相关论文: Assessing the similarity of real matrices with arb…

The widespread relevance of complex networks is a valuable tool in the analysis of a broad range of systems. There is a demand for tools which enable the extraction of meaningful information and allow the comparison between different…

We propose a novel measure to assess the presence of meso-scale structures in complex networks. This measure is based on the identification of regular patterns in the adjacency matrix of the network, and on the calculation of the quantity…

Positive semidefinite (PSD) matrices are indispensable in many fields of science. A similarity measurement for such matrices is usually an essential ingredient in the mathematical modelling of a scientific problem. This paper proposes a…

The statistical shape analysis called Procrustes analysis minimizes the distance between matrices by similarity transformations. The method returns a set of optimal orthogonal matrices, which project each matrix into a common space. This…

Similarity measures are widely used to interpret the representational geometries used by neural networks to solve tasks. Yet, because existing methods compare the extrinsic geometry of representations in state space, rather than their…

How can we tell whether two neural networks utilize the same internal processes for a particular computation? This question is pertinent for multiple subfields of neuroscience and machine learning, including neuroAI, mechanistic…

Similarity search in math is to find mathematical expressions that are similar to a user's query. We conceptualized the similarity factors between mathematical expressions, and proposed an approach to math similarity search (MSS) by…

In the assessment and selection of supersaturated designs, the aliasing structure of interaction effects is usually ignored by traditional criteria such as $E(s^2)$-optimality. We introduce the Summary of Effect Aliasing Structure (SEAS)…

The extent to which different biological and artificial neural systems rely on equivalent internal representations to support similar tasks remains a central question in neuroscience and machine learning. Prior work typically compares…

A multitude of (dis)similarity measures between neural network representations have been proposed, resulting in a fragmented research landscape. Most of these measures fall into one of two categories. First, measures such as linear…

We introduce a manifold analysis technique for neural network representations. Normalized Space Alignment (NSA) compares pairwise distances between two point clouds derived from the same source and having the same size, while potentially…

We propose SADGE, a quantitative similarity metric that predicts the performance of synthetic image datasets for common computer vision tasks without downstream model training. Estimating whether a synthetic dataset will lead to a model…

Representational similarity analysis (RSA) tests models of brain computation by investigating how neural activity patterns reflect experimental conditions. Instead of predicting activity patterns directly, the models predict the geometry of…

We consider methods for quantifying the similarity of vertices in networks. We propose a measure of similarity based on the concept that two vertices are similar if their immediate neighbors in the network are themselves similar. This leads…

Small-angle scattering (SAS) is a key experimental technique for analyzing nano-scale structures in various materials.In SAS data analysis, selecting an appropriate mathematical model for the scattering intensity is critical, as it…

We present a model to measure the similarity in appearance between different materials, which correlates with human similarity judgments. We first create a database of 9,000 rendered images depicting objects with varying materials, shape…

Shape2SAS is a web application that allows researchers and students to build intuition and understanding of small-angle scattering. It is available at https://somo.chem.utk.edu/shape2sas. The user defines a model of arbitrary shape by…

Accurate segmentation of anatomical structures in ultrasound (US) images, particularly small ones, is challenging due to noise and variability in imaging conditions (e.g., probe position, patient anatomy, tissue characteristics and…

The basic problem of shape complementarity analysis appears fundamental to applications as diverse as mechanical design, assembly automation, robot motion planning, micro- and nano-fabrication, protein-ligand binding, and rational drug…

Deep-feature-based perceptual similarity models have demonstrated strong alignment with human visual perception in Image Quality Assessment (IQA). However, most existing approaches operate at a single spatial scale, implicitly assuming that…