We consider sufficient dimension reduction (SDR) for spatial point processes. SDR methods aim to identify a lower dimensional sufficient subspace of a data set, in a model-free manner. Most SDR results are based on independent data, and also often do not work well with binary data. [13] introduced a SDR framework for spatial point processes by characterizing point processes as a binary process, and applied several popular SDR methods to spatial point data. On the other hand, [29] proposed Weighted Principal Support Vector Machines (WPSVM) for SDR and showed that it performed better than other methods with binary data. We combine these two works and examine WPSVM for spatial point processes. We show consistency and asymptotic normality of the WPSVM estimated sufficient subspace under some conditions on the spatial process, and compare it with other SDR methods via a simulation study and an application to real data.

中文翻译：

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使用加权主支持向量机对空间点过程进行足够的降维

我们认为空间点过程有足够的降维（SDR）。SDR 方法旨在以无模型的方式识别数据集的低维足够子空间。大多数 SDR 结果基于独立数据，并且通常不适用于二进制数据。[ 13 ]通过将点过程表征为二进制过程，引入了空间点过程的SDR框架，并将几种流行的SDR方法应用于空间点数据。另一方面，[ 29] 为 SDR 提出了加权主支持向量机 (WPSVM)，并表明它比其他处理二进制数据的方法表现更好。我们将这两项工作结合起来，并检查 WPSVM 的空间点过程。我们展示了 WPSVM 在空间过程的某些条件下估计足够子空间的一致性和渐近正态性，并通过模拟研究和对真实数据的应用将其与其他 SDR 方法进行了比较。