k* Distribution: Evaluating the Latent Space of Deep Neural Networks Using Local Neighborhood Analysis

Most examinations of neural networks' learned latent spaces typically employ dimensionality reduction techniques such as t-distributed stochastic neighbor embedding (t-SNE) or uniform manifold approximation and projection (UMAP). These methods distort the local neighborhood in the visualization, making it hard to distinguish the structure of a subset of samples in the latent space. In response to this challenge, we introduce the k* distribution and its corresponding visualization technique. This method uses local neighborhood analysis to guarantee the preservation of the structure of sample distributions for individual classes within the subset of the learned latent space. This facilitates easy comparison of different k* distributions, enabling analysis of how various classes are processed by the same neural network. Our study reveals three distinct distributions of samples within the learned latent space subset: 1) fractured; 2) overlapped; and 3) clustered, providing a more profound understanding of the existing contemporary visualizations. Experiments show that the distribution of samples within the network's learned latent space significantly varies depending on the class. Furthermore, we illustrate that our analysis can be applied to explore the latent space of diverse neural network architectures, various layers within neural networks, transformations applied to input samples, and the distribution of training and testing data for neural networks. Thus, the k* distribution should aid in visualizing the structure inside neural networks and further foster their understanding.