Deep Double Sparsity Encoder: Learning to Sparsify Not Only Features But Also Parameters

This paper emphasizes the significance to jointly exploit the problem structure and the parameter structure, in the context of deep modeling. As a specific and interesting example, we describe the deep double sparsity encoder (DDSE), which is inspired by the double sparsity model for dictionary learning. DDSE simultaneously sparsities the output features and the learned model parameters, under one unified framework. In addition to its intuitive model interpretation, DDSE also possesses compact model size and low complexity. Extensive simulations compare DDSE with several carefully-designed baselines, and verify the consistently superior performance of DDSE. We further apply DDSE to the novel application domain of brain encoding, with promising preliminary results achieved.

[1]  Geoffrey E. Hinton,et al.  ImageNet classification with deep convolutional neural networks , 2012, Commun. ACM.

[2]  Wei-Yun Yau,et al.  Deep Subspace Clustering with Sparsity Prior , 2016, IJCAI.

[3]  T. Blumensath,et al.  Iterative Thresholding for Sparse Approximations , 2008 .

[4]  Jiayu Zhou,et al.  Learning A Task-Specific Deep Architecture For Clustering , 2015, SDM.

[5]  Luca Maria Gambardella,et al.  Deep Big Simple Neural Nets Excel on Handwritten Digit Recognition , 2010, ArXiv.

[6]  Geoffrey E. Hinton,et al.  On the importance of initialization and momentum in deep learning , 2013, ICML.

[7]  Volkan Cevher,et al.  Model-Based Compressive Sensing , 2008, IEEE Transactions on Information Theory.

[8]  Jonathan Winawer,et al.  A Two-Stage Cascade Model of BOLD Responses in Human Visual Cortex , 2013, PLoS Comput. Biol..

[9]  Shuicheng Yan,et al.  Training Skinny Deep Neural Networks with Iterative Hard Thresholding Methods , 2016, ArXiv.

[10]  Léon Bottou,et al.  Large-Scale Machine Learning with Stochastic Gradient Descent , 2010, COMPSTAT.

[11]  Luca Maria Gambardella,et al.  Better Digit Recognition with a Committee of Simple Neural Nets , 2011, 2011 International Conference on Document Analysis and Recognition.

[12]  Michael Elad,et al.  Double Sparsity: Learning Sparse Dictionaries for Sparse Signal Approximation , 2010, IEEE Transactions on Signal Processing.

[13]  Yann LeCun,et al.  Learning Fast Approximations of Sparse Coding , 2010, ICML.

[14]  Qing Ling,et al.  Learning Deep $\ell_0$ Encoders , 2015, 1509.00153.

[15]  Wen Gao,et al.  Maximal Sparsity with Deep Networks? , 2016, NIPS.

[16]  Yoshua Bengio,et al.  Why Does Unsupervised Pre-training Help Deep Learning? , 2010, AISTATS.

[17]  David J. Field,et al.  Sparse coding with an overcomplete basis set: A strategy employed by V1? , 1997, Vision Research.

[18]  Haichao Zhang,et al.  Sparse Coding and its Applications in Computer Vision , 2015 .

[19]  Luca Maria Gambardella,et al.  Deep, Big, Simple Neural Nets for Handwritten Digit Recognition , 2010, Neural Computation.

[20]  Qing Ling,et al.  $\mathbf{D^3}$: Deep Dual-Domain Based Fast Restoration of JPEG-Compressed Images , 2016, ArXiv.

[21]  Zhang Yi,et al.  Connections Between Nuclear-Norm and Frobenius-Norm-Based Representations , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[22]  Andrew Y. Ng,et al.  The Importance of Encoding Versus Training with Sparse Coding and Vector Quantization , 2011, ICML.

[23]  J. Gallant,et al.  Identifying natural images from human brain activity , 2008, Nature.

[24]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[25]  Qing Ling,et al.  Learning A Deep ℓ∞ Encoder for Hashing , 2016, IJCAI.

[26]  Jian Sun,et al.  Deep Residual Learning for Image Recognition , 2015, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[27]  Qing Ling,et al.  Stacked Approximated Regression Machine: A Simple Deep Learning Approach , 2016, ArXiv.

[28]  Yann LeCun,et al.  Regularization of Neural Networks using DropConnect , 2013, ICML.