Related papers: Topological Approaches to Deep Learning
Social network analysis is an important problem in data mining. A fundamental step for analyzing social networks is to encode network data into low-dimensional representations, i.e., network embeddings, so that the network topology…
Convolutional neural networks (CNNs) learn abstract features to perform object classification, but understanding these features remains challenging due to difficult-to-interpret results or high computational costs. We propose an automatic…
Topological states in photonics offer novel prospects for guiding and manipulating photons and facilitate the development of modern optical components for a variety of applications. Over the past few years, photonic topology physics has…
The irreducible complexity of natural phenomena has led Graph Neural Networks to be employed as a standard model to perform representation learning tasks on graph-structured data. While their capacity to capture local and global patterns is…
In the current era of neural networks and big data, higher dimensional data is processed for automation of different application areas. Graphs represent a complex data organization in which dependencies between more than one object or…
In recent years, convolutional neural networks (CNNs) have shown great performance in various fields such as image classification, pattern recognition, and multi-media compression. Two of the feature properties, local connectivity and…
Machine Learning with Deep Neural Networks (DNNs) has become a successful tool in solving tasks across various fields of application. However, the complexity of DNNs makes it difficult to understand how they solve their learned task. To…
Convolutional Neural Network (CNN) struggle to capture the multi-dimensional structural information of complex high-dimensional data, which limits their feature learning capability. This paper proposes a feature fusion method based on…
Graph Convolutional Neural Networks (Graph CNNs) are generalizations of classical CNNs to handle graph data such as molecular data, point could and social networks. Current filters in graph CNNs are built for fixed and shared graph…
Dynamic Textures (DTs) are sequences of images of moving scenes that exhibit certain stationarity properties in time such as smoke, vegetation and fire. The analysis of DT is important for recognition, segmentation, synthesis or retrieval…
Convolutional neural networks for computer vision are fairly intuitive. In a typical CNN used in image classification, the first layers learn edges, and the following layers learn some filters that can identify an object. But CNNs for…
There is a growing body of work that leverages features extracted via topological data analysis to train machine learning models. While this field, sometimes known as topological machine learning (TML), has seen some notable successes, an…
Inspired by the generation power of generative adversarial networks (GANs) in image domains, we introduce a novel hierarchical architecture for learning characteristic topological features from a single arbitrary input graph via GANs. The…
With the remarkable success of representation learning for prediction problems, we have witnessed a rapid expansion of the use of machine learning and deep learning for the analysis of digital pathology and biopsy image patches. However,…
We present a way to apply topological data analysis for classifying encrypted bits into distinct classes. Persistent homology is applied to generate topological features of a point cloud obtained from sets of encryptions. We see that this…
Topological learning is a wide research area aiming at uncovering the mutual spatial relationships between the elements of a set. Some of the most common and oldest approaches involve the use of unsupervised competitive neural networks.…
Convolutional Neural Networks are very efficient at processing signals defined on a discrete Euclidean space (such as images). However, as they can not be used on signals defined on an arbitrary graph, other models have emerged, aiming to…
In this paper, we introduce deep learning technology to tackle two traditional low-level image processing problems, companding and inverse halftoning. We make two main contributions. First, to the best knowledge of the authors, this is the…
Depth is one of the keys that make neural networks succeed in the task of large-scale image recognition. The state-of-the-art network architectures usually increase the depths by cascading convolutional layers or building blocks. In this…
Understanding how neural networks generalize on unseen data is crucial for designing more robust and reliable models. In this paper, we study the generalization gap of neural networks using methods from topological data analysis. For this…