Unsupervised deep kernel for high dimensional data

In this paper we propose a method for visualizing unlabeled high dimensional data in a 3-dimensional space using Kernel Principal Component Analysis (KPCA) with the proposed unsupervised deep kernel. First, an optimal cluster structure of the data is determined using an unsupervised procedure. Second, an unsupervised deep kernel is learned via the clustered data. Then, deep kernel based PCA is applied to map the data into a 3-dimensional space for visualization. To ensure the visualization on a 3-dimensional space is reliable, we proposed the V_3D (Visualizability in 3 Dimension) measurement to evaluate the amount of structural information is maintained by the dimension reduction process. V_3D is computed based on the comparison of the clustering structures of the data before and after dimension reduction. The reduction and visualization results using the deep kernel based PCA are compared with several other methods include Principal Component Analysis, PCA based on other kernel functions, Entropy Component Analysis, and deep learning approaches. The experimental results show that the deep kernel outperforms all other methods in dimension reductions with respect to the V_3D measure.