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Persistent homology is a common technique in topological data analysis providing geometrical and topological information about the sample space. All this information, known as topological features, is summarized in persistence diagrams, and…

Directed hypergraphs are vital for modeling complex polyadic relationships in domains such as discrete mathematics, computer science, network security, and systems modeling. However, their inherent complexity often impedes effective…

Due to the diverse sparsity, high dimensionality, and large temporal variation of dynamic point clouds, it remains a challenge to design an efficient point cloud compression method. We propose to code the geometry of a given point cloud by…

There are now over 20 commercial vector database management systems (VDBMSs), all produced within the past five years. But embedding-based retrieval has been studied for over ten years, and similarity search a staggering half century and…

Vertex Subset Problems (VSPs) are a class of combinatorial optimization problems on graphs where the goal is to find a subset of vertices satisfying a predefined condition. Two prominent approaches for solving VSPs are dynamic programming…

Modern processor architectures, in addition to having still more cores, also require still more consideration to memory-layout in order to run at full capacity. The usefulness of most languages is deprecating as their abstractions,…

In this dissertation we report results of our research on dense distributed representations of text data. We propose two novel neural models for learning such representations. The first model learns representations at the document level,…

Vectorization is a compiler optimization that replaces multiple operations on scalar values with a single operation on vector values. Although common in traditional compilers such as rustc, clang, and gcc, vectorization is not common in the…

Topological Data Analysis (TDA) combines computational topology and data science to extract and analyze intrinsic topological and geometric structures in data set in a metric space. While the persistent homology (PH), a widely used tool in…

One approach to understanding complex data is to study its shape through the lens of algebraic topology. While the early development of topological data analysis focused primarily on static data, in recent years, theoretical and applied…

This work investigates dataset vectorization for two dataset-level tasks: assessing training set suitability and test set difficulty. The former measures how suitable a training set is for a target domain, while the latter studies how…

Reference tracking is a key objective in many control systems, including those characterized by complex nonlinear dynamics. In these settings, traditional control approaches can effectively ensure steady-state accuracy but often struggle to…

Hyperbolic geometry has emerged as an effective latent space for representing complex networks, owing to its ability to capture hierarchical organization and heterogeneous connectivity patterns using low-dimensional embeddings. As a result,…

With the increased availability of 3D scanning technology, point clouds are moving into the focus of computer vision as a rich representation of everyday scenes. However, they are hard to handle for machine learning algorithms due to their…

Topological data analysis (TDA) is a rapidly developing collection of methods for studying the shape of point cloud and other data types. One popular approach, designed to be robust to noise and outliers, is to first use a smoothing…

Mathematical notation makes up a large portion