论文标题
大数据的多维缩放
Multidimensional Scaling for Big Data
论文作者
论文摘要
我们提出了一组针对大数据集实现多维缩放（MDS）的算法。 MDS是使用$ n \ times n $距离矩阵作为输入的降低降低技术的家族，其中$ n $是个人的数量，并产生低维配置：a $ n \ times r $矩阵，带有$ r << n $。当$ n $很大时，MDS与经典MDS算法无法承受，因为它们的内存和时间要求非常大。我们比较了六种旨在克服这些困难的非标准算法。它们基于将数据集分为小片段的核心思想，经典MDS方法可以在其中工作。这些算法中的两种是原始建议。为了检查算法的性能以及比较它们，我们进行了仿真研究。此外，我们已经使用算法来获得EMNIST的MDS配置：一个超过800000美元的真实大数据集。我们得出的结论是，所有算法都适合获取MDS配置，但是我们建议使用我们的一项建议，因为它是一种快速算法，在使用大数据时具有令人满意的统计属性。已经创建了实现算法的R软件包。
We present a set of algorithms implementing multidimensional scaling (MDS) for large data sets. MDS is a family of dimensionality reduction techniques using a $n \times n$ distance matrix as input, where $n$ is the number of individuals, and producing a low dimensional configuration: a $n\times r$ matrix with $r<<n$. When $n$ is large, MDS is unaffordable with classical MDS algorithms because of their extremely large memory and time requirements. We compare six non-standard algorithms intended to overcome these difficulties. They are based on the central idea of partitioning the data set into small pieces, where classical MDS methods can work. Two of these algorithms are original proposals. In order to check the performance of the algorithms as well as to compare them, we have done a simulation study. Additionally, we have used the algorithms to obtain an MDS configuration for EMNIST: a real large data set with more than $800000$ points. We conclude that all the algorithms are appropriate to use for obtaining an MDS configuration, but we recommend using one of our proposals since it is a fast algorithm with satisfactory statistical properties when working with big data. An R package implementing the algorithms has been created.
