论文标题
局部线性嵌入，因子分析和概率PCA之间的理论联系
Theoretical Connection between Locally Linear Embedding, Factor Analysis, and Probabilistic PCA
论文作者
论文摘要
局部线性嵌入（LLE）是一种非线性光谱维度降低和多种学习方法。它有两个主要步骤，分别是线性重建和分别在输入空间和嵌入空间中的点的线性嵌入。在这项工作中，我们从随机的角度看线性重建步骤，其中假定每个数据点都以其线性重建权重为潜在因素。 LLE的随机线性重建是使用预期最大化解决的。我们表明，三种基本维度降低方法（即LLE，因子分析和概率主成分分析（PCA））之间存在理论上的联系。 LLE的随机线性重建类似于因子分析和概率PCA。这也解释了为什么因子分析和概率PCA是线性的，而LLE是一种非线性方法。这项工作结合了两种降低维数的广泛方法，即光谱和概率算法。
Locally Linear Embedding (LLE) is a nonlinear spectral dimensionality reduction and manifold learning method. It has two main steps which are linear reconstruction and linear embedding of points in the input space and embedding space, respectively. In this work, we look at the linear reconstruction step from a stochastic perspective where it is assumed that every data point is conditioned on its linear reconstruction weights as latent factors. The stochastic linear reconstruction of LLE is solved using expectation maximization. We show that there is a theoretical connection between three fundamental dimensionality reduction methods, i.e., LLE, factor analysis, and probabilistic Principal Component Analysis (PCA). The stochastic linear reconstruction of LLE is formulated similar to the factor analysis and probabilistic PCA. It is also explained why factor analysis and probabilistic PCA are linear and LLE is a nonlinear method. This work combines and makes a bridge between two broad approaches of dimensionality reduction, i.e., the spectral and probabilistic algorithms.
