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2016 | OriginalPaper | Buchkapitel

Alternating Optimization Method Based on Nonnegative Matrix Factorizations for Deep Neural Networks

verfasst von : Tetsuya Sakurai, Akira Imakura, Yuto Inoue, Yasunori Futamura

Erschienen in: Neural Information Processing

Verlag: Springer International Publishing

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Abstract

The backpropagation algorithm for calculating gradients has been widely used in computation of weights for deep neural networks (DNNs). This method requires derivatives of objective functions and has some difficulties finding appropriate parameters such as learning rate. In this paper, we propose a novel approach for computing weight matrices of fully-connected DNNs by using two types of semi-nonnegative matrix factorizations (semi-NMFs). In this method, optimization processes are performed by calculating weight matrices alternately, and backpropagation (BP) is not used. We also present a method to calculate stacked autoencoder using a NMF. The output results of the autoencoder are used as pre-training data for DNNs. The experimental results show that our method using three types of NMFs attains similar error rates to the conventional DNNs with BP.

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Literatur
1.
Zurück zum Zitat Bengio, Y., Lamblin, P., Popovici, D., Larochelle, H.: Greedy layer-wise training of deep networks. In: Proceedings of Advances in Neural Information Processing Systems, vol. 19, pp. 153–160 (2006) Bengio, Y., Lamblin, P., Popovici, D., Larochelle, H.: Greedy layer-wise training of deep networks. In: Proceedings of Advances in Neural Information Processing Systems, vol. 19, pp. 153–160 (2006)
2.
Zurück zum Zitat Ciresan, D.C., Meier, U., Masci, J., Gambardella, L.M., Schmidhuber, J.: Flexible, high performance convolutional neural networks for image classification. In: Proceedings of 22nd International Joint Conference on Artificial Intelligence, pp. 1237–1242 (2011) Ciresan, D.C., Meier, U., Masci, J., Gambardella, L.M., Schmidhuber, J.: Flexible, high performance convolutional neural networks for image classification. In: Proceedings of 22nd International Joint Conference on Artificial Intelligence, pp. 1237–1242 (2011)
3.
Zurück zum Zitat Chorowski, J., Member, S.: Learning understandable neural networks with non-negative weight constraints. IEEE Trans. Neural Netw. Learn. Syst. 26, 62–69 (2015)MathSciNetCrossRef Chorowski, J., Member, S.: Learning understandable neural networks with non-negative weight constraints. IEEE Trans. Neural Netw. Learn. Syst. 26, 62–69 (2015)MathSciNetCrossRef
4.
Zurück zum Zitat Ding, D., Li, T., Jordan, M.I.: Convex and semi-nonnegative matrix factorizations. IEEE Trans. Pattern Anal. Mach. Intell. 32, 45–55 (2010)CrossRef Ding, D., Li, T., Jordan, M.I.: Convex and semi-nonnegative matrix factorizations. IEEE Trans. Pattern Anal. Mach. Intell. 32, 45–55 (2010)CrossRef
5.
Zurück zum Zitat Glorot, X., Bengio, Y.: Understanding the difficulty of training deep feedforward neural networks. In: International Conference on Artificial Intelligence and Statistics, pp. 249–256 (2010) Glorot, X., Bengio, Y.: Understanding the difficulty of training deep feedforward neural networks. In: International Conference on Artificial Intelligence and Statistics, pp. 249–256 (2010)
6.
