Dictionary Learning for Sparse Representation: A Novel Approach
Dictionary Learning for Sparse Representation: A Novel Approach
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DOI：
10.1109/lsp.2013.2285218
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发表时间：
2013-10
影响因子：
3.9
通讯作者：
M. Sadeghi;M. Babaie-zadeh;C. Jutten
中科院分区：
文献类型：
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作者：
M. Sadeghi;M. Babaie-zadeh;C. Jutten
字典学习问题是一个矩阵分解，其目标是将训练数据矩阵Y分解为字典D和稀疏系数矩阵X的乘积，如下所示，Y <$DX。目前的字典学习算法最小化表示误差受到D（通常具有单位列范数）和X的稀疏性的约束。由此产生的问题相对于对（D，X）不是凸的。在这封信中，我们推导出一个一阶级数展开公式的因式分解，DX。所得到的目标函数关于D和X是联合凸的。我们简单地使用交替最小化来解决由此产生的问题，并将之前提出的一些算法应用到我们的新问题上。一个已知的字典和字典学习自然图像补丁的恢复的仿真结果表明，我们的新问题大大提高了性能与一点额外的计算负载。
A dictionary learning problem is a matrix factorization in which the goal is to factorize a training data matrix, Y, as the product of a dictionary, D, and a sparse coefficient matrix, X, as follows, Y ≃ DX. Current dictionary learning algorithms minimize the representation error subject to a constraint on D (usually having unit column-norms) and sparseness of X. The resulting problem is not convex with respect to the pair (D,X). In this letter, we derive a first order series expansion formula for the factorization, DX. The resulting objective function is jointly convex with respect to D and X. We simply solve the resulting problem using alternating minimization and apply some of the previously suggested algorithms onto our new problem. Simulation results on recovery of a known dictionary and dictionary learning for natural image patches show that our new problem considerably improves performance with a little additional computational load.