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Interactive exploration of large, multidimensional datasets plays a very important role in various scientific fields. It makes it possible not only to identify important structural features and forms, such as clusters of vertices and their…

Neural implicit representations have had a significant impact on simultaneous localization and mapping (SLAM) by enabling robots to build continuous, differentiable, and high-fidelity 3D maps from sensor data. However, as the scale and…

While the existence of low-dimensional embedding manifolds has been shown in patterns of collective motion, the current battery of nonlinear dimensionality reduction methods are not amenable to the analysis of such manifolds. This is mainly…

In this paper, we investigate Dimensionality reduction (DR) maps in an information retrieval setting from a quantitative topology point of view. In particular, we show that no DR maps can achieve perfect precision and perfect recall…

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…

Both uncertainty-assisted and iteration-based methods have achieved great success in stereo matching. However, existing uncertainty estimation methods take a single image and the corresponding disparity as input, which imposes higher…

Several complex systems can be modeled as large networks in which the state of the nodes continuously evolves through interactions among neighboring nodes, forming a high-dimensional nonlinear dynamical system. One of the main challenges of…

This article introduces an approach to facilitate cooperative exploration and mapping of large-scale, near-ground, underground, or indoor spaces via a novel integration framework for locally-dense agent map data. The effort targets limited…

The current state-of-the art techniques for image segmentation are often based on U-Net architectures, a U-shaped encoder-decoder networks with skip connections. Despite the powerful performance, the architecture often does not perform well…

This paper presents a comprehensive comparative analysis of prominent clustering algorithms K-means, DBSCAN, and Spectral Clustering on high-dimensional datasets. We introduce a novel evaluation framework that assesses clustering…

Quantum embedding methods enable the study of large, strongly correlated quantum systems by (usually self-consistent) decomposition into computationally manageable subproblems, in the spirit of divide-and-conquer methods. Among these,…

Dimensionality reduction techniques play important roles in the analysis of big data. Traditional dimensionality reduction approaches, such as principal component analysis (PCA) and linear discriminant analysis (LDA), have been studied…

The state-of-the-art models for medical image segmentation are variants of U-Net and fully convolutional networks (FCN). Despite their success, these models have two limitations: (1) their optimal depth is apriori unknown, requiring…

A main challenge for tasks on panorama lies in the distortion of objects among images. In this work, we propose a Distortion-Aware Monocular Omnidirectional (DAMO) dense depth estimation network to address this challenge on indoor panoramas…

Dimensionality reduction is a common method for analyzing and visualizing high-dimensional data across domains. Dimensionality-reduction algorithms involve complex optimizations and the reduced dimensions computed by these algorithms…

Dimensionality Reduction (DR) scatterplot layouts have become a ubiquitous visualization tool for analyzing multidimensional datasets. Despite their popularity, such scatterplots suffer from occlusion, especially when informative glyphs are…

Dimensionality reduction is crucial both for visualization and preprocessing high dimensional data for machine learning. We introduce a novel method based on a hierarchy built on 1-nearest neighbor graphs in the original space which is used…

Due to rapid advancements in technology, datasets are available from various domains. In order to carry out more relevant and appropriate analysis, it is often necessary to project the dataset into a higher or lower dimensional space based…

Double machine learning (DML) delivers valid inference on low-dimensional causal parameters while permitting flexible nuisance estimation, but its computational cost becomes prohibitive once cross-fitted learners must be trained on massive…

Recent works have shown that the computational efficiency of 3D medical image (e.g. CT and MRI) segmentation can be impressively improved by dynamic inference based on slice-wise complexity. As a pioneering work, a dynamic architecture…