Functional Parallel Factor Analysis for Functions of One- and Two-dimensional Arguments
Functional Parallel Factor Analysis for Functions of One- and Two-dimensional Arguments
复制标题
一维和二维参数函数的函数平行因子分析
作者：
Ji Yeh Choi;Heungsun Hwang;M. Timmerman
平行因子分析（PARAFAC）是一种有用的多变量方法，用于分解同时由三种不同类型实体组成的三向数据。该方法估计三线性分量，其中每一个都是一组实体的低维表示，通常称为模式，以解释数据的最大方差。功能性PARAFAC允许不同模式下的实体是平滑的函数或曲线，在连续体上变化，而不是不连接响应的集合。现有的函数式PARAFAC方法只处理一维参数（例如，时间）的函数。在本文中，我们提出了功能PARAFAC的一个新扩展，用于处理响应沿二维域（例如，具有x轴和y轴坐标的平面）和一维参数排序的三向数据。在技术上，该方法将PARAFAC与基函数展开近似相结合，使用一组分段二次元基函数估计二维光滑函数，使用一组一维基函数估计一维光滑函数。在仿真研究中，所提出的方法似乎优于传统的PARAFAC。我们将该方法应用于脑电图数据，以证明其经验有效性。
Parallel factor analysis (PARAFAC) is a useful multivariate method for decomposing three-way data that consist of three different types of entities simultaneously. This method estimates trilinear components, each of which is a low-dimensional representation of a set of entities, often called a mode, to explain the maximum variance of the data. Functional PARAFAC permits the entities in different modes to be smooth functions or curves, varying over a continuum, rather than a collection of unconnected responses. The existing functional PARAFAC methods handle functions of a one-dimensional argument (e.g., time) only. In this paper, we propose a new extension of functional PARAFAC for handling three-way data whose responses are sequenced along both a two-dimensional domain (e.g., a plane with x- and y-axis coordinates) and a one-dimensional argument. Technically, the proposed method combines PARAFAC with basis function expansion approximations, using a set of piecewise quadratic finite element basis functions for estimating two-dimensional smooth functions and a set of one-dimensional basis functions for estimating one-dimensional smooth functions. In a simulation study, the proposed method appeared to outperform the conventional PARAFAC. We apply the method to EEG data to demonstrate its empirical usefulness.
DOI：
10.1006/cbmr.1996.0014
发表时间：
1996-06-01
期刊：
COMPUTERS AND BIOMEDICAL RESEARCH
影响因子：
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作者：
Cox, RW
通讯作者：
Cox, RW