Related papers: Persistent Homology with Improved Locality Informa…
Persistence diagrams, combining geometry and topology for an effective shape description used in pattern recognition, have already proven to be an effective tool for shape representation with respect to a certainfiltering function.…
Two-dimensional (2D) particle systems, such as magnetic skyrmions, exhibit topological phase transitions between unique 2D phases. However, a simple and computationally efficient methodology to capture lattice configurational properties and…
Node2vec is a graph embedding method that learns a vector representation for each node of a weighted graph while seeking to preserve relative proximity and global structure. Numerical experiments suggest Node2vec struggles to recreate the…
Topological data analysis (TDA) is gaining prominence across a wide spectrum of machine learning tasks that spans from manifold learning to graph classification. A pivotal technique within TDA is persistent homology (PH), which furnishes an…
The latest deep learning approaches perform better than the state-of-the-art signal processing approaches in various image restoration tasks. However, if an image contains many patterns and structures, the performance of these CNNs is still…
Phase separation mechanisms can produce a variety of complicated and intricate microstructures, which often can be difficult to characterize in a quantitative way. In recent years, a number of novel topological metrics for microstructures…
Given a pedestrian image as a query, the purpose of person re-identification is to identify the correct match from a large collection of gallery images depicting the same person captured by disjoint camera views. The critical challenge is…
This paper focuses on developing an efficient algorithm for analyzing a directed network (graph) from a topological viewpoint. A prevalent technique for such topological analysis involves computation of homology groups and their…
Recently, many deep networks have introduced hypercomplex and related calculations into their architectures. In regard to convolutional networks for classification, these enhancements have been applied to the convolution operations in the…
In real-world systems, the relationships and connections between components are highly complex. Real systems are often described as networks, where nodes represent objects in the system and edges represent relationships or connections…
It is challenging to directly estimate the human geometry from a single image due to the high diversity and complexity of body shapes with the various clothing styles. Most of model-based approaches are limited to predict the shape and pose…
We present a powerful new loss function and training scheme for learning binary hash functions. In particular, we demonstrate our method by creating for the first time a neural network that outperforms state-of-the-art Haar wavelets and…
Retinal fundus photography enhancement is important for diagnosing and monitoring retinal diseases. However, early approaches to retinal image enhancement, such as those based on Generative Adversarial Networks (GANs), often struggle to…
In this paper we develop a novel Topological Data Analysis (TDA) approach for studying graph representations of time series of dynamical systems. Specifically, we show how persistent homology, a tool from TDA, can be used to yield a…
Persistent homology, a fundamental technique within Topological Data Analysis (TDA), captures structural and shape characteristics of graphs, yet encounters computational difficulties when applied to dynamic directed graphs. This paper…
Optimization, a key tool in machine learning and statistics, relies on regularization to reduce overfitting. Traditional regularization methods control a norm of the solution to ensure its smoothness. Recently, topological methods have…
Due to the impressive learning power, deep learning has achieved a remarkable performance in supervised hash function learning. In this paper, we propose a novel asymmetric supervised deep hashing method to preserve the semantic structure…
Line matching plays an essential role in structure from motion (SFM) and simultaneous localization and mapping (SLAM), especially in low-textured and repetitive scenes. In this paper, we present a new method of using a graph convolution…
Persistent homology is an effective method for extracting topological information, represented as persistent diagrams, of spatial structure data. Hence it is well-suited for the study of protein structures. Attempts to incorporate…
This paper aims to discuss a method of quantifying the 'shape' of data, via a methodology called topological data analysis. The main tool within topological data analysis is persistent homology; this is a means of measuring the shape of…