Related papers: An Incremental Non-Linear Manifold Approximation M…
Dimension reduction (DR) algorithms have proven to be extremely useful for gaining insight into large-scale high-dimensional datasets, particularly finding clusters in transcriptomic data. The initial phase of these DR methods often…
The problem of identifying geometric structure in data is a cornerstone of (unsupervised) learning. As a result, Geometric Representation Learning has been widely applied across scientific and engineering domains. In this work, we…
Large scale dynamical systems (e.g. many nonlinear coupled differential equations) can often be summarized in terms of only a few state variables (a few equations), a trait that reduces complexity and facilitates exploration of behavioral…
In this paper, we consider the problem of fast and efficient indexing techniques for sequences evolving in non-Euclidean spaces. This problem has several applications in the areas of human activity analysis, where there is a need to perform…
Identifying changes in a pair of 3D aerial LiDAR point clouds, obtained during two distinct time periods over the same geographic region presents a significant challenge due to the disparities in spatial coverage and the presence of noise…
Understanding how nonlinear dynamical systems (e.g., artificial neural networks and neural circuits) process information requires comparing their underlying dynamics at scale, across diverse architectures and large neural recordings. While…
Scientists and engineers rely on accurate mathematical models to quantify the objects of their studies, which are often high-dimensional. Unfortunately, high-dimensional models are inherently difficult, i.e. when observations are sparse or…
Extracting real-time insights from multi-modal data streams from various domains such as healthcare, intelligent transportation, and satellite remote sensing remains a challenge. High computational demands and limited knowledge scope…
Information visualization significantly enhances human perception by graphically representing complex data sets. The variety of visualization designs makes it challenging to efficiently evaluate all possible designs catering to users'…
Methodologies for multidimensionality reduction aim at discovering low-dimensional manifolds where data ranges. Principal Component Analysis (PCA) is very effective if data have linear structure. But fails in identifying a possible…
Dimensionality reduction (DR) on the manifold includes effective methods which project the data from an implicit relational space onto a vectorial space. Regardless of the achievements in this area, these algorithms suffer from the lack of…
Graph Neural Network (GNNs) based methods have recently become a popular tool to deal with graph data because of their ability to incorporate structural information. The only hurdle in the performance of GNNs is the lack of labeled data.…
This paper introduces an online approach for identifying time-varying subspaces defined by linear dynamical systems. The approach of representing linear systems by non-parametric subspace models has received significant interest in the…
Deep learning-based methods have shown remarkable success for various image restoration tasks such as denoising and deblurring. The current state-of-the-art networks are relatively deep and utilize (variants of) self attention mechanisms.…
This paper addresses classification problems with matrix-valued data, which commonly arise in applications such as neuroimaging and signal processing. Building on the assumption that the data from each class follows a matrix normal…
Large-scale incremental mapping is fundamental to the development of robust and reliable autonomous systems, as it underpins incremental environmental understanding with sequential inputs for navigation and decision-making. LiDAR is widely…
Graph Neural Networks (GNNs) have been widely used for modeling graph-structured data. With the development of numerous GNN variants, recent years have witnessed groundbreaking results in improving the scalability of GNNs to work on static…
Clustering and dimensionality reduction have been crucial topics in machine learning and computer vision. Clustering high-dimensional data has been challenging for a long time due to the curse of dimensionality. For that reason, a more…
Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…
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…