有序因子的贪婪发现
Greedy Discovery of Ordinal Factors
摘要：
在大型数据集中，很难发现和分析结构。因此，通常为项目引入标签或关键字。在应用程序中，这些数据集然后根据这些标签进行过滤。尽管如此，即使是带有几个标签的中等大小的数据集也会导致复杂的，对人类来说难以导航的系统。在这项工作中，我们采用有序因子分析的方法来解决这个问题。有序因子基于标记的底层结构以线性顺序排列标记的子集。一个完整的序数因子分解，它由这样的序数因子组成，精确地表示原始数据集。基于这样的顺序因子分解，我们提供了一种方法来发现和解释数据集中不同项目和属性之间的关系。然而，即使仅计算一个高基数的有序因子也是计算复杂的。因此，我们提出了贪心算法在这项工作中。该算法利用已有的形式概念分析中的快速算法提取有序因子。然后，我们利用提出一种全面的方法来发现数据集中的关系。此外，我们引入了一个距离度量的基础上出现的顺序分解的表示，以发现相似的项目。为了评估该方法，我们对不同的数据集进行了案例研究。
英文摘要：
In large datasets, it is hard to discover and analyze structure. It is thus common to introduce tags or keywords for the items. In applications, such datasets are then filtered based on these tags. Still, even medium-sized datasets with a few tags result in complex and for humans hard-to-navigate systems. In this work, we adopt the method of ordinal factor analysis to address this problem. An ordinal factor arranges a subset of the tags in a linear order based on their underlying structure. A complete ordinal factorization, which consists of such ordinal factors, precisely represents the original dataset. Based on such an ordinal factorization, we provide a way to discover and explain relationships between different items and attributes in the dataset. However, computing even just one ordinal factor of high cardinality is computationally complex. We thus propose the greedy algorithm in this work. This algorithm extracts ordinal factors using already existing fast algorithms developed in formal concept analysis. Then, we leverage to propose a comprehensive way to discover relationships in the dataset. We furthermore introduce a distance measure based on the representation emerging from the ordinal factorization to discover similar items. To evaluate the method, we conduct a case study on different datasets.
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