极值K分类样本问题
Extreme-K categorical samples problem
摘要：
以直方图为基础，发展了基于极端$K$样本问题的分类探索性数据分析（CEDA），并通过4个一维分类数据集说明了CEDA的普遍适用性。给定一个相当大的$K$，CEDA的最终目标是通过执行两个数据驱动的计算任务来发现数据的信息内容：1）在$K$种群上建立一个树几何结构，作为发现种群之间广泛的模式的平台; 2）评估每个几何模式的可靠性。在CEDA开发中，每个总体产生类别比例的行向量。在数据矩阵的行轴上，我们讨论了欧氏距离与其加权版本的优点和缺点，用于构建二叉聚类树几何。选择的标准取决于由该二叉聚类树框定的列块的均匀度。每个树叶（人口），然后编码的二进制代码序列，所以是基于树的模式。为了评估可靠性，我们采用按行的多项式随机性来产生一个矩阵模仿的集成，所以模仿二叉树的集成。任何观察到的模式的可靠性是它在树集合中的重现率。高可靠性值意味着确定性模式。我们的CEDA的四个应用阐明了极端$K$样本问题的四个重要方面。
英文摘要：
With histograms as its foundation, we develop Categorical Exploratory Data Analysis (CEDA) under the extreme-$K$ sample problem, and illustrate its universal applicability through four 1D categorical datasets. Given a sizable $K$, CEDA's ultimate goal amounts to discover by data's information content via carrying out two data-driven computational tasks: 1) establish a tree geometry upon $K$ populations as a platform for discovering a wide spectrum of patterns among populations; 2) evaluate each geometric pattern's reliability. In CEDA developments, each population gives rise to a row vector of categories proportions. Upon the data matrix's row-axis, we discuss the pros and cons of Euclidean distance against its weighted version for building a binary clustering tree geometry. The criterion of choice rests on degrees of uniformness in column-blocks framed by this binary clustering tree. Each tree-leaf (population) is then encoded with a binary code sequence, so is tree-based pattern. For evaluating reliability, we adopt row-wise multinomial randomness to generate an ensemble of matrix mimicries, so an ensemble of mimicked binary trees. Reliability of any observed pattern is its recurrence rate within the tree ensemble. A high reliability value means a deterministic pattern. Our four applications of CEDA illuminate four significant aspects of extreme-$K$ sample problems.
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