We consider the problem of generating hypothesis from data based on ideas from logic. We introduce a notion of barcodes, which we call sequent barcodes, that mirrors the barcodes in persistent homology theory in topological data analysis. We prove a theoretical result on the stability of these barcodes in analogy with similar results in persistent homology theory. Additionally we show that our new notion of barcodes can be interpreted in terms of a persistent homology of a particular filtration of topological spaces induced by the data. Finally, we discuss a concrete application of the sequent barcodes in a discovery problem arising from the area of cancer genomics.
翻译：我们考虑从逻辑观点的数据中产生假设的问题。我们引入了条形码的概念,我们称之为序列条形码,它反映了在地形数据分析中持续存在的同族主义理论中的条形码。我们证明这些条形码的稳定性的理论结果与持续同理理论的类似结果是类似的。此外,我们表明,我们新的条形码概念可以被解释为数据引起的特定地形空间的持续同质化。最后,我们讨论了在癌症基因组学领域出现的发现问题中具体应用序列条形码的问题。
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