Similarity search in graph databases is one of the most fundamental operations in graph analytics. Among various distance functions, graph and subgraph edit distances (GED and SED respectively) are two of the most popular and expressive measures. Unfortunately, exact computations for both are NP-hard. To overcome this computational bottleneck, neural approaches to learn and predict edit distance in polynomial time have received much interest. While considerable progress has been made, there exist limitations that need to be addressed.

Similarity search in graph databases is one of the most fundamental operations in graph analytics. Among various distance functions, graph and subgraph edit distances (GED and SED respectively) are two of the most popular and expressive measures. Unfortunately, exact computations for both are NP-hard. To overcome this computational bottleneck, neural approaches to learn and predict edit distance in polynomial time have received much interest. While considerable progress has been made, there exist limitations that need to be addressed.

For multiple scientific endeavors it is common to measure a phenomenon of interest in more than one ways. We make observations of objects from several different perspectives in space, at different points in time; we may also measure different properties of a mixture using different types of instruments. After collecting this heterogeneous information, it is necessary to be able to synthesize a complete picture of what is `common' across its sources: the subject we ultimately want to study. However, isolated (`clean') observations of a system are not always possible: observations often contain information about other systems in its environment, or about the measuring instruments themselves. In that sense, each observation may contain information that `does not matter' to the original object of study; this `uncommon' information between sensors observing the same object may still be important, and decoupling it from the main signal(s) useful. We introduce a neural network autoencoder framework capable of both tasks: it is structured to identify `common' variables, and, making use of orthogonality constraints to define geometric independence, to also identify disentangled `uncommon' information originating from the heterogeneous sensors. We demonstrate applications in several computational examples.

Reconstructing a 3D surface from colonoscopy video is challenging due to illumination and reflectivity variation in the video frame that can cause defective shape predictions. Aiming to overcome this challenge, we utilize the characteristics of surface normal vectors and develop a two-step neural framework that significantly improves the colonoscopy reconstruction quality. The normal-based depth initialization network trained with self-supervised normal consistency loss provides depth map initialization to the normal-depth refinement module, which utilizes the relationship between illumination and surface normals to refine the frame-wise normal and depth predictions recursively. Our framework's depth accuracy performance on phantom colonoscopy data demonstrates the value of exploiting the surface normals in colonoscopy reconstruction, especially on en face views. Due to its low depth error, the prediction result from our framework will require limited post-processing to be clinically applicable for real-time colonoscopy reconstruction.