Related papers: Multi-Scale Local Shape Analysis and Feature Selec…

Many tools and techniques measure local structure in materials in contexts ranging from biology to geology. We provide a survey of those tools and metrics that are especially useful for analyzing particulate soft matter. The metrics we…

In a world abundant with diverse data arising from complex acquisition techniques, there is a growing need for new data analysis methods. In this paper we focus on high-dimensional data that are organized into several hierarchical datasets.…

Detecting and analyzing the local environment is crucial for investigating the dynamical processes of crystal nucleation and shape colloidal particle self-assembly. Recent developments in machine learning provide a promising avenue for…

This paper introduces and demonstrates a computational pipeline for the statistical analysis of shape graph datasets, namely geometric networks embedded in 2D or 3D spaces. Unlike traditional abstract graphs, our purpose is not only to…

When considering sparse motion capture marker data, one typically struggles to balance its overfitting via a high dimensional blendshape system versus underfitting caused by smoothness constraints. With the current trend towards using more…

We describe a framework for defining high-order image models that can be used in a variety of applications. The approach involves modeling local patterns in a multiscale representation of an image. Local properties of a coarsened image…

The development of neuromorphic hardware and modeling of biological neural networks requires algorithms with local learning rules. Artificial neural networks using local learning rules to perform principal subspace analysis (PSA) and…

For many complex systems the interaction of different scales is among the most interesting and challenging features. It seems not very successful to extract the physical properties in different scale regimes by the existing approaches, such…

Learning a Bayesian network structure from data is an NP-hard problem and thus exact algorithms are feasible only for small data sets. Therefore, network structures for larger networks are usually learned with various heuristics. Another…

Amphiphilic molecules spontaneously form self-assembled structures of various shapes depending on their molecular structures, the temperature, and other physical conditions. The functionalities of these structures are dictated by their…

Machine learning models usually assume that a set of feature values used to obtain an output is fixed in advance. However, in many real-world problems, a cost is associated with measuring these features. To address the issue of reducing…

Feature extraction and dimensionality reduction are important tasks in many fields of science dealing with signal processing and analysis. The relevance of these techniques is increasing as current sensory devices are developed with ever…

Shape from texture refers to the extraction of 3D information from 2D images with irregular texture. This paper introduces a statistical framework to learn shape from texture where convex texture elements in a 2D image are represented…

Feature selection is a crucial step in machine learning, especially for high-dimensional datasets, where irrelevant and redundant features can degrade model performance and increase computational costs. This paper proposes a novel…

We present Multi-Scale Manifold Alignment(MSMA), an information-geometric framework that decomposes LLM representations into local, intermediate, and global manifolds and learns cross-scale mappings that preserve geometry and information.…

In this article, we develop and investigate a new classifier based on features extracted using spatial depth. Our construction is based on fitting a generalized additive model to the posterior probabilities of the different competing…

With systems for acquiring 3D surface data being evermore commonplace, it has become important to reliably extract specific shapes from the acquired data. In the presence of noise and occlusions, this can be done through the use of…

This thesis presents a new methodology to analyze one-dimensional signals trough a new approach called Multi Layer Analysis, for short MLA. It also provides some new insights on the relationship between one-dimensional signals processed by…

Characterizing the loss of a neural network with respect to model parameters, i.e., the loss landscape, can provide valuable insights into properties of that model. Various methods for visualizing loss landscapes have been proposed, but…

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…