Rapid multivariate analysis of 3D ToF-SIMS data: graphical processor units (GPUs) and low-discrepancy subsampling for large-scale principal component analysis
Rapid multivariate analysis of 3D ToF-SIMS data: graphical processor units (GPUs) and low-discrepancy subsampling for large-scale principal component analysis
复制标题
3D ToF-SIMS 数据的快速多变量分析：图形处理器单元 (GPU) 和用于大规模主成分分析的低差异子采样
DOI：
10.1002/sia.6042
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发表时间：
2016
影响因子：
1.7
通讯作者：
Cumpson P
中科院分区：
文献类型：
--
作者：
Cumpson P
主成分分析（PCA）和其他多变量分析方法已越来越多地用于分析和理解XPS，AES和西姆斯中的深度分布。对于大型图像或三维（3D）成像深度剖面，到目前为止，PCA一直难以应用，这仅仅是因为所涉及的数据矩阵的大小。在最近的一篇论文中，我们描述了两种算法，随机向量1（RV1）和随机向量2（RV2），它们分别提高了PCA的速度和允许无限大小的数据集。在本文中，我们现在应用RV2算法首次在没有子采样的情况下对完整的3D飞行西姆斯数据执行PCA。我们以这种方式处理的数据集是一个120层的128 × 128像素深度剖面，每个体素具有与其相关的70 439值质谱。这在未压缩时形成了超过1TB的数据，使用RV2算法使用传统的Windows桌面个人计算机（PC）处理需要27小时。虽然完整的PCA（例如使用RV2）是最终报告或出版物的首选方法，但在分析过程中需要一种更快速的方法，以便为下一个分析步骤的决策提供信息。因此，我们已经实现了RV1算法的PC上有一个图形处理器单元（GPU）卡包含2880个单独的处理器内核。与使用仅具有中央处理单元的快速商用台式PC相比，这将计算速度提高了约4.1倍，并且在不到7秒的时间内执行完整的PCA。可以以这种方式处理的数据集的大小受到GPU卡上内存大小的限制。这通常对于二维图像是足够的，但对于没有采样的3D深度剖面是不够的。因此，我们研究了有效的采样方案，允许一个很好的近似解决方案的PCA问题的大型3D数据集。我们发现，低差异序列（如Sobol序列抽样）比随机抽样更快收敛，我们推荐这种方法用于日常使用。同时使用GPU和低差异系列，我们预计任何飞行西姆斯数据集，无论大小，都可以使用具有广泛可用GPU卡的商用PC在最多约10秒内有效准确地处理成PCA分量，尽管更长的RV2方法仍然是呈现最终结果的首选方法，例如在已发表的论文中。Copyright © 2016 The Authors Surface and Interface Analysis Published by John Wiley & Sons Ltd
Principal component analysis (PCA) and other multivariate analysis methods have been used increasingly to analyse and understand depth‐profiles in XPS, AES and SIMS. For large images or three‐dimensional (3D) imaging depth‐profiles, PCA has been difficult to apply until now simply because of the size of the matrices of data involved. In a recent paper, we described two algorithms, random vector 1 (RV1) and random vector 2 (RV2), that improve the speed of PCA and allow datasets of unlimited size, respectively. In this paper, we now apply the RV2 algorithm to perform PCA on full 3D time‐of‐flight SIMS data for the first time without subsampling. The dataset we process in this way is a 128 × 128 pixel depth‐profile of 120 layers, each voxel having a 70 439 value mass spectrum associated with it. This forms over a terabyte of data when uncompressed and took 27 h to process using the RV2 algorithm using a conventional windows desktop personal computer (PC). While full PCA (e.g. using RV2) is to be preferred for final reports or publications, a much more rapid method is needed during analysis sessions to inform decisions on the next analytical step. We have therefore implemented the RV1 algorithm on a PC having a graphical processor unit (GPU) card containing 2880 individual processor cores. This increases the speed of calculation by a factor of around 4.1 compared with what is possible using a fast commercially available desktop PC having central processing units alone, and full PCA is performed in less than 7 s. The size of the dataset that can be processed in this way is limited by the size of the memory on the GPU card. This is typically sufficient for two‐dimensional images but not 3D depth‐profiles without sampling. We have therefore examined efficient sampling schemes that allow a good approximate solution to the PCA problem for large 3D datasets. We find that low‐discrepancy series such as Sobol series sampling gives more rapid convergence than random sampling, and we recommend such methods for routine use. Using the GPU and low‐discrepancy series together, we anticipate that any time‐of‐flight SIMS dataset, of whatever size, can be efficiently and accurately processed into PCA components in a maximum of around 10 s using a commercial PC with a widely available GPU card, although the longer RV2 approach is still to be preferred for the presentation of final results, such as in published papers. Copyright © 2016 The Authors Surface and Interface Analysis Published by John Wiley & Sons Ltd