Learning to Represent Spatial Transformations with Factored Higher-Order Boltzmann Machines

To allow the hidden units of a restricted Boltzmann machine to model the transformation between two successive images, Memisevic and Hinton (2007) introduced three-way multiplicative interactions that use the intensity of a pixel in the first image as a multiplicative gain on a learned, symmetric weight between a pixel in the second image and a hidden unit. This creates cubicly many parameters which form a three-dimensional interaction tensor. We describe a low-rank approximation to this interaction tensor that uses a sum of “factors” each of which is a three-way outer-product. This approximation allows efficient learning of transformations between larger image patches. Since each factor can be viewed as an image filter, the model as a whole learns optimal filter pairs for efficiently representing transformations. We demonstrate the learning of optimal filter pairs from various synthetic and real image sequences. We also show how learning about image transformations allows the...

• Type: Journal
• Year: 2010
• Where: NECO
• Authors: Roland Memisevic, Geoffrey E. Hinton
• Keywords: Hidden Unit, Image, NECO 2010, Optimal filter Pairs