Second-Order Networks in PyTorch

Classification of Symmetric Positive Definite (SPD) matrices is gaining momentum in a variety machine learning application fields. In this work we propose a Python library which implements neural networks on SPD matrices, based on the popular deep learning framework Pytorch.

[1]  Cristian Sminchisescu,et al.  Matrix Backpropagation for Deep Networks with Structured Layers , 2015, 2015 IEEE International Conference on Computer Vision (ICCV).

[2]  Christian Jutten,et al.  Classification of covariance matrices using a Riemannian-based kernel for BCI applications , 2013, Neurocomputing.

[3]  Bamdev Mishra,et al.  Manopt, a matlab toolbox for optimization on manifolds , 2013, J. Mach. Learn. Res..

[4]  Christian Jutten,et al.  Multiclass Brain–Computer Interface Classification by Riemannian Geometry , 2012, IEEE Transactions on Biomedical Engineering.

[5]  Alan Edelman,et al.  The Geometry of Algorithms with Orthogonality Constraints , 1998, SIAM J. Matrix Anal. Appl..

[6]  Xavier Pennec,et al.  A Riemannian Framework for Tensor Computing , 2005, International Journal of Computer Vision.

[7]  W. F. Harris,et al.  The average eye , 2004, Ophthalmic & physiological optics : the journal of the British College of Ophthalmic Opticians.

[8]  Xavier Pennec,et al.  geomstats: a Python Package for Riemannian Geometry in Machine Learning , 2018, ArXiv.

[9]  Florian Yger,et al.  A review of kernels on covariance matrices for BCI applications , 2013, 2013 IEEE International Workshop on Machine Learning for Signal Processing (MLSP).

[10]  Hiroyuki Kasai,et al.  McTorch, a manifold optimization library for deep learning , 2018, ArXiv.

[11]  Luc Van Gool,et al.  A Riemannian Network for SPD Matrix Learning , 2016, AAAI.

[12]  A. Povzner,et al.  Thirteen Papers on Functional Analysis and Partial Differential Equations , 1965 .

[13]  Mathieu Salzmann,et al.  Second-order Convolutional Neural Networks , 2017, ArXiv.

[14]  Luca Antiga,et al.  Automatic differentiation in PyTorch , 2017 .

[15]  Masashi Sugiyama,et al.  Supervised LogEuclidean Metric Learning for Symmetric Positive Definite Matrices , 2015, ArXiv.

[16]  Luc Van Gool,et al.  Building Deep Networks on Grassmann Manifolds , 2016, AAAI.

[17]  Lei Wang,et al.  DeepKSPD: Learning Kernel-matrix-based SPD Representation for Fine-grained Image Recognition , 2017, ECCV.

[18]  Yunde Jia,et al.  Learning a Robust Representation via a Deep Network on Symmetric Positive Definite Manifolds , 2017, Pattern Recognit..

[19]  Luc Van Gool,et al.  Deep Learning on Lie Groups for Skeleton-Based Action Recognition , 2016, 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[20]  Zygmunt L. Szpak,et al.  A Study of the Region Covariance Descriptor: Impact of Feature Selection and Image Transformations , 2015, 2015 International Conference on Digital Image Computing: Techniques and Applications (DICTA).

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

[22]  Cristian Sminchisescu,et al.  Training Deep Networks with Structured Layers by Matrix Backpropagation , 2015, ArXiv.