Abstract
Sparsely connected Multi-Layer Perceptrons (MLPs) differ from conventional MLPs in that only a small fraction of entries in their weight matrices are nonzero. Using sparse matrix-vector multiplication algorithms reduces the computational complexity of classification. Training of sparsely connected MLPs is achieved in two consecutive stages. In the first stage, initial values for the network’s parameters are given by the solution to an unsupervised matrix factorization problem, minimizing the reconstruction error. In the second stage, a modified version of the supervised backpropagation algorithm optimizes the MLP’s parameters with respect to the classification error. Experiments on the MNIST database of handwritten digits show that the proposed approach achieves equal classification performance compared to a densely connected MLP while speeding-up classification by a factor of seven.
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References
Bishop, C.M.: Neural Networks for Pattern Recognition. Clarendon Press, Oxford (1995)
Burges, C.J.C., Schölkopf, B.: Improving the Accuracy and Speed of Support Vector Machines. In: NIPS, vol. 9, pp. 375–381 (1997)
Cireşan, D.C., Meier, U., Gambardella, L.M., Schmidhuber, J.: Deep, Big, Simple Neural Nets for Handwritten Digit Recognition. Neural Computation 22(12), 3207–3220 (2010)
DeCoste, D., Schölkopf, B.: Training Invariant Support Vector Machines. Machine Learning 46, 161–190 (2002)
Elliott, D.: A Better Activation Function for Artificial Neural Networks. Tech. Rep. ISR TR 93-8, Institute for Systems Research, University of Maryland (1993)
Fan, R.E., Chang, K.W., Hsieh, C.J., Wang, X.R., Lin, C.J.: LIBLINEAR: A Library for Large Linear Classification. JMLR 9, 1871–1874 (2008)
Field, D.J.: What is the Goal of Sensory Coding? Neural Computation 6, 559–601 (1994)
Hinton, G.E., Salakhutdinov, R.R.: Reducing the Dimensionality of Data with Neural Networks. Science 313(5786), 1527–1554 (2006)
Hoyer, P.O.: Non-negative Matrix Factorization with Sparseness Constraints. JMLR 5, 1457–1469 (2004)
LeCun, Y., Jackel, L., Bottou, L., Brunot, A., Cortes, C., Denker, J., Drucker, H., Guyon, I., Müller, U., Säckinger, E., Simard, P., Vapnik, V.: Comparison Of Learning Algorithms For Handwritten Digit Recognition. In: Proceedings of ICANN, pp. 53–60 (1995)
LeCun, Y., Bottou, L., Bengio, Y., Haffner, P.: Gradient-Based Learning Applied to Document Recognition. Proceedings of the IEEE 86, 2278–2324 (1998)
LeCun, Y., Cortes, C.: The MNIST Database of Handwritten Digits, http://yann.lecun.com/exdb/mnist
LeCun, Y., Kanter, I., Solla, S.A.: Eigenvalues of Covariance Matrices: Application to Neural-Network Learning. Physical Review Letters 66(18), 2396–2399 (1991)
Lee, D.D., Seung, H.S.: Learning the parts of objects by nonnegative matrix factorization. Nature 401, 788–791 (1999)
Ortigosa, E.M., Cañas, A., Rodríguez, R., Díaz, J., Mota, S.: Towards an Optimal Implementation of MLP in FPGA. In: Bertels, K., Cardoso, J.M.P., Vassiliadis, S. (eds.) ARC 2006. LNCS, vol. 3985, pp. 46–51. Springer, Heidelberg (2006)
Ranzato, M., Boureau, Y., LeCun, Y.: Sparse Feature Learning for Deep Belief Networks. In: NIPS, vol. 20, pp. 1185–1192 (2008)
Rast, A.D., Welbourne, S., Jin, X., Furber, S.: Optimal Connectivity In Hardware-Targetted MLP Networks. In: Proceedings of IJCNN, pp. 2619–2626 (2009)
Rumelhart, D.E., Hinton, G.E., Williams, R.J.: Learning representations by back-propagating errors. Nature 323, 533–536 (1986)
Simard, P.Y., Steinkraus, D., Platt, J.C.: Best Practices for Convolutional Neural Networks Applied to Visual Document Analysis. In: Proceedings of ICDAR, pp. 958–962 (2003)
Theis, F.J., Stadlthanner, K., Tanaka, T.: First results on uniqueness of sparse non-negative matrix factorization. In: Proceedings of EUSIPCO (2005)
Thom, M., Schweiger, R., Palm, G.: Supervised Matrix Factorization with Sparseness Constraints and Fast Inference. In: Proceedings of IJCNN (to appear, 2011)
Yoshimura, Y., Dantzker, J.L.M., Callaway, E.M.: Excitatory cortical neurons form fine-scale functional networks. Nature 433(7028), 868–873 (2005)
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Thom, M., Schweiger, R., Palm, G. (2011). Training of Sparsely Connected MLPs. In: Mester, R., Felsberg, M. (eds) Pattern Recognition. DAGM 2011. Lecture Notes in Computer Science, vol 6835. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23123-0_36
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DOI: https://doi.org/10.1007/978-3-642-23123-0_36
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