Data Visualization with Structural Control of Global Cohort and Local Data Neighborhoods

A typical objective of data visualization is to generate low-dimensional plots that maximally convey the information within the data. The visualization output should help the user to not only identify the local neighborhood structure of individual samples, but also obtain a global view of the relative positioning and separation between cohorts. Here, we propose a very novel visualization framework designed to satisfy these needs. By incorporating additional cohort positioning and discriminative constraints into local neighbor preservation models through the use of computed cohort prototypes, effective control over the arrangements and proximities of data cohorts can be obtained. We introduce various embedding and projection algorithms based on objective functions addressing the different visualization requirements. Their underlying models are optimized effectively using matrix manifold procedures to incorporate the problem constraints. Additionally, to facilitate large-scale applications, a matrix decomposition based model is also proposed to accelerate the computation. The improved capabilities of the new methods are demonstrated using various state-of-the-art dimensionality reduction algorithms. We present many qualitative and quantitative comparisons, on both synthetic problems and real-world tasks of complex text and image data, that show notable improvements over existing techniques.