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Low-dimensional tracking of association structures in categorical data

机译：分类数据中关联结构的低维跟踪

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In modern applications, such as text mining and signal processing, large amounts of categorical data are produced at a high rate and are characterized by association structures changing over time. Multiple correspondence analysis (MCA) is a well established dimension reduction method to explore the associations within a set of categorical variables. A critical step of the MCA algorithm is a singular value decomposition (SVD) or an eigenvalue decomposition (EVD) of a suitably transformed matrix. The high computational and memory requirements of ordinary SVD and EVD make their application impractical on massive or sequential data sets. Several enhanced SVD/EVD approaches have been recently introduced in an effort to overcome these issues. The aim of the present contribution is twofold: (1) to extend MCA to a split-apply-combine framework, that leads to an exact and parallel MCA implementation; (2) to allow for incremental updates (downdates) of existing MCA solutions, which lead to an approximate yet highly accurate solution. For this purpose, two incremental EVD and SVD approaches with desirable properties are revised and embedded in the context of MCA.
机译：在诸如文本挖掘和信号处理之类的现代应用中，大量分类数据以高速率产生，并且其特征在于关联结构随时间而变化。多重对应分析（MCA）是一种完善的降维方法，用于探索一组类别变量中的关联。 MCA算法的关键步骤是适当转换的矩阵的奇异值分解（SVD）或特征值分解（EVD）。普通SVD和EVD对计算和内存的高要求使其在大量或顺序数据集上的应用不切实际。为了克服这些问题，最近引入了几种增强的SVD / EVD方法。本贡献的目的是双重的：（1）将MCA扩展到可拆分合并框架，从而实现精确且并行的MCA实现； （2）允许对现有MCA解决方案进行增量更新（更新），从而得出近似而高度准确的解决方案。为此，在MCA的上下文中修订并嵌入了具有所需属性的两种增量EVD和SVD方法。

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