Schatten范数的光滑性与滑动窗口矩阵流
Smoothness of Schatten Norms and Sliding-Window Matrix Streams
摘要：
大型矩阵通常作为行顺序流访问。我们认为设置行是时间敏感的（即他们到期），这可以描述的滑动窗口行顺序模型，并提供了第一个$(1+ε)$近似Schatten $p$ -规范在此设置。我们的主要技术贡献是证明了Schatten $p$ -范数在行顺序流中是平滑的，因此适合于滑动窗口流的Braverman和Ostrovsky（FOCS 2007）的平滑直方图技术。
英文摘要：
Large matrices are often accessed as a row-order stream. We consider the setting where rows are time-sensitive (i.e. they expire), which can be described by the sliding-window row-order model, and provide the first $(1+ε)$-approximation of Schatten $p$-norms in this setting. Our main technical contribution is a proof that Schatten $p$-norms in row-order streams are smooth, and thus fit the smooth-histograms technique of Braverman and Ostrovsky (FOCS 2007) for sliding-window streams.
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