公共信息成分分析
Common Information Components Analysis
摘要：
我们给出了典型相关分析（CCA）通过（放松）Wyner的共同信息的信息论解释。CCA允许从两个高维数据集中提取低维描述（特征），这些描述（特征）使用相关性和线性变换的框架来捕获数据集之间的共性。我们的解释首先提取公共信息，达到预先选择的分辨率水平，然后将其投影回每个数据集。在高斯统计的情况下，该过程精确地简化为CCA，其中分辨率级别指定提取的CCA分量的数量。这也提出了一种新的算法，公共信息成分分析（CICA），具有几个理想的功能，包括自然扩展到两个数据集之外。
英文摘要：
We give an information-theoretic interpretation of Canonical Correlation Analysis (CCA) via (relaxed) Wyner's common information. CCA permits to extract from two high-dimensional data sets low-dimensional descriptions (features) that capture the commonalities between the data sets, using a framework of correlations and linear transforms. Our interpretation first extracts the common information up to a pre-selected resolution level, and then projects this back onto each of the data sets. In the case of Gaussian statistics, this procedure precisely reduces to CCA, where the resolution level specifies the number of CCA components that are extracted. This also suggests a novel algorithm, Common Information Components Analysis (CICA), with several desirable features, including a natural extension to beyond just two data sets.
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