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Milan Stehlík - One of the best experts on this subject based on the ideXlab platform.
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Correction to: “SPOCU”: scaled Polynomial Constant unit activation function
Neural Computing and Applications, 2020Co-Authors: Jozef Kiseľák, Ján Švihra, Peter Szépe, Milan StehlíkAbstract:Addendum on SPOCU fitting and Erratum.
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“SPOCU”: scaled Polynomial Constant unit activation function
Neural Computing and Applications, 2020Co-Authors: Jozef Kiseľák, Ying Lu, Ján Švihra, Peter Szépe, Milan StehlíkAbstract:We address the following problem: given a set of complex images or a large database, the numerical and computational complexity and quality of approximation for neural network may drastically differ from one activation function to another. A general novel methodology, scaled Polynomial Constant unit activation function “SPOCU,” is introduced and shown to work satisfactorily on a variety of problems. Moreover, we show that SPOCU can overcome already introduced activation functions with good properties, e.g., SELU and ReLU, on generic problems. In order to explain the good properties of SPOCU, we provide several theoretical and practical motivations, including tissue growth model and memristive cellular nonlinear networks. We also provide estimation strategy for SPOCU parameters and its relation to generation of random type of Sierpinski carpet, related to the [ pppq ] model. One of the attractive properties of SPOCU is its genuine normalization of the output of layers. We illustrate SPOCU methodology on cancer discrimination, including mammary and prostate cancer and data from Wisconsin Diagnostic Breast Cancer dataset. Moreover, we compared SPOCU with SELU and ReLU on large dataset MNIST, which justifies usefulness of SPOCU by its very good performance.
Jozef Kiseľák - One of the best experts on this subject based on the ideXlab platform.
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Correction to: “SPOCU”: scaled Polynomial Constant unit activation function
Neural Computing and Applications, 2020Co-Authors: Jozef Kiseľák, Ján Švihra, Peter Szépe, Milan StehlíkAbstract:Addendum on SPOCU fitting and Erratum.
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“SPOCU”: scaled Polynomial Constant unit activation function
Neural Computing and Applications, 2020Co-Authors: Jozef Kiseľák, Ying Lu, Ján Švihra, Peter Szépe, Milan StehlíkAbstract:We address the following problem: given a set of complex images or a large database, the numerical and computational complexity and quality of approximation for neural network may drastically differ from one activation function to another. A general novel methodology, scaled Polynomial Constant unit activation function “SPOCU,” is introduced and shown to work satisfactorily on a variety of problems. Moreover, we show that SPOCU can overcome already introduced activation functions with good properties, e.g., SELU and ReLU, on generic problems. In order to explain the good properties of SPOCU, we provide several theoretical and practical motivations, including tissue growth model and memristive cellular nonlinear networks. We also provide estimation strategy for SPOCU parameters and its relation to generation of random type of Sierpinski carpet, related to the [ pppq ] model. One of the attractive properties of SPOCU is its genuine normalization of the output of layers. We illustrate SPOCU methodology on cancer discrimination, including mammary and prostate cancer and data from Wisconsin Diagnostic Breast Cancer dataset. Moreover, we compared SPOCU with SELU and ReLU on large dataset MNIST, which justifies usefulness of SPOCU by its very good performance.
Peter Szépe - One of the best experts on this subject based on the ideXlab platform.
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Correction to: “SPOCU”: scaled Polynomial Constant unit activation function
Neural Computing and Applications, 2020Co-Authors: Jozef Kiseľák, Ján Švihra, Peter Szépe, Milan StehlíkAbstract:Addendum on SPOCU fitting and Erratum.
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“SPOCU”: scaled Polynomial Constant unit activation function
Neural Computing and Applications, 2020Co-Authors: Jozef Kiseľák, Ying Lu, Ján Švihra, Peter Szépe, Milan StehlíkAbstract:We address the following problem: given a set of complex images or a large database, the numerical and computational complexity and quality of approximation for neural network may drastically differ from one activation function to another. A general novel methodology, scaled Polynomial Constant unit activation function “SPOCU,” is introduced and shown to work satisfactorily on a variety of problems. Moreover, we show that SPOCU can overcome already introduced activation functions with good properties, e.g., SELU and ReLU, on generic problems. In order to explain the good properties of SPOCU, we provide several theoretical and practical motivations, including tissue growth model and memristive cellular nonlinear networks. We also provide estimation strategy for SPOCU parameters and its relation to generation of random type of Sierpinski carpet, related to the [ pppq ] model. One of the attractive properties of SPOCU is its genuine normalization of the output of layers. We illustrate SPOCU methodology on cancer discrimination, including mammary and prostate cancer and data from Wisconsin Diagnostic Breast Cancer dataset. Moreover, we compared SPOCU with SELU and ReLU on large dataset MNIST, which justifies usefulness of SPOCU by its very good performance.
Ján Švihra - One of the best experts on this subject based on the ideXlab platform.
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Correction to: “SPOCU”: scaled Polynomial Constant unit activation function
Neural Computing and Applications, 2020Co-Authors: Jozef Kiseľák, Ján Švihra, Peter Szépe, Milan StehlíkAbstract:Addendum on SPOCU fitting and Erratum.
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“SPOCU”: scaled Polynomial Constant unit activation function
Neural Computing and Applications, 2020Co-Authors: Jozef Kiseľák, Ying Lu, Ján Švihra, Peter Szépe, Milan StehlíkAbstract:We address the following problem: given a set of complex images or a large database, the numerical and computational complexity and quality of approximation for neural network may drastically differ from one activation function to another. A general novel methodology, scaled Polynomial Constant unit activation function “SPOCU,” is introduced and shown to work satisfactorily on a variety of problems. Moreover, we show that SPOCU can overcome already introduced activation functions with good properties, e.g., SELU and ReLU, on generic problems. In order to explain the good properties of SPOCU, we provide several theoretical and practical motivations, including tissue growth model and memristive cellular nonlinear networks. We also provide estimation strategy for SPOCU parameters and its relation to generation of random type of Sierpinski carpet, related to the [ pppq ] model. One of the attractive properties of SPOCU is its genuine normalization of the output of layers. We illustrate SPOCU methodology on cancer discrimination, including mammary and prostate cancer and data from Wisconsin Diagnostic Breast Cancer dataset. Moreover, we compared SPOCU with SELU and ReLU on large dataset MNIST, which justifies usefulness of SPOCU by its very good performance.
Malik Magdon-ismail - One of the best experts on this subject based on the ideXlab platform.
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NP-hardness and inapproximability of sparse PCA
Information Processing Letters, 2017Co-Authors: Malik Magdon-ismailAbstract:Abstract We give a reduction from clique to establish that sparse Principal Components Analysis (sparse PCA) is NP-hard. Using our reduction, we exclude a fully Polynomial time approximation scheme (FPTAS) for sparse PCA (unless P=NP). Under stronger average case complexity assumptions, we also exclude Polynomial Constant-factor approximation algorithms.
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NP-Hardness and Inapproximability of Sparse PCA
arXiv: Learning, 2015Co-Authors: Malik Magdon-ismailAbstract:We give a reduction from {\sc clique} to establish that sparse PCA is NP-hard. The reduction has a gap which we use to exclude an FPTAS for sparse PCA (unless P=NP). Under weaker complexity assumptions, we also exclude Polynomial Constant-factor approximation algorithms.