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Observable Covariance and Principal Observable Analysis for Data on Metric Spaces
Ece Karacam, Washington Mio, Osman Berat Okutan
https://arxiv.org/abs/2506.04003

Observable Covariance and Principal Observable Analysis for Data on Metric Spaces
Datasets consisting of objects such as shapes, networks, images, or signals overlaid on such geometric objects permeate data science. Such datasets are often equipped with metrics that quantify the similarity or divergence between any pair of elements turning them into metric spaces $(X,d)$, or a metric measure space $(X,d,μ)$ if data density is also accounted for through a probability measure $μ$. This paper develops a Lipschitz geometry approach to analysis of metric measure spaces based on…

This https://arxiv.org/abs/2502.10527 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDS_…

Algorithms and Hardness for Estimating Statistical Similarity
We introduce and study the computational problem of determining statistical similarity between probability distributions. For distributions $P$ and $Q$ over a finite sample space, their statistical similarity is defined as $S_{\mathrm{stat}}(P, Q) := \sum_x \min(P(x), Q(x))$. Despite its fundamental nature as a measure of similarity between distributions, capturing essential concepts such as Bayes error in prediction and hypothesis testing, this computational problem has not been previously exp…

More sophisticated is not always better: comparison of similarity measures for unsupervised learning of pathways in biomolecular simulations
Miriam J\"ager, Steffen Wolf
https://arxiv.org/abs/2507.01725

More sophisticated is not always better: comparison of similarity measures for unsupervised learning of pathways in biomolecular simulations
Finding process pathways in molecular simulations such as the unbinding paths of small molecule ligands from their binding sites at protein targets in a set of trajectories via unsupervised learning approaches requires the definition of a suitable similarity measure between trajectories. We here evaluate the performance of four such measures with varying degree of sophistication, i.e., Euclidean and Wasserstein distances, Procrustes analysis and dynamical time warping, when analyzing trajectory…

Are Pixel-Wise Metrics Reliable for Sparse-View Computed Tomography Reconstruction?
Tianyu Lin, Xinran Li, Chuntung Zhuang, Qi Chen, Yuanhao Cai, Kai Ding, Alan L. Yuille, Zongwei Zhou
https://arxiv.org/abs/2506.02093

Are Pixel-Wise Metrics Reliable for Sparse-View Computed Tomography Reconstruction?
Widely adopted evaluation metrics for sparse-view CT reconstruction--such as Structural Similarity Index Measure and Peak Signal-to-Noise Ratio--prioritize pixel-wise fidelity but often fail to capture the completeness of critical anatomical structures, particularly small or thin regions that are easily missed. To address this limitation, we propose a suite of novel anatomy-aware evaluation metrics designed to assess structural completeness across anatomical structures, including large organs, …

Evaluating Sound Similarity Metrics for Differentiable, Iterative Sound-Matching
Amir Salimi, Abram Hindle, Osmar R. Zaiane
https://arxiv.org/abs/2506.22628

Evaluating Sound Similarity Metrics for Differentiable, Iterative Sound-Matching
Manual sound design with a synthesizer is inherently iterative: an artist compares the synthesized output to a mental target, adjusts parameters, and repeats until satisfied. Iterative sound-matching automates this workflow by continually programming a synthesizer under the guidance of a loss function (or similarity measure) toward a target sound. Prior comparisons of loss functions have typically favored one metric over another, but only within narrow settings: limited synthesis methods, few l…

Using Neurogram Similarity Index Measure (NSIM) to Model Hearing Loss and Cochlear Neural Degeneration
Ahsan J. Cheema, Sunil Puria
https://arxiv.org/abs/2506.12705

Using Neurogram Similarity Index Measure (NSIM) to Model Hearing Loss and Cochlear Neural Degeneration
Trouble hearing in noisy situations remains a common complaint for both individuals with hearing loss and individuals with normal hearing. This is hypothesized to arise due to condition called: cochlear neural degeneration (CND) which can also result in significant variabilities in hearing aids outcomes. This paper uses computational models of auditory periphery to simulate various hearing tasks. We present an objective method to quantify hearing loss and CND by comparing auditory nerve fiber r…