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arXiv 1807.04734cs.LGstat.ML
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基于约束递归稀疏自编码器的可扩展卷积字典学习

Scalable Convolutional Dictionary Learning with Constrained Recurrent Sparse Auto-encoders

Harvard University(哈佛大学);Manifold AI(Manifold人工智能公司)

Bahareh Tolooshams, Sourav Dey, Demba Ba

摘要:

给定一组观测信号的卷积字典,精心设计的自动编码器能否在存在噪声的情况下恢复字典?我们引入了一个自动编码器架构,称为约束循环稀疏自动编码器(CRsAE),回答这个问题的肯定。给定输入信号和近似字典,编码器使用FISTA找到稀疏近似。解码器通过将字典应用于编码器的输出来重构信号。CRsAE中的编码器和解码器在用于字典学习的基于优化的交替最小化方案中并行稀疏编码和字典更新步骤。因此,编码器和解码器的参数不是独立的,这是我们第一次强制执行的约束。我们推导出反向传播算法CRsAE。CRsAE是一个盲声源分离的框架,只有知道源(字典元素)的数量,并假设稀疏-许多可以重叠,是能够分离它们。我们证明了它的实用程序的背景下,尖峰排序,计算神经科学中的声源分离问题。我们证明了CRsAE的能力,以恢复潜在的字典,并表征其灵敏度作为SNR的函数。

英文摘要:

Given a convolutional dictionary underlying a set of observed signals, can a carefully designed auto-encoder recover the dictionary in the presence of noise? We introduce an auto-encoder architecture, termed constrained recurrent sparse auto-encoder (CRsAE), that answers this question in the affirmative. Given an input signal and an approximate dictionary, the encoder finds a sparse approximation using FISTA. The decoder reconstructs the signal by applying the dictionary to the output of the encoder. The encoder and decoder in CRsAE parallel the sparse-coding and dictionary update steps in optimization-based alternating-minimization schemes for dictionary learning. As such, the parameters of the encoder and decoder are not independent, a constraint which we enforce for the first time. We derive the back-propagation algorithm for CRsAE. CRsAE is a framework for blind source separation that, only knowing the number of sources (dictionary elements), and assuming sparsely-many can overlap, is able to separate them. We demonstrate its utility in the context of spike sorting, a source separation problem in computational neuroscience. We demonstrate the ability of CRsAE to recover the underlying dictionary and characterize its sensitivity as a function of SNR.

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