论文标题
部分可观测时空混沌系统的无模型预测
ABID: Angle Based Intrinsic Dimensionality
论文作者
论文摘要
固有维度是指数据的``true''维度，而不是数据表示的维度。例如，当属性高度相关时，固有维度可能比变量数量低得多。局部内在维度是指以下观察结果：数据集的不同部分可能会有所不同。固有维度可以作为数据集局部难度的代理。 估计局部内在维度的最流行方法是基于距离，而距离最近邻居的距离增加的速度是``扩展维度''的概念。在本文中，我们引入了一个正交概念，该概念不使用任何距离：我们使用邻居点之间的角度分布。我们得出角度的理论分布，并使用它来构建估计器的内在维度。 在实验上，我们验证了该措施的行为相似，但与现有的内在维度衡量标准相辅相成。通过向研究界引入一种内在维度的新想法，我们希望为对内在维度的更好理解，并刺激这一方向的新研究。
The intrinsic dimensionality refers to the ``true'' dimensionality of the data, as opposed to the dimensionality of the data representation. For example, when attributes are highly correlated, the intrinsic dimensionality can be much lower than the number of variables. Local intrinsic dimensionality refers to the observation that this property can vary for different parts of the data set; and intrinsic dimensionality can serve as a proxy for the local difficulty of the data set. Most popular methods for estimating the local intrinsic dimensionality are based on distances, and the rate at which the distances to the nearest neighbors increase, a concept known as ``expansion dimension''. In this paper we introduce an orthogonal concept, which does not use any distances: we use the distribution of angles between neighbor points. We derive the theoretical distribution of angles and use this to construct an estimator for intrinsic dimensionality. Experimentally, we verify that this measure behaves similarly, but complementarily, to existing measures of intrinsic dimensionality. By introducing a new idea of intrinsic dimensionality to the research community, we hope to contribute to a better understanding of intrinsic dimensionality and to spur new research in this direction.
