草图和比例：地理分布的tSNE和UMAP
Sketch and Scale: Geo-distributed tSNE and UMAP
摘要：
在确保隐私和数据安全的数据管理策略领域，对地理分布的数据集运行机器学习分析是一个迅速出现的问题。使用t分布随机邻域嵌入（tSNE）和均匀流形近似和投影（UMAP）等工具可视化高维数据已成为数据科学家的常见做法。这两种工具在时间和内存方面的扩展性都很差。虽然最近的优化显示成功处理了10，000个数据点，但扩展到超过百万个点仍然具有挑战性。我们介绍了一个新的框架：草图和规模（SnS）。它利用Count Sketch数据结构来压缩边缘节点上的数据，在主节点上聚合尺寸减小的草图，并在摘要上运行vanilla tSNE或UMAP，表示从聚合草图中提取的分布式区域。我们展示了这种技术是完全并行的，在时间上线性扩展，在内存和通信上具有时序性，使得分析分布在全球多个数据中心的数百万甚至数十亿个数据点的数据集成为可能。我们在两个中等规模的数据集上展示了我们的方法的强大功能：来自肿瘤活检多个图像的5200万35波段像素的癌症数据;以及来自斯隆数字巡天（SDSS）的1亿颗恒星的多色测光的天体物理学数据。
英文摘要：
Running machine learning analytics over geographically distributed datasets is a rapidly arising problem in the world of data management policies ensuring privacy and data security. Visualizing high dimensional data using tools such as t-distributed Stochastic Neighbor Embedding (tSNE) and Uniform Manifold Approximation and Projection (UMAP) became common practice for data scientists. Both tools scale poorly in time and memory. While recent optimizations showed successful handling of 10,000 data points, scaling beyond million points is still challenging. We introduce a novel framework: Sketch and Scale (SnS). It leverages a Count Sketch data structure to compress the data on the edge nodes, aggregates the reduced size sketches on the master node, and runs vanilla tSNE or UMAP on the summary, representing the densest areas, extracted from the aggregated sketch. We show this technique to be fully parallel, scale linearly in time, logarithmically in memory, and communication, making it possible to analyze datasets with many millions, potentially billions of data points, spread across several data centers around the globe. We demonstrate the power of our method on two mid-size datasets: cancer data with 52 million 35-band pixels from multiple images of tumor biopsies; and astrophysics data of 100 million stars with multi-color photometry from the Sloan Digital Sky Survey (SDSS).
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