Perception of sensory signals is strongly influenced by their context, both in space and time. In this paper, we propose a novel hierarchical model, called convolutional dynamic networks, that effectively utilizes this contextual information, while inferring the representations of the visual inputs. We build this model based on a predictive coding framework and use the idea of empirical priors to incorporate recurrent and top-down connections. These connections endow the model with contextual information coming from temporal as well as abstract knowledge from higher layers. To perform inference efficiently in this hierarchical model, we rely on a novel scheme based on a smoothing proximal gradient method. When trained on unlabeled video sequences, the model learns a hierarchy of stable attractors, representing low-level to high-level parts of the objects. We demonstrate that the model effectively utilizes contextual information to produce robust and stable representations for object recognition in video sequences, even in case of highly corrupted inputs.
The self organizing map (SOM) is one of the popular clustering and data visualization algorithms and has evolved as a useful tool in pattern recognition, data mining since it was first introduced by Kohonen. However, it is observed that the magnification factor for such mappings deviates from the information-theoretically optimal value of 1 (for the SOM it is 2/3). This can be attributed to the use of the mean square error to adapt the system, which distorts the mapping by oversampling the low probability regions.In this work, we first discuss the kernel SOM in terms of a similarity measure called correntropy induced metric (CIM) and empirically show that this can enhance the magnification of the mapping without much increase in the computational complexity of the algorithm. We also show that adapting the SOM in the CIM sense is equivalent to reducing the localized cross information potential, an information-theoretic function that quantifies the similarity between two probability distributions. Using this property we propose a kernel bandwidth adaptation algorithm for Gaussian kernels, with both homoscedastic and heteroscedastic components. We show that the * Corresponding author
Preprint submitted to ElsevierDecember 1, 2013 proposed model can achieve a mapping with optimal magnification and can automatically adapt the parameters of the kernel function.
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