Thin Plate Spline Latent Variable Models for dimensionality reduction

Dimensionality reduction (DR) has been considered as one of the most significant tools for data analysis. In this paper we propose a new latent variable model based on the thin plate splines, named Thin Plate Spline Latent Variable Model (TPSLVM). It has strong connection with the so-called Gaussian Process Latent Variable Model (GPLVM). We demonstrate that the proposed TPSLVM can be viewed as the GPLVM with a fairly peculiar covariance function. Moreover, compared to GPLVM, TPSLVM is more powerful especially when the dimensionality of the latent space is very low (e.g., 2D or 3D). One of main purposes of DR algorithms is to visualize data in 2D/3D spaces. Therefore, TPSLVM will benefit this process. Experimental results show that TPSLVM provides better data visualization and more efficient dimensionality reduction than GPLVM.