Related papers: TopoLines: Topological Smoothing for Line Charts
We present a comprehensive framework for evaluating line chart smoothing methods under a variety of visual analytics tasks. Line charts are commonly used to visualize a series of data samples. When the number of samples is large, or the…
Topological methods, including persistent homology, are powerful tools for analysis of high-dimensional data sets but these methods rely almost exclusively on thresholding techniques. In noisy data sets, thresholding does not always allow…
Time series visualization plays a crucial role in identifying patterns and extracting insights across various domains. However, as datasets continue to grow in size, visualizing them effectively becomes challenging. Downsampling, which…
Line charts surface many features in time series data, from trends to periodicity to peaks and valleys. However, not every potentially important feature in the data may correspond to a visual feature which readers can detect or prioritize.…
Data analysts often need to work with multiple series of data---conventionally shown as line charts---at once. Few visual representations allow analysts to view many lines simultaneously without becoming overwhelming or cluttered. In this…
The discovery of small world and scale free properties of many real world networks has revolutionized the way we study, analyze, model and process networks. An important way to analyze these complex networks is to visualize them using graph…
Graph Signal Processing deals with the problem of analyzing and processing signals defined on graphs. In this paper, we introduce a novel filtering method for graph-based signals by employing ideas from topological data analysis. We begin…
Inspired by cartographic generalization principles, we present a generalization technique for rendering line charts at different sizes, preserving the important semantics of the data at that display size. The algorithm automatically…
Optimization, a key tool in machine learning and statistics, relies on regularization to reduce overfitting. Traditional regularization methods control a norm of the solution to ensure its smoothness. Recently, topological methods have…
Splines are a popular and attractive way of smoothing noisy data. Computing splines involves minimizing a functional which is a linear combination of a fitting term and a regularization term. The former is classically computed using a…
Topological Data Analysis (TDA) is the collection of mathematical tools that capture the structure of shapes in data. Despite computational topology and computational geometry, the utilization of TDA in time series and signal processing is…
Despite the success of the carefully-annotated benchmarks, the effectiveness of existing graph neural networks (GNNs) can be considerably impaired in practice when the real-world graph data is noisily labeled. Previous explorations in…
Topological data analysis is a relatively new branch of machine learning that excels in studying high dimensional data, and is theoretically known to be robust against noise. Meanwhile, data objects with mixed numeric and categorical…
Simplifying line charts for responsive displays typically applies a single algorithm uniformly across devices, despite the availability of multiple techniques that preserve different signal characteristics (e.g., peaks, trends,…
Topological Data Analysis has grown in popularity in recent years as a way to apply tools from algebraic topology to large data sets. One of the main tools in topological data analysis is persistent homology. This paper uses undergraduate…
In this paper, we develop topological data analysis methods for classification tasks on univariate time series. As an application, we perform binary and ternary classification tasks on two public datasets that consist of physiological…
Neural networks encode inputs as high-dimensional vectors, known as representations, that capture how models process data by encoding task-relevant structure and semantics. Representation alignment refers to the degree to which different…
The utilization of statistical methods an their applications within the new field of study known as Topological Data Analysis has has tremendous potential for broadening our exploration and understanding of complex, high-dimensional data…
Surface-based data is commonly observed in diverse practical applications spanning various fields. In this paper, we introduce a novel nonparametric method to discover the underlying signals from data distributed on complex surface-based…
This paper focuses on devising graph signal processing tools for the treatment of data defined on the edges of a graph. We first show that conventional tools from graph signal processing may not be suitable for the analysis of such signals.…