Statistical embeddings using a multilayer union of subspaces

Toward the goal of improved representation learning, we propose a novel deep architecture for unsupervised feature learning based on a recursive multilayered union of subspaces (UoS) model. The model is able to accurately generate recursive nested signal segments at increasing fields of view as we progress from one layer to the next. The local subspace dimension (latent space) grows linearly while the observation space grows exponentially at increasing layers. We apply locally linear coordination to our model output at the top layer to create a globally aligned coordinate system. This enables a very low-dimensional statistical embedding useful for tasks like compression and retrieval. Although the architecture is able to model arbitrary sensor modalities, we focus on image modeling in this study. We compare the performance of our model to the deep belief network by measuring the structural similarity index for a fixed dimensionality reduction on sample face images from CalTech-101. We also show samples of content-based retrieval results on image patches using the statistical embedding.