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In many modern applications, including analysis of gene expression and text documents, the data are noisy, high-dimensional, and unordered--with no particular meaning to the given order of the variables. Yet, successful learning is often…
Dimensionality reduction is an integral part of data visualization. It is a process that obtains a structure preserving low-dimensional representation of the high-dimensional data. Two common criteria can be used to achieve a dimensionality…
Merge trees are a type of topological descriptors that record the connectivity among the sublevel sets of scalar fields. They are among the most widely used topological tools in visualization. In this paper, we are interested in sketching a…
Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field.…
Topological structures such as the merge tree provide an abstract and succinct representation of scalar fields. They facilitate effective visualization and interactive exploration of feature-rich data. A merge tree captures the topology of…
Human subject studies that map-like visualizations are as good or better than standard node-link representations of graphs, in terms of task performance, memorization and recall of the underlying data, and engagement [SSKB14, SSKB15]. With…
With the rapid adoption of machine learning techniques for large-scale applications in science and engineering comes the convergence of two grand challenges in visualization. First, the utilization of black box models (e.g., deep neural…
Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems. Methods from topological data analysis, e.g., persistent homology, enable us to obtain such information,…
This study introduces a new method of visualizing complex tree structured objects. The usefulness of this method is illustrated in the context of detecting unexpected features in a data set of very large trees. The major contribution is a…
Representation learning on graphs is a fundamental problem that can be crucial in various tasks. Graph neural networks, the dominant approach for graph representation learning, are limited in their representation power. Therefore, it can be…
We develop a language for describing the relationship among observations, mathematical models, and the underlying principles from which they are derived. Using Information Geometry, we consider geometric properties of statistical models for…
Understanding and predicting thermal transport in disordered materials remains a significant challenge due to the absence of periodicity and the complex nature of medium-range structural motifs. In this work, we investigate amorphous…
Tree-based methods are powerful nonparametric techniques in statistics and machine learning. However, their effectiveness, particularly in finite-sample settings, is not fully understood. Recent applications have revealed their surprising…
Topological data analysis uses tools from topology -- the mathematical area that studies shapes -- to create representations of data. In particular, in persistent homology, one studies one-parameter families of spaces associated with data,…
Physical phenomena in science and engineering are frequently modeled using scalar fields. In scalar field topology, graph-based topological descriptors such as merge trees, contour trees, and Reeb graphs are commonly used to characterize…
In this work, we propose trait-based merge trees a generalization of merge trees to feature level sets, targeting the analysis of tensor field or general multi-variate data. For this, we employ the notion of traits defined in attribute…
In recent years, topological data analysis has been utilized for a wide range of problems to deal with high dimensional noisy data. While text representations are often high dimensional and noisy, there are only a few work on the…
Comparative analysis of scalar fields is an important problem with various applications including feature-directed visualization and feature tracking in time-varying data. Comparing topological structures that are abstract and succinct…
Topological Data Analysis (TDA) is a rising field of computational topology in which the topological structure of a data set can be observed by persistent homology. By considering a sequence of sublevel sets, one obtains a filtration that…
The high performance of tree ensemble classifiers benefits from a large set of rules, which, in turn, makes the models hard to understand. To improve interpretability, existing methods extract a subset of rules for approximation using model…