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Researcher profile

Luis Gustavo Nonato

Luis Gustavo Nonato contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Machine LearningHuman-Computer InteractionComputer VisionGraphicsComputational Geometry

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Published work

5 published item(s)

preprint2026arXiv

Topo-GS: Continuous Volumetric Embedding of High-Dimensional Data via Topological Gaussian Splatting

Dimensionality reduction algorithms map high-dimensional data into visualizable 2D or 3D spaces, but traditionally rely on a discrete point-cloud paradigm. This discrete abstraction is susceptible to visual occlusion and artificial discontinuities, often failing to represent the continuous density of the underlying manifold. To address these limitations, we introduce Topo-GS, a framework that repurposes 3D Gaussian Splatting (3DGS) to cast multidimensional projection as a meshless volumetric reconstruction process. Instead of standard photometric losses, Topo-GS is driven by local geometric constraints. By solving orthogonal Procrustes targets, the optimization enforces an As-Rigid-As-Possible prior while explicitly aligning the spatial covariance of each Gaussian to the local tangent space. Recognizing that unrolling data of varying intrinsic dimensionalities requires distinct spatial treatments, we utilize a topology-aware strategy that tailors the loss formulation to preserve either continuous 1D trajectories or cohesive 2D surfaces. Quantitative and visual evaluations demonstrate that Topo-GS successfully transforms discrete scatter plots into continuous volumetric representations, where inherent projection distortions explicitly manifest as observable geometric variations, while preserving local topological fidelity comparable to discrete baselines.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Calibrate: Interactive Analysis of Probabilistic Model Output

Analyzing classification model performance is a crucial task for machine learning practitioners. While practitioners often use count-based metrics derived from confusion matrices, like accuracy, many applications, such as weather prediction, sports betting, or patient risk prediction, rely on a classifier's predicted probabilities rather than predicted labels. In these instances, practitioners are concerned with producing a calibrated model, that is, one which outputs probabilities that reflect those of the true distribution. Model calibration is often analyzed visually, through static reliability diagrams, however, the traditional calibration visualization may suffer from a variety of drawbacks due to the strong aggregations it necessitates. Furthermore, count-based approaches are unable to sufficiently analyze model calibration. We present Calibrate, an interactive reliability diagram that addresses the aforementioned issues. Calibrate constructs a reliability diagram that is resistant to drawbacks in traditional approaches, and allows for interactive subgroup analysis and instance-level inspection. We demonstrate the utility of Calibrate through use cases on both real-world and synthetic data. We further validate Calibrate by presenting the results of a think-aloud experiment with data scientists who routinely analyze model calibration.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Topological Representations of Local Explanations

Local explainability methods -- those which seek to generate an explanation for each prediction -- are becoming increasingly prevalent due to the need for practitioners to rationalize their model outputs. However, comparing local explainability methods is difficult since they each generate outputs in various scales and dimensions. Furthermore, due to the stochastic nature of some explainability methods, it is possible for different runs of a method to produce contradictory explanations for a given observation. In this paper, we propose a topology-based framework to extract a simplified representation from a set of local explanations. We do so by first modeling the relationship between the explanation space and the model predictions as a scalar function. Then, we compute the topological skeleton of this function. This topological skeleton acts as a signature for such functions, which we use to compare different explanation methods. We demonstrate that our framework can not only reliably identify differences between explainability techniques but also provides stable representations. Then, we show how our framework can be used to identify appropriate parameters for local explainability methods. Our framework is simple, does not require complex optimizations, and can be broadly applied to most local explanation methods. We believe the practicality and versatility of our approach will help promote topology-based approaches as a tool for understanding and comparing explanation methods.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Melody: Generating and Visualizing Machine Learning Model Summary to Understand Data and Classifiers Together

With the increasing sophistication of machine learning models, there are growing trends of developing model explanation techniques that focus on only one instance (local explanation) to ensure faithfulness to the original model. While these techniques provide accurate model interpretability on various data primitive (e.g., tabular, image, or text), a holistic Explainable Artificial Intelligence (XAI) experience also requires a global explanation of the model and dataset to enable sensemaking in different granularity. Thus, there is a vast potential in synergizing the model explanation and visual analytics approaches. In this paper, we present MELODY, an interactive algorithm to construct an optimal global overview of the model and data behavior by summarizing the local explanations using information theory. The result (i.e., an explanation summary) does not require additional learning models, restrictions of data primitives, or the knowledge of machine learning from the users. We also design MELODY UI, an interactive visual analytics system to demonstrate how the explanation summary connects the dots in various XAI tasks from a global overview to local inspections. We present three usage scenarios regarding tabular, image, and text classifications to illustrate how to generalize model interpretability of different data. Our experiments show that our approaches: (1) provides a better explanation summary compared to a straightforward information-theoretic summarization and (2) achieves a significant speedup in the end-to-end data modeling pipeline.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

TopoMap: A 0-dimensional Homology Preserving Projection of High-Dimensional Data

Multidimensional Projection is a fundamental tool for high-dimensional data analytics and visualization. With very few exceptions, projection techniques are designed to map data from a high-dimensional space to a visual space so as to preserve some dissimilarity (similarity) measure, such as the Euclidean distance for example. In fact, although adopting distinct mathematical formulations designed to favor different aspects of the data, most multidimensional projection methods strive to preserve dissimilarity measures that encapsulate geometric properties such as distances or the proximity relation between data objects. However, geometric relations are not the only interesting property to be preserved in a projection. For instance, the analysis of particular structures such as clusters and outliers could be more reliably performed if the mapping process gives some guarantee as to topological invariants such as connected components and loops. This paper introduces TopoMap, a novel projection technique which provides topological guarantees during the mapping process. In particular, the proposed method performs the mapping from a high-dimensional space to a visual space, while preserving the 0-dimensional persistence diagram of the Rips filtration of the high-dimensional data, ensuring that the filtrations generate the same connected components when applied to the original as well as projected data. The presented case studies show that the topological guarantee provided by TopoMap not only brings confidence to the visual analytic process but also can be used to assist in the assessment of other projection methods.

0 citations0 reviewsNo code linkedOpen access