Zurück zum Zitat Glorot, X., Bordes, A., Bengio., Y.: Deep sparse rectifier neural networks. In: Proceedings of 14th International Conference on Artificial Intelligence and Statistics, pp. 315–323 (2011) Glorot, X., Bordes, A., Bengio., Y.: Deep sparse rectifier neural networks. In: Proceedings of 14th International Conference on Artificial Intelligence and Statistics, pp. 315–323 (2011)
7.
Zurück zum Zitat Hinton, G.E., Deng, L., Yu, D., Dahl, G.E., Mohamed, A., Jaitly, N., Senior, A., Vanhoucke, V.: Deep neural networks for acoustic modeling in speech recognition. IEEE Signal Process. Mag. 29, 82–97 (2012)CrossRef Hinton, G.E., Deng, L., Yu, D., Dahl, G.E., Mohamed, A., Jaitly, N., Senior, A., Vanhoucke, V.: Deep neural networks for acoustic modeling in speech recognition. IEEE Signal Process. Mag. 29, 82–97 (2012)CrossRef
8.
Zurück zum Zitat Kingma, D.P., Ba, J.: ADAM: a method for stochastic optimization. In: The International Conference on Learning Representations (ICLR), San Diego (2015) Kingma, D.P., Ba, J.: ADAM: a method for stochastic optimization. In: The International Conference on Learning Representations (ICLR), San Diego (2015)
9.
Zurück zum Zitat Krizhevsky, A., Hinton, G.: Learning multiple layers of features from tiny images. Technical report, Computer Science Department, University of Toronto, vol. 1, p. 7 (2009) Krizhevsky, A., Hinton, G.: Learning multiple layers of features from tiny images. Technical report, Computer Science Department, University of Toronto, vol. 1, p. 7 (2009)
11.
Zurück zum Zitat Lee, D.D., Seung, H.S.: Learning the parts of objects by non-negative matrix factorization. Nature 401, 788–791 (1999)CrossRef Lee, D.D., Seung, H.S.: Learning the parts of objects by non-negative matrix factorization. Nature 401, 788–791 (1999)CrossRef
12.
Zurück zum Zitat LeCun, Y., Bottou, L., Bengio, Y., Huffier, P.: Gradient-based learning applied to document recognition. Proc. IEEE 86, 2278–2324 (1998)CrossRef LeCun, Y., Bottou, L., Bengio, Y., Huffier, P.: Gradient-based learning applied to document recognition. Proc. IEEE 86, 2278–2324 (1998)CrossRef
13.
Zurück zum Zitat Nair, V., Hinton, G.E.: Rectified linear units improve restricted Boltzmann machines. In: Proceedings of ICML (2010) Nair, V., Hinton, G.E.: Rectified linear units improve restricted Boltzmann machines. In: Proceedings of ICML (2010)
14.
Zurück zum Zitat Paatero, P., Tapper, U.: Positive matrix factorization: a non-negative factor model with optimal utilization of error estimates of data values. Environmetrics 5, 111–126 (1994)CrossRef Paatero, P., Tapper, U.: Positive matrix factorization: a non-negative factor model with optimal utilization of error estimates of data values. Environmetrics 5, 111–126 (1994)CrossRef
15.
Zurück zum Zitat Rumelhart, D.E., Hinton, G.E., Williams, R.J.: Learning representations by back-propagating errors. Nature 323, 533–536 (1986)CrossRef Rumelhart, D.E., Hinton, G.E., Williams, R.J.: Learning representations by back-propagating errors. Nature 323, 533–536 (1986)CrossRef
16.
Zurück zum Zitat Srivastava, N., Hinton, G.E., Krizhevsky, A., Sutskever, I., Salakhutdinov, R.: Dropout: a simple way to prevent neural networks from overfitting. J. Mach. Learn. Res. 15, 1929–1958 (2014)MathSciNetMATH Srivastava, N., Hinton, G.E., Krizhevsky, A., Sutskever, I., Salakhutdinov, R.: Dropout: a simple way to prevent neural networks from overfitting. J. Mach. Learn. Res. 15, 1929–1958 (2014)MathSciNetMATH
Metadaten
Titel
Alternating Optimization Method Based on Nonnegative Matrix Factorizations for Deep Neural Networks
verfasst von
Tetsuya Sakurai
Akira Imakura
Yuto Inoue
Yasunori Futamura
Copyright-Jahr
2016
DOI
https://doi.org/10.1007/978-3-319-46681-1_43