Learning Multiple Non-linear Sub-spaces Using K-RBMs

Understanding the nature of data is the key to building good representations. In domains such as natural images, the data comes from very complex distributions which are hard to capture. Feature learning intends to discover or best approximate these underlying distributions and use their knowledge to weed out irrelevant information, preserving most of the relevant information. Feature learning can thus be seen as a form of dimensionality reduction. In this paper, we describe a feature learning scheme for natural images. We hypothesize that image patches do not all come from the same distribution, they lie in multiple non-linear subspaces. We propose a framework that uses K Restricted Boltzmann Machines (K-RBMs) to learn multiple non-linear subspaces in the raw image space. Projections of the image patches into these subspaces gives us features, which we use to build image representations. Our algorithm solves the coupled problem of finding the right non-linear subspaces in the input space and associating image patches with those subspaces in an iterative EM like algorithm to minimize the overall reconstruction error. Extensive empirical results over several popular image classification datasets show that representations based on our framework outperform the traditional feature representations such as the SIFT based Bag-of-Words (BoW) and convolutional deep belief networks.