The Sparse Manifold Transform
The Sparse Manifold Transform
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发表时间：
2018-06
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通讯作者：
Yubei Chen;Dylan M. Paiton;B. Olshausen
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作者：
Yubei Chen;Dylan M. Paiton;B. Olshausen
我们提出了一种称为稀疏流形变换的信号表示框架，它结合了稀疏编码、流形学习和慢特征分析的关键思想。它将主要感觉信号空间中的非线性变换转化为表征嵌入空间中的线性插值，同时保持近似可逆性。稀疏流形变换是一种无监督的生成框架，它明确地、同时地对自然场景中的稀疏离散性和低维流形结构进行建模。当堆叠时，它还可以模拟分层组合。我们提供了转换的理论描述，并证明了在合成数据和自然视频上学习到的表示的性质。
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.