal based on DCWPT is put forward. It is concluded by subjective and objective indicators from the experiment that the new method is better than the traditional DCT method.
Oliver King - One of the best experts on this subject based on the ideXlab platform.
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on the Decomposition Matrix of the partition algebra in positive characteristic
Journal of Algebra, 2016Co-Authors: Oliver KingAbstract:We examine the structure of the partition algebra Pn(δ) over a field k of characteristic p>0. In particular, we describe the Decomposition Matrix of Pn(δ) when n
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on the Decomposition Matrix of the partition algebra in positive characteristic
arXiv: Representation Theory, 2014Co-Authors: Oliver KingAbstract:We examine the structure of the partition algebra $P_n(\delta)$ over a field $k$ of characteristic $p>0$. In particular, we describe the Decomposition Matrix of $P_n(\delta)$ when $n
Wei Tan - One of the best experts on this subject based on the ideXlab platform.
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discrete cosine wavelet packet transform and its application in compressed sensing for speech signal
International Symposium on Information Science and Engineering, 2012Co-Authors: Changqing Zhang, Yanpu Chen, Wei TanAbstract:This paper concerns the compressed sensing of speech signal. Discrete cosine wavelet packet transform (DCWPT) is proposed for speech signal based on the properties of discrete cosine transform (DCT) and wavelet packet transform (WPT). Coefficients of DCWPT can be obtained by WPT from the DCT coefficients, and speech signals are sparser in DCWPT domain than in DCT domain. In order to apply this newly efficient transform into the compressed sensing for speech signal successfully, the sparse Decomposition Matrix of DCWPT is constructed at first. The orthogonal matching pursuit reconstruction algorithm has also be optimized according to the sparse Decomposition Matrix and psycho-acoustics, and a new framework of the compressed sensing for speech signal based on DCWPT is established. The conclusion that the new method is better than the traditional DCT method is made from experiment by subjective and objective indicators.
