论文标题
内在维度和差分熵的偏置校正估计器 - 一种视觉多尺度方法
Bias-corrected estimator for intrinsic dimension and differential entropy--a visual multiscale approach
论文作者
论文摘要
本文研究了内在维度和差分熵估计量，包括它们的系统偏见。提出了对这两种基本措施的联合估计和偏差校正的务实方法。突出显示了两个估计量的共同步骤，以及它们对数据分析的有用后果。结果表明，两个估计量都可以是单个方法的互补部分，并且差异熵和内在维度的同时估计彼此具有含义，在不同的观察量表上的估计传达了不同的基础歧管观点。提出了合成和真实数据集的实验，以说明如何从视觉检查中提取含义以及如何补偿偏见。
Intrinsic dimension and differential entropy estimators are studied in this paper, including their systematic bias. A pragmatic approach for joint estimation and bias correction of these two fundamental measures is proposed. Shared steps on both estimators are highlighted, along with their useful consequences to data analysis. It is shown that both estimators can be complementary parts of a single approach, and that the simultaneous estimation of differential entropy and intrinsic dimension give meaning to each other, where estimates at different observation scales convey different perspectives of underlying manifolds. Experiments with synthetic and real datasets are presented to illustrate how to extract meaning from visual inspections, and how to compensate for biases.
