Related papers: Nonlinear Dimensionality Reduction on Graphs
Dimensionality reduction techniques map data represented on higher dimensions onto lower dimensions with varying degrees of information loss. Graph dimensionality reduction techniques adopt the same principle of providing latent…
Nonlinear dimensionality reduction methods have demonstrated top-notch performance in many pattern recognition and image classification tasks. Despite their popularity, they suffer from highly expensive time and memory requirements, which…
Analyzing interconnection structures among underlying entities or objects in a dataset through the use of graph analytics has been shown to provide tremendous value in many application domains. However, graphs are not the primary…
Dimensionality reduction (DR) plays a vital role in the visual analysis of high-dimensional data. One main aim of DR is to reveal hidden patterns that lie on intrinsic low-dimensional manifolds. However, DR often overlooks important…
The quest for simplification in physics drives the exploration of concise mathematical representations for complex systems. This Dissertation focuses on the concept of dimensionality reduction as a means to obtain low-dimensional…
Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…
In recent years, manifold methods have moved into focus as tools for dimension reduction. Assuming that the high-dimensional data actually lie on or close to a low-dimensional nonlinear manifold, these methods have shown convincing results…
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…
Graph coarsening is a widely used dimensionality reduction technique for approaching large-scale graph machine learning problems. Given a large graph, graph coarsening aims to learn a smaller-tractable graph while preserving the properties…
Deep neural networks are widely used in various domains. However, the nature of computations at each layer of the deep networks is far from being well understood. Increasing the interpretability of deep neural networks is thus important.…
Complex dynamical systems are prevalent in various domains, but their analysis and prediction are hindered by their high dimensionality and nonlinearity. Dimensionality reduction techniques can simplify the system dynamics by reducing the…
Visualizing high dimensional data by projecting them into two or three dimensional space is one of the most effective ways to intuitively understand the data's underlying characteristics, for example their class neighborhood structure.…
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…
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…
We present a novel, domain-agnostic, model-independent, unsupervised, and universally applicable Machine Learning approach for dimensionality reduction based on the principles of algorithmic complexity. Specifically, but without loss of…
Complex systems are ubiquitous in nature and engineering, but their analysis and control are hampered by their high dimensionality and the influence of various factors on their dynamics. Dimensionality reduction aims to find a…
Real-world data usually have high dimensionality and it is important to mitigate the curse of dimensionality. High-dimensional data are usually in a coherent structure and make the data in relatively small true degrees of freedom. There are…
Graph compression is a data analysis technique that consists in the replacement of parts of a graph by more general structural patterns in order to reduce its description length. It notably provides interesting exploration tools for the…
Dynamical systems on networks are inherently high-dimensional unless the number of nodes is extremely small. Dimension reduction methods for dynamical systems on networks aim to find a substantially lower-dimensional system that preserves…
Finding patterns in graphs is a fundamental problem in databases and data mining. In many applications, graphs are temporal and evolve over time, so we are interested in finding durable patterns, such as triangles and paths, which persist…