Sample complexity bounds for dictionary learning of tensor data
Sample complexity bounds for dictionary learning of tensor data
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DOI：
10.1109/icassp.2017.7953008
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发表时间：
2017-03
期刊：
影响因子：
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通讯作者：
Z. Shakeri;W. Bajwa;A. Sarwate
中科院分区：
文献类型：
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作者：
Z. Shakeri;W. Bajwa;A. Sarwate
本文给出了K阶张量数据的Kronecker结构字典估计的样本复杂度的界。训练样本由这些结构化字典原子的线性组合生成，并通过白色高斯噪声进行观察。下限遵循一般系数分布的极大极小风险的下限，并且可以进一步专门用于稀疏高斯系数。这个界限与张量数据的（较小的）坐标字典的维度的乘积之和线性缩放。还提供了一种二阶张量数据的显式字典估计算法，其样本复杂度在尺度意义上与下界相匹配。数值实验突出了在字典学习过程中明确考虑数据的张量结构的优势。
This paper provides bounds on the sample complexity of estimating Kronecker-structured dictionaries for Kth-order tensor data. The training samples are generated by linear combinations of these structured dictionary atoms and observed through white Gaussian noise. The lower bound follows from a lower bound on the minimax risk for general coefficient distributions and can be further specialized to sparse-Gaussian coefficients. This bound scales linearly with the sum of the product of the dimensions of the (smaller) coordinate dictionaries for tensor data. An explicit dictionary estimation algorithm for 2nd-order tensor data is also provided whose sample complexity matches the lower bound in the scaling sense. Numerical experiments highlight the advantages associated with explicitly accounting for tensor structure of data during dictionary learning.