The Sparse Manifold Transform
This work addresses the challenge of modeling sparse and low-dimensional structures in sensory data for machine learning and AI applications, presenting a novel theoretical framework.
The paper tackles the problem of representing natural scenes by developing the sparse manifold transform, an unsupervised generative framework that combines sparse coding, manifold learning, and slow feature analysis to convert non-linear signal transformations into linear interpolations while maintaining invertibility, and demonstrates its properties on synthetic data and natural videos.
We present a signal representation framework called the sparse manifold transform that combines key ideas from sparse coding, manifold learning, and slow feature analysis. It turns non-linear transformations in the primary sensory signal space into linear interpolations in a representational embedding space while maintaining approximate invertibility. The sparse manifold transform is an unsupervised and generative framework that explicitly and simultaneously models the sparse discreteness and low-dimensional manifold structure found in natural scenes. When stacked, it also models hierarchical composition. We provide a theoretical description of the transform and demonstrate properties of the learned representation on both synthetic data and natural videos.