基于数据打结的近似消失理想
Approximate Vanishing Ideal via Data Knotting
摘要：
消失理想是一组在给定数据点上取零值的多项式。消失理想最初是在计算机代数中提出的，最近在许多应用中被用于提取数据的非线性结构。为了避免对噪声数据的过拟合，多项式通常被设计为在指定数据上近似等于零而不是精确等于零。虽然这样的近似经验证明高性能，声音消失理想的代数结构丢失。本文提出了一种消失理想，它是容忍噪声数据，也追求有一个更好的代数结构。作为一个新的问题，我们同时找到一组多项式和数据点，多项式近似消失的输入数据点，几乎完全消失的发现的数据点。在实验分类测试中，我们的方法发现了比现有的最先进的方法少得多，次数更低的多项式。因此，我们的方法加快了分类任务的运行时间，而不会降低分类精度。
英文摘要：
The vanishing ideal is a set of polynomials that takes zero value on the given data points. Originally proposed in computer algebra, the vanishing ideal has been recently exploited for extracting the nonlinear structures of data in many applications. To avoid overfitting to noisy data, the polynomials are often designed to approximately rather than exactly equal zero on the designated data. Although such approximations empirically demonstrate high performance, the sound algebraic structure of the vanishing ideal is lost. The present paper proposes a vanishing ideal that is tolerant to noisy data and also pursued to have a better algebraic structure. As a new problem, we simultaneously find a set of polynomials and data points for which the polynomials approximately vanish on the input data points, and almost exactly vanish on the discovered data points. In experimental classification tests, our method discovered much fewer and lower-degree polynomials than an existing state-of-the-art method. Consequently, our method accelerated the runtime of the classification tasks without degrading the classification accuracy.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
