Lossless Visual Knowledge Discovery in High Dimensional Data with Elliptic Paired Coordinates

Abstract

It is challenging for humans to enable visual knowledge discovery in data with more than 2-3 dimensions with a naked eye. This chapter explores the efficiency of discovering predictive machine learning models interactively using new Elliptic Paired coordinates (EPC) visualizations. It is shown that EPC are capable to visualize multidimensional data and support visual machine learning with preservation of multidimensional information in 2-D. Relative to parallel and radial coordinates, EPC visualization requires only a half of the visual elements for each n-D point. An interactive software system EllipseVis, which is developed in this work, processes high-dimensional datasets, creates EPC visualizations, and produces predictive classification models by discovering dominance rules in EPC. By using interactive and automatic processes it discovers zones in EPC with a high dominance of a single class. The EPC methodology has been successful in discovering non-linear predictive models with high coverage and precision in the computational experiments. This can benefit multiple domains by producing visually appealing dominance rules. This chapter presents results of successful testing the EPC non-linear methodology in experiments using real and simulated data, EPC generalized to the Dynamic Elliptic Paired Coordinates (DEPC), incorporation of the weights of coordinates to optimize the visual discovery, introduction of an alternative EPC design and introduction of the concept of incompact machine learning methodology based on EPC/DEPC.

Visual Knowledge Discovery with Artificial Intelligence: Challenges and Future Directions

“…Problem 1 Developing new lossless visualizations of multidimensional data. Several types of General Line Coordinates Kovalerchuk [2018] are developed, explored, and applied at different levels (parallel coordinates, radial coordinates, shifted paired coordinates, collocated pairs coordinates, in-line coordinates, GLC-L) Kovalerchuk [2018], Kovalerchuk et al [2021], Kovalerchuk and Phan [2021], Dovhalets et al [2018], , Kovalerchuk and Gharawi [2018], McDonald and Kovalerchuk [2020], Wagle and Kovalerchuk [2020]. Many other GLCs are just defined in Kovalerchuk [2018].…”

“…Dovhalets et al [2018],,Kovalerchuk and Gharawi [2018],McDonald and Kovalerchuk [2020], Wagle andKovalerchuk [2020]. The studies in this realm can be traced to Parallel CoordinatesInselberg [1998Inselberg [ , 2009.Often 2-D studies in ML cover only simple 2-D examples to illustrate ML algorithms visually.…”

Full interpretable machine learning in 2D with inline coordinates

“…In the series of our prior work [5,12,10,14,20] we demonstrated feasibility of full 2-D ML with other types of General Line Coordinates (Shifted Paired Coordinates, Elliptic Paired Coordinates, CPC-R and GLC-L). The studies in this realm can be traced to [3,4] for Parallel Coordinates and [17] for 2-D modeling of non-image data.…”

A Knowledge Discovery Process Extended to Experimental Data for the Identification of Motor Misalignment Patterns

“…Furthermore, ref. [22] evaluated a current approach, elliptic paired coordinates, which should allow a lossless depiction of high-dimensional data. The evaluation of the results from DM can be done through 2D interpretation of the results combined with various criteria such as understandability, expressed through the number of features needed for classification, or interestingness, which is a combination of validity, novelty, usefulness, and simplicity.…”