The Sparse Manifold Transform

2018/06/23 by Yubei Chen, Dylan M. Paiton, Chen, Yubei +3 · 1 voice · 9 citations
Computer Science · Engineering · Mathematics · Neuroscience · #Advanced Vision and Imaging #Computer science #Engineering #Manifold (fluid mechanics) #Mathematics #Neural dynamics and brain function #Visual perception and processing mechanisms #cs.LG #eess.IV #stat.ML

paper · pdf · doi:10.48550/arxiv.1806.08887

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2018/06/23 · arxiv created 2018/12/02 · arxiv updated 2018/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Efficient Visual Coding: From Retina To V2
• The Emerging Field of Signal Processing on Graphs: Extending High-Dimensional Data Analysis to Networks and Other Irregular Domains
• Sparse coding with an overcomplete basis set: A strategy employed by V1?
• An Information-Maximization Approach to Blind Separation and Blind Deconvolution
• Slow Feature Analysis: Unsupervised Learning of Invariances
• Unsupervised Learning of Disentangled Representations from Video
• Signal Recovery from Pooling Representations

Cited by

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• Cloning Deterministic Worlds: The Critical Role of Latent Geometry in Long-Horizon World Models
• Scaling Non-Parametric Sampling with Representation
• Unsupervised Sparse Coding-based Spiking Neural Network for Real-time Spike Sorting
• Do Sparse Autoencoders Capture Concept Manifolds?

Discussions

• The Sparse Manifold Transform (2018) [pdf] [hn, 36 points, 1 comments]

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