Dimensionality reduction for binary data through the projection of natural parameters
Dimensionality reduction for binary data through the projection of natural parameters
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DOI：
10.1016/j.jmva.2020.104668
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发表时间：
2020-11-01
影响因子：
1.6
通讯作者：
Lee, Yoonkyung
中科院分区：
文献类型：
--
作者：
Landgraf, Andrew J.;Lee, Yoonkyung
二进制数据的主成分分析（PCA），称为逻辑PCA，已经成为二进制数据降维的一种流行的替代方法。它的动机是通过矩阵分解，类似于奇异值分解，最大化伯努利对数似然的普通PCA的扩展。我们提出了一个新的制剂的逻辑PCA扩展皮尔逊的制定低维数据表示与最小误差的二进制数据。我们的公式不需要矩阵分解，因为以前的方法，而是寻找从饱和模型的自然参数的投影。由于这种差异，参数的数量不会随着观测值的数量而增加，并且可以通过简单的矩阵乘法来计算新数据的主成分得分。我们推导出特殊结构的数据矩阵的显式解，并提供了一个计算效率高的算法求解主成分负荷。通过模拟实验和对医疗诊断数据的分析，我们将我们的逻辑PCA公式与以前的公式以及普通PCA进行了比较，以证明其优点。(C)2020爱思唯尔公司All rights reserved.
Principal component analysis (PCA) for binary data, known as logistic PCA, has become a popular alternative to dimensionality reduction of binary data. It is motivated as an extension of ordinary PCA by means of a matrix factorization, akin to the singular value decomposition, that maximizes the Bernoulli log-likelihood. We propose a new formulation of logistic PCA which extends Pearson's formulation of a low dimensional data representation with minimum error to binary data. Our formulation does not require a matrix factorization, as previous methods do, but instead looks for projections of the natural parameters from the saturated model. Due to this difference, the number of parameters does not grow with the number of observations and the principal component scores on new data can be computed with simple matrix multiplication. We derive explicit solutions for data matrices of special structure and provide a computationally efficient algorithm for solving for the principal component loadings. Through simulation experiments and an analysis of medical diagnoses data, we compare our formulation of logistic PCA to the previous formulation as well as ordinary PCA to demonstrate its benefits. (C) 2020 Elsevier Inc. All rights reserved.