Extracting relevant urban patterns from multiple data sources can be difficult using classical clustering algorithms since we have to make a suitable setup of the hyperparameters of the algorithms and deal with outliers. It should be addressed correctly to help urban planners in the decision-making process for the further development of a big city. For instance, experts' main interest in criminology is comprehending the relationship between crimes and the socio-economic characteristics at specific georeferenced locations. In addition, the classical clustering algorithms take little notice of the intricate spatial correlations in georeferenced data sources. This paper presents a new approach to detecting the most relevant urban patterns from multiple data sources based on tensor decomposition. Compared to classical methods, the proposed approach's performance is attested to validate the identified patterns' quality. The result indicates that the approach can effectively identify functional patterns to characterize the data set for further analysis in achieving good clustering quality. Furthermore, we developed a generic framework named TensorAnalyzer, where the effectiveness and usefulness of the proposed methodology are tested by a set of experiments and a real-world case study showing the relationship between the crime events around schools and students performance and other variables involved in the analysis.
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.
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.
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.