Related papers: Measuring Dataset Diversity from a Geometric Persp…
Topological data analysis (TDA) has emerged as one of the most promising techniques to reconstruct the unknown shapes of high-dimensional spaces from observed data samples. TDA, thus, yields key shape descriptors in the form of persistent…
The manifold of empirical mean values of statistical data ad infinitum has a geometric shape that depends on the probability measure that governs the generating model. Large deviation theory produces entropy functions that depend on both…
Most Machine Learning (ML) methods, from clustering to classification, rely on a distance function to describe relationships between datapoints. For complex datasets it is hard to avoid making some arbitrary choices when defining a distance…
Data visualization is the process by which data of any size or dimensionality is processed to produce an understandable set of data in a lower dimensionality, allowing it to be manipulated and understood more easily by people. The goal of…
We develop in this paper a theoretical framework for the topological study of time series data. Broadly speaking, we describe geometrical and topological properties of sliding window (or time-delay) embeddings, as seen through the lens of…
Data Science and Machine Learning have become fundamental assets for companies and research institutions alike. As one of its fields, supervised classification allows for class prediction of new samples, learning from given training data.…
We propose a novel measure for template matching named Deformable Diversity Similarity -- based on the diversity of feature matches between a target image window and the template. We rely on both local appearance and geometric information…
Multi-source spatial point data prediction is crucial in fields like environmental monitoring and natural resource management, where integrating data from various sensors is the key to achieving a holistic environmental understanding.…
Generative methods now produce outputs nearly indistinguishable from real data but often fail to fully capture the data distribution. Unlike quality issues, diversity limitations in generative models are hard to detect visually, requiring…
Two-dimensional array-based datasets are pervasive in a variety of domains. Current approaches for generative modeling have typically been limited to conventional image datasets and performed in the pixel domain which do not explicitly…
Diffusion models excel at creating visually impressive images but often struggle to generate images with a specified topology. The Betti number, which represents the number of structures in an image, is a fundamental measure in topology.…
Understanding geometric properties of natural language processing models' latent spaces allows the manipulation of these properties for improved performance on downstream tasks. One such property is the amount of data spread in a model's…
Assessing the diversity of a dataset of information associated with people is crucial before using such data for downstream applications. For a given dataset, this often involves computing the imbalance or disparity in the empirical…
Entropy is useful in statistical problems as a measure of irreversibility, randomness, mixing, dispersion, and number of microstates. However, there remains ambiguity over the precise mathematical formulation of entropy, generalized beyond…
In this paper, we investigate the relationship between diversity metrics, accuracy, and resiliency to natural image corruptions of Deep Learning (DL) image classifier ensembles. We investigate the potential of an attribution-based diversity…
Despite encouraging recent progresses in ensemble approaches, classification methods seem to have reached a plateau in development. Further advances depend on a better understanding of geometrical and topological characteristics of point…
Techniques from metric geometry have become fundamental tools in modern mathematical data science, providing principled methods for comparing datasets modeled as finite metric spaces. Two of the central tools in this area are the…
The network density matrix formalism allows for describing the dynamics of information on top of complex structures and it has been successfully used to analyze from system's robustness to perturbations to coarse graining multilayer…
Understanding the role of demographic diversity in group settings requires effective quantitative metrics. Intersectional feminist theory has highlighted that demographic identities can intersect in complex ways, but most metrics used to…
Recently introduced privacy legislation has aimed to restrict and control the amount of personal data published by companies and shared to third parties. Much of this real data is not only sensitive requiring anonymization, but also…