Summarising a high dimensional data set with a low dimensional embeddingis a standard approach for exploring its structure. In this paperwe provide an overview of some existing techniques for discoveringsuch embeddings. We then introduce a novel probabilistic interpretationof principal component analysis (PCA) that we term dual probabilisticPCA (DPPCA). The DPPCA model has the additional advantage that thelinear mappings from the embedded space can easily be non-linearisedthrough Gaussian processes. We refer to this model as a Gaussian processlatent variable model (GP-LVM). Through analysis of the GP-LVM objectivefunction, we relate the model to popular spectral techniques suchas kernel PCA and multidimensional scaling. We then review a practicalalgorithm for GP-LVMs in the context of large data sets and developit to also handle discrete valued data and missing attributes. Wedemonstrate the model on a range of real-world and artificially generateddata sets. color="gray">
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机译：用低维嵌入概括高维数据集是探索其结构的标准方法。在本文中，我们提供了一些发现此类嵌入的现有技术的概述。然后，我们介绍了一种新的主成分分析（PCA）概率解释，我们称之为对偶概率PCA（DPPCA）。 DPPCA模型的另一个优点是，通过高斯过程可以轻松地将来自嵌入式空间的线性映射非线性化。我们将此模型称为高斯过程潜变量模型（GP-LVM）。通过分析GP-LVM目标函数，我们将模型与流行的频谱技术（例如内核PCA和多维缩放）相关联。然后，我们在大型数据集的背景下回顾了GP-LVM的实用算法，并发展为还处理离散值数据和缺失属性。在一系列实际和人工生成的数据集上演示该模型。 color =“ gray”>
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