Entropy-based sliced inverse regression
Entropy-based sliced inverse regression
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DOI：
10.1016/j.csda.2013.05.017
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发表时间：
2013-11
期刊：
影响因子：
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通讯作者：
H. Hino;Keigo Wakayama;Noboru Murata
中科院分区：
文献类型：
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作者：
H. Hino;Keigo Wakayama;Noboru Murata
随着数据量的增加，数据降维的重要性日益突出。适当的原始数据降维方法有助于减少计算时间和揭示复杂数据的内在结构。切片逆回归是一种著名的回归降维方法，它假设解释变量服从椭圆分布，巧妙地将降维问题转化为简单的特征值问题。切片逆回归是建立在对数据分布和回归函数形式的强假设基础上的，有许多方法可以放松或去除这些假设，以扩展逆回归方法的适用性。然而，每种方法都有其缺点，无论是理论上还是经验上。针对现有方法的不足，提出了一种基于条件熵最小化的回归降维方法。使用熵作为数据分散性的度量，估计低维子空间，而不假设任何特定的分布或任何回归函数。通过人工和真实世界的数据集进行实验，所提出的方法表现出可比或上级的传统方法。
The importance of dimension reduction has been increasing according to the growth of the size of available data in many fields. An appropriate dimension reduction method of raw data helps to reduce computational time and to expose the intrinsic structure of complex data. Sliced inverse regression is a well-known dimension reduction method for regression, which assumes an elliptical distribution for the explanatory variable, and ingeniously reduces the problem of dimension reduction to a simple eigenvalue problem. Sliced inverse regression is based on the strong assumptions on the data distribution and the form of regression function, and there are a number of methods to relax or remove these assumptions to extend the applicability of the inverse regression method. However, each method is known to have its drawbacks either theoretically or empirically. To alleviate drawbacks in the existing methods, a dimension reduction method for regression based on the notion of conditional entropy minimization is proposed. Using entropy as a measure of dispersion of data, a low dimensional subspace is estimated without assuming any specific distribution nor any regression function. The proposed method is shown to perform comparable or superior to the conventional methods through experiments using artificial and real-world datasets.