Related papers: Bridging Graph Drawing and Dimensionality Reductio…
A popular method of force-directed graph drawing is multidimensional scaling using graph-theoretic distances as input. We present an algorithm to minimize its energy function, known as stress, by using stochastic gradient descent (SGD) to…
Readability criteria, such as distance or neighborhood preservation, are often used to optimize node-link representations of graphs to enable the comprehension of the underlying data. With few exceptions, graph drawing algorithms typically…
Stochastic gradient descent (SGD) is a widely adopted iterative method for optimizing differentiable objective functions. In this paper, we propose and discuss a novel approach to scale up SGD in applications involving non-convex functions…
Stochastic gradient descent (SGD) provides a simple and efficient way to solve a broad range of machine learning problems. Here, we focus on distribution regression (DR), involving two stages of sampling: Firstly, we regress from…
Graph Visualization, also known as Graph Drawing, aims to find geometric embeddings of graphs that optimize certain criteria. Stress is a widely used metric; stress is minimized when every pair of nodes is positioned at their shortest path…
Stochastic gradient descent (SGD) is a standard optimization method to minimize a training error with respect to network parameters in modern neural network learning. However, it typically suffers from proliferation of saddle points in the…
Stochastic convex optimization algorithms are the most popular way to train machine learning models on large-scale data. Scaling up the training process of these models is crucial, but the most popular algorithm, Stochastic Gradient Descent…
Multidimensional scaling (MDS) is a popular dimensionality reduction techniques that has been widely used for network visualization and cooperative localization. However, the traditional stress minimization formulation of MDS necessitates…
This paper challenges the convention of using graph-theoretic shortest distance in stress-based graph drawing. We propose a new paradigm based on resistance distance, derived from the graph Laplacian's spectrum, which better captures global…
In the vast landscape of visualization research, Dimensionality Reduction (DR) and graph analysis are two popular subfields, often essential to most visual data analytics setups. DR aims to create representations to support neighborhood and…
In multimodal graph learning, graph structures that integrate information from multiple sources, such as vision and text, can more comprehensively model complex entity relationships. However, the continuous growth of their data scale poses…
This paper considers a general data-fitting problem over a networked system, in which many computing nodes are connected by an undirected graph. This kind of problem can find many real-world applications and has been studied extensively in…
Efficient layout of large-scale graphs remains a challenging problem: the force-directed and dimensionality reduction-based methods suffer from high overhead for graph distance and gradient computation. In this paper, we present a new graph…
Stochastic Gradient Descent (SGD) has proven to be remarkably effective in optimizing deep neural networks that employ ever-larger numbers of parameters. Yet, improving the efficiency of large-scale optimization remains a vital and highly…
Stochastic gradient descent (\textsc{Sgd}) methods are the most powerful optimization tools in training machine learning and deep learning models. Moreover, acceleration (a.k.a. momentum) methods and diagonal scaling (a.k.a. adaptive…
Stress minimization is among the best studied force-directed graph layout methods because it reliably yields high-quality layouts. It thus comes as a surprise that a novel approach based on stochastic gradient descent (Zheng, Pawar and…
There is an increased interest in building data analytics frameworks with advanced algebraic capabilities both in industry and academia. Many of these frameworks, e.g., TensorFlow and BIDMach, implement their compute-intensive primitives in…
We describe a computationally efficient, stochastic graph-regularization technique that can be utilized for the semi-supervised training of deep neural networks in a parallel or distributed setting. We utilize a technique, first described…
Multi-layer neural networks are among the most powerful models in machine learning, yet the fundamental reasons for this success defy mathematical understanding. Learning a neural network requires to optimize a non-convex high-dimensional…
Stochastic gradient descent (SGD), which dates back to the 1950s, is one of the most popular and effective approaches for performing stochastic optimization. Research on SGD resurged recently in machine learning for optimizing convex loss…