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In computational mechanics, multiple models are often present to describe a physical system. While Bayesian model selection is a helpful tool to compare these models using measurement data, it requires the computationally expensive…
LiDAR place recognition is a crucial module in localization that matches the current location with previously observed environments. Most existing approaches in LiDAR place recognition dominantly focus on the spinning type LiDAR to exploit…
Deep neural networks (DNNs) enable innovative applications of machine learning like image recognition, machine translation, or malware detection. However, deep learning is often criticized for its lack of robustness in adversarial settings…
Manifold learning now plays a very important role in machine learning and many relevant applications. Although its superior performance in dealing with nonlinear data distribution, data sparsity is always a thorny knot. There are few…
Learning the embedding space, where semantically similar objects are located close together and dissimilar objects far apart, is a cornerstone of many computer vision applications. Existing approaches usually learn a single metric in the…
Restricted Boltzmann Machines (RBMs) are widely used probabilistic undirected graphical models with visible and latent nodes, playing an important role in statistics and machine learning. The task of structure learning for RBMs involves…
Human experts cannot efficiently access the physical information of quantum many-body states by simply "reading" the coefficients, but have to reply on the previous knowledge such as order parameters and quantum measurements. In this work,…
The purpose of this paper is twofold. On a technical side, we propose an extension of the Hausdorff distance from metric spaces to spaces equipped with asymmetric distance measures. Specifically, we focus on the family of Bregman…
This study focuses on the application of deep geometric models to solve the 3x3x3 Rubik's Cube. We begin by discussing the cube's graph representation and defining distance as the model's optimization objective. The distance approximation…
Deep metric learning has gained promising improvement in recent years following the success of deep learning. It has been successfully applied to problems in few-shot learning, image retrieval, and open-set classifications. However,…
We propose and apply simple machine learning approaches for recognition and classification of complex non-collinear magnetic structures in two-dimensional materials. The first approach is based on the implementation of the…
The learning of appropriate distance metrics is a critical problem in image classification and retrieval. In this work, we propose a boosting-based technique, termed \BoostMetric, for learning a Mahalanobis distance metric. One of the…
Linear mixed models (LMMs) are widely used for heritability estimation in genome-wide association studies (GWAS). In standard approaches to heritability estimation with LMMs, a genetic relationship matrix (GRM) must be specified. In GWAS,…
Distance metric learning has attracted much attention in recent years, where the goal is to learn a distance metric based on user feedback. Conventional approaches to metric learning mainly focus on learning the Mahalanobis distance metric…
The problem of extending a function $f$ defined on a training data $\mathcal{C}$ on an unknown manifold $\mathbb{X}$ to the entire manifold and a tubular neighborhood of this manifold is considered in this paper. For $\mathbb{X}$ embedded…
Distance metric learning (DML) has been successfully applied to object classification, both in the standard regime of rich training data and in the few-shot scenario, where each category is represented by only a few examples. In this work,…
We present a geometric formulation of the Multiple Kernel Learning (MKL) problem. To do so, we reinterpret the problem of learning kernel weights as searching for a kernel that maximizes the minimum (kernel) distance between two convex…
Unsupervised deep metric learning (UDML) focuses on learning a semantic representation space using only unlabeled data. This challenging problem requires accurately estimating the similarity between data points, which is used to supervise a…
In this work, we used deep neural networks (DNNs) to solve a fundamental problem in differential geometry. One can find many closed-form expressions for calculating curvature, length, and other geometric properties in the literature. As we…
We explore how information in images of nearby galaxies can be used to estimate their distance. We train a convolutional Neural Network (NN) to do this, using galaxy images from the Illustris simulation. We show that if the NN is trained on…