The cumulative distribution transform and linear pattern classification
The cumulative distribution transform and linear pattern classification
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DOI：
10.1016/j.acha.2017.02.002
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发表时间：
2018-11-01
影响因子：
2.5
通讯作者：
Rohde, Gustavo K.
中科院分区：
文献类型：
--
作者：
Park, Se Rim;Kolouri, Soheil;Rohde, Gustavo K.
识别来自传感器的数据类别是许多科学技术应用中的一个重要问题。我们描述了一种新的模式表示变换，它将模式解释为概率密度函数，并且在分类方面具有特殊的性质。我们称之为累积分布变换（CDT）的变换是可逆的，具有定义良好的正向和逆操作。我们证明，通过将拉格朗日变化（位移和强度变化）转换为变换空间中的“欧拉”变化（强度变化），它可以在“解析”出拉格朗日变化（混淆）时很有用。这种转换是我们主要结果的基础，该结果描述了CDT何时可以在变换空间中允许线性分类。我们还描述了变换的几个特性，并通过使用真实和模拟数据的计算实验表明，CDT可以帮助使各种现实世界的问题更容易解决。(C) 2017爱思唯尔公司版权所有。
Discriminating data classes emanating from sensors is an important problem with many applications in science and technology. We describe a new transform for pattern representation that interprets patterns as probability density functions, and has special properties with regards to classification. The transform, which we denote as the Cumulative Distribution Transform (CDT), is invertible, with well defined forward and inverse operations. We show that it can be useful in 'parsing out' variations (confounds) that are lagrangian' (displacement and intensity variations) by converting these to 'Eulerian' (intensity variations) in transform space. This conversion is the basis for our main result that describes when the CDT can allow for linear classification to be possible in transform space. We also describe several properties of the transform and show, with computational experiments that used both real and simulated data, that the CDT can help render a variety of real world problems simpler to solve. (C) 2017 Elsevier Inc. All rights reserved.