Topological features in locally connected RBMs

Unsupervised learning algorithms find ways to model latent structure present in the data. These latent structures can then serve as a basis for supervised classification methods. A common choice for unsupervised feature discovery is the Restricted Boltzmann Machine (RBM). Since the RBM is a general purpose learning machine, it is not particularly tailored for image data. Representations found by RBMs are consequently not image-like. Since it is essential to exploit the known topological structure for image analysis, it is desirable not to discard the topology property when learning new representations. Then, the same learning methods can be applied to the latent representation in a hierarchical manner. In this work, we propose a modification to the learning rule of locally connected RBMs, which ensures that topological image structure is preserved in the latent representation. To this end, we use a Gaussian kernel to transfer topological properties of the image space to the feature space. The learned model is then used as an initialization for a neural network trained to classify the images. We evaluate our approach on the MNIST and Caltech 101 datasets and demonstrate that we are able to learn topological feature maps.