Measuring Dependency via Intrinsic Dimensionality
Measuring Dependency via Intrinsic Dimensionality
复制标题
通过内在维度测量依赖性
DOI：
10.1109/icpr.2016.7899801
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Michael E. Houle
中科院分区：
文献类型：
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作者：
Simone Romano;Oussama Chelly;Xuan Vinh Nguyen;James Bailey;Michael E. Houle
度量多个变量之间的相关性是模式识别中的一项重要任务。在过去的几年里，许多新的依赖措施已经开发的功能关系的探索。在本文中，我们开发了一个变量之间的依赖性措施的基础上的极值理论处理的内在维度。我们的测量识别具有低内在维度的变量-即那些支持将数据嵌入低维流形的变量。为了建立一个强有力的基础上的依赖措施，我们从理论上证明了信息理论和内在维度理论之间的联系。这也使我们能够提出新的估计的内在维度。最后，我们表明，我们的依赖性措施，使找到其他国家的最先进的措施不能找到的模式，对真实的和合成数据。
Measuring the amount of dependency among multiple variables is an important task in pattern recognition. In the last few years, many new dependency measures have been developed for the exploration of functional relationships. In this paper, we develop a dependency measure between variables based on an extreme-value theoretic treatment of intrinsic dimensionality. Our measure identifies variables with low intrinsic dimension - that is, those that support embeddings of the data within low-dimensional manifolds. To build a dependency measure on strong foundations, we theoretically prove a connection between information theory and intrinsic dimensionality theory. This allows us also to propose novel estimators of intrinsic dimensionality. Finally, we show that our dependency measure enables to find patterns that cannot be found by other state-of-the-art measures on real and synthetic data.