A Gaussian Process Decoder with Spectral Mixtures and a Locally Estimated Manifold for Data Visualization

Dimensionality reduction plays an important role in interpreting and visualizing high-dimensional data. Previous methods for data visualization overestimate the local structure and lack the consideration of global preservation. In this study, we develop a Gaussian process latent variable model (GP-LVM) for data visualization. GP-LVMs are one of the frameworks of principal component analysis and preserve the global structure effectively. The drawbacks of GP-LVMs are the absence of local structure preservation and the use of low-expressive kernel functions. Therefore, we introduce regularization for local preservation and an expressive kernel function into GP-LVMs to overcome these limitations. As a result, we reflect the global and local structures in low-dimensional representations, improving the reliability and visibility of embeddings. We conduct qualitative and quantitative experiments comparing baselines and state-of-the-art methods on image and text datasets.

Automated summary

Dimensionality reduction is crucial for interpreting and visualizing high-dimensional data. However, previous methods tend to overestimate local structure and overlook global preservation. In this study, we propose a Gaussian process latent variable model (GP-LVM) for data visualization, which effectively preserves global structure. To address the limitations of GP-LVM in terms of local structure preservation and expressive kernel functions, we introduce regularization and an expressive kernel function. The results demonstrate that our approach captures both global and local structures in low-dimensional representations, enhancing the reliability and visibility of embeddings. We conduct qualitative and quantitative experiments, comparing our method with baselines and state-of-the-art techniques on image and text datasets.