Optimization by Vector Space Methods
Optimization by Vector Space Methods
Slow feature analysis: unsupervised learning of invariances
Neural Computation
Distinctive Image Features from Scale-Invariant Keypoints
International Journal of Computer Vision
Histograms of Oriented Gradients for Human Detection
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
Object Recognition with Features Inspired by Visual Cortex
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Topographic Product Models Applied to Natural Scene Statistics
Neural Computation
A two-layer ICA-like model estimated by score matching
ICANN'07 Proceedings of the 17th international conference on Artificial neural networks
Fast and robust fixed-point algorithms for independent component analysis
IEEE Transactions on Neural Networks
The FastICA Algorithm Revisited: Convergence Analysis
IEEE Transactions on Neural Networks
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In this paper, we propose a model for natural images to learn topographic representations and complex cell properties. Different from the estimation of traditional models, e.g., pooling the outputs of filters in neighboring regions, our method maximizes a simple form of binary relations between two adjacent complex cells--"pairwise cumulant", which contains the favorable nonlinearity as high order cumulant, and can exploit the "sparseness" and "correlation" of cells in primary visual cortex. By means of choosing nonlinearity properly, our model is related to cumulant-based ICA model, and the derived fixed-point algorithm is close to the well-known FastICA algorithm. The local convergence analysis proves that our fixed-point algorithm is cubic convergence and experiments on nature images show its high efficiency than traditional algorithms. Besides, simulations demonstrate the effectiveness of our model in capturing nonlinear dependencies among these neighboring complex cells. The learnt filters preserve properties of complex cells, and their orientation, spatial frequency and location change smoothly over the topographic map. In addition, these learnt filters can be used as feature descriptors. They produce features that are invariant to object transformations, and achieve better results than traditional models on digit recognition tasks.