Building on existing work with Hyperblocks, which classify data using minimum and maximum bounds for each attribute, we focus on enhancing interpretability, decreasing training time, and reducing model complexity without sacrificing accuracy. This system allows subject matter experts (SMEs) to directly inspect and understand the model's decision logic without requiring extensive machine learning expertise. To reduce Hyperblock complexity while retaining performance, we introduce a suite of algorithms for Hyperblock simplification. These include removing redundant attributes, removing redundant blocks through overlap analysis, and creating disjunctive units. These methods eliminate unnecessary parameters, dramatically reducing model size without harming classification power. We increase robustness by introducing an interpretable fallback mechanism using k-Nearest Neighbor (k-NN) classifiers for points not covered by any block, ensuring complete data coverage while preserving model transparency. Our results demonstrate that interpretable models can scale to high-dimensional, large-volume datasets while maintaining competitive accuracy. On benchmark datasets such as WBC (9-D), we achieve strong predictive performance with significantly reduced complexity. On MNIST (784-D), our method continues to improve through tuning and simplification, showing promise as a transparent alternative to black-box models in domains where trust, clarity, and control are crucial.

High-risk artificial intelligence and machine learning classification tasks, such as healthcare diagnosis, require accurate and interpretable prediction models. However, classifier algorithms typically sacrifice individual case-accuracy for overall model accuracy, limiting analysis of class overlap areas regardless of task significance. The Adaptive Boosting meta-algorithm, which won the 2003 G\"odel Prize, analytically assigns higher weights to misclassified cases to reclassify. However, it relies on weaker base classifiers that are iteratively strengthened, limiting improvements from base classifiers. Combining visual and computational approaches enables selecting stronger base classifiers before boosting. This paper proposes moving boosting methodology from focusing on only misclassified cases to all cases in the class overlap areas using Computational and Interactive Visual Learning (CIVL) with a Human-in-the-Loop. It builds classifiers in lossless visualizations integrating human domain expertise and visual insights. A Divide and Classify process splits cases to simple and complex, classifying these individually through computational analysis and data visualization with lossless visualization spaces of Parallel Coordinates or other General Line Coordinates. After finding pure and overlap class areas simple cases in pure areas are classified, generating interpretable sub-models like decision rules in Propositional and First-order Logics. Only multidimensional cases in the overlap areas are losslessly visualized simplifying end-user cognitive tasks to identify difficult case patterns, including engineering features to form new classifiable patterns. Demonstration shows a perfectly accurate and losslessly interpretable model of the Iris dataset, and simulated data shows generalized benefits to accuracy and interpretability of models, increasing end-user confidence in discovered models.

The optimization of cooling systems is important in many cases, for example for cabin and battery cooling in electric cars. Such an optimization is governed by multiple, conflicting objectives and it is performed across a multi-dimensional parameter space. The extent of the parameter space, the complexity of the non-linear model of the system, as well as the time needed per simulation run and factors that are not modeled in the simulation necessitate an iterative, semi-automatic approach. We present an interactive visual optimization approach, where the user works with a p-h diagram to steer an iterative, guided optimization process. A deep learning (DL) model provides estimates for parameters, given a target characterization of the system, while numerical simulation is used to compute system characteristics for an ensemble of parameter sets. Since the DL model only serves as an approximation of the inverse of the cooling system and since target characteristics can be chosen according to different, competing objectives, an iterative optimization process is realized, developing multiple sets of intermediate solutions, which are visually related to each other. The standard p-h diagram, integrated interactively in this approach, is complemented by a dual, also interactive visual representation of additional expressive measures representing the system characteristics. We show how the known four-points semantic of the p-h diagram meaningfully transfers to the dual data representation. When evaluating this approach in the automotive domain, we found that our solution helped with the overall comprehension of the cooling system and that it lead to a faster convergence during optimization.

This work uses visual knowledge discovery in parallel coordinates to advance methods of interpretable machine learning. The graphic data representation in parallel coordinates made the concepts of hypercubes and hyperblocks (HBs) simple to understand for end users. It is suggested to use mixed and pure hyperblocks in the proposed data classifier algorithm Hyper. It is shown that Hyper models generalize decision trees. The algorithm is presented in several settings and options to discover interactively or automatically overlapping or non-overlapping hyperblocks. Additionally, the use of hyperblocks in conjunction with language descriptions of visual patterns is demonstrated. The benchmark data from the UCI ML repository were used to evaluate the Hyper algorithm. It enabled the discovery of mixed and pure HBs evaluated using 10-fold cross validation. Connections among hyperblocks, dimension reduction and visualization have been established. The capability of end users to find and observe hyperblocks, as well as the ability of side-by-side visualizations to make patterns evident, are among major advantages ofhyperblock technology and the Hyper algorithm. A new method to visualize incomplete n-D data with missing values is proposed, while the traditional parallel coordinates do not support it. The ability of HBs to better prevent both overgeneralization and overfitting of data over decision trees is demonstrated as another benefit of the hyperblocks. The features of VisCanvas 2.0 software tool that implements Hyper technology are presented.

To increase the interpretability and prediction accuracy of the Machine Learning (ML) models, visualization of ML models is a key part of the ML process. Decision Trees (DTs) are essential in machine learning (ML) because they are used to understand many black box ML models including Deep Learning models. In this research, two new methods for creation and enhancement with complete visualizing Decision Trees as understandable models are suggested. These methods use two versions of General Line Coordinates (GLC): Bended Coordinates (BC) and Shifted Paired Coordinates (SPC). The Bended Coordinates are a set of line coordinates, where each coordinate is bended in a threshold point of the respective DT node. In SPC, each n-D point is visualized in a set of shifted pairs of 2-D Cartesian coordinates as a directed graph. These new methods expand and complement the capabilities of existing methods to visualize DT models more completely. These capabilities allow us to observe and analyze: (1) relations between attributes, (2) individual cases relative to the DT structure, (3) data flow in the DT, (4) sensitivity of each split threshold in the DT nodes, and (5) density of cases in parts of the n-D space. These features are critical for DT models' performance evaluation and improvement by domain experts and end users as they help to prevent overgeneralization and overfitting of the models. The advantages of this methodology are illustrated in the case studies on benchmark real-world datasets. The paper also demonstrates how to generalize them for decision tree visualizations in different General Line Coordinates.

We report on a novel use of parallel coordinates as a pedagogical tool for illustrating the non-intuitive properties of high dimensional spaces with special emphasis on the phenomenon of Curse of Dimensionality. Also, we have collated what we believe to be a representative sample of diverse approaches that exist in literature to conceptualize the Curse of Dimensionality. We envisage that the paper will have pedagogical value in structuring the way Curse of Dimensionality is presented in classrooms and associated lab sessions.