非负贪婪稀疏分解的简化加速搜索
Accelerated Search for Non-Negative Greedy Sparse Decomposition via Dimensionality Reduction
摘要：
非负信号是一类重要的稀疏信号。许多算法已经被提出来恢复这样的非负表示，其中贪婪和凸松弛算法是最流行的方法。一种快速实现是FNNOMP算法，其以迭代方式更新非负系数。尽管FNNOMP在处理小规模库时是一种很好的方法，但当库的大小很大时，算法的操作时间会显著增加。这主要是由于算法的选择步骤依赖于矩阵向量乘法。我们在这里介绍嵌入式最近邻（E-NN）算法，该算法在保证找到最相关的原子的同时，加速了对大型数据集的搜索。然后，我们用E-NN代替FNNOMP的选择步骤。此外，我们在FNNOMP的查找表中引入更新最近邻（U-NN），以确保FNNOMP的非负性准则。结果表明，所提出的方法可以加速FNNOMP的一个因素4的真实数据集的拉曼光谱和一个因素22的合成数据集。
英文摘要：
Non-negative signals form an important class of sparse signals. Many algorithms have already beenproposed to recover such non-negative representations, where greedy and convex relaxed algorithms are among the most popular methods. One fast implementation is the FNNOMP algorithm that updates the non-negative coefficients in an iterative manner. Even though FNNOMP is a good approach when working on libraries of small size, the operational time of the algorithm grows significantly when the size of the library is large. This is mainly due to the selection step of the algorithm that relies on matrix vector multiplications. We here introduce the Embedded Nearest Neighbor (E-NN) algorithm which accelerates the search over large datasets while it is guaranteed to find the most correlated atoms. We then replace the selection step of FNNOMP by E-NN. Furthermore we introduce the Update Nearest Neighbor (U-NN) at the look up table of FNNOMP in order to assure the non-negativity criteria of FNNOMP. The results indicate that the proposed methodology can accelerate FNNOMP with a factor 4 on a real dataset of Raman Spectra and with a factor of 22 on a synthetic dataset.
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