太阳黑子和活动区的图像补丁分析。I.内在维数与相关分析
Image patch analysis of sunspots and active regions. I. Intrinsic dimension and correlation analysis
摘要：
活动区的耀斑生产率与其空间复杂性有关。威尔逊山或麦金托什太阳黑子分类测量这种复杂性，但以分类的方式，因此可能不会使用所有的信息在观测。此外，这样的分类方案阻碍了对活动区域演化的系统研究。我们提出了一个活动区域的复杂性，并将它们与威尔逊山分类细尺度定量描述符。我们分析了连续谱和磁图数据的局部相关结构，以及连续谱和磁图数据之间的互相关。我们计算的内在尺寸，偏相关，典型相关分析（CCA）的连续和磁图活动区的图像补丁从SOHO-MDI仪器。我们使用来自连续体的太阳黑子的掩模以及来自磁图的磁活动区的较大掩模来分别分析活动区的核心部分及其周围部分。我们发现的复杂性之间的关系的一个活跃的区域，测量威尔逊山和其图像补丁的内在尺寸。偏相关模式表现出近似三阶马尔可夫结构。CCA揭示了不同的模式之间的相关性连续和磁记录内的太阳黑子和太阳黑子周围的地区。这些结果也铺平了道路，基于补丁的字典学习，以期自动聚类的活动区域。
英文摘要：
The flare-productivity of an active region is observed to be related to its spatial complexity. Mount Wilson or McIntosh sunspot classifications measure such complexity but in a categorical way, and may therefore not use all the information present in the observations. Moreover, such categorical schemes hinder a systematic study of an active region's evolution for example. We propose fine-scale quantitative descriptors for an active region's complexity and relate them to the Mount Wilson classification. We analyze the local correlation structure within continuum and magnetogram data, as well as the cross-correlation between continuum and magnetogram data. We compute the intrinsic dimension, partial correlation, and canonical correlation analysis (CCA) of image patches of continuum and magnetogram active region images taken from the SOHO-MDI instrument. We use masks of sunspots derived from continuum as well as larger masks of magnetic active regions derived from the magnetogram to analyze separately the core part of an active region from its surrounding part. We find the relationship between complexity of an active region as measured by Mount Wilson and the intrinsic dimension of its image patches. Partial correlation patterns exhibit approximately a third-order Markov structure. CCA reveals different patterns of correlation between continuum and magnetogram within the sunspots and in the region surrounding the sunspots. These results also pave the way for patch-based dictionary learning with a view towards automatic clustering of active regions.
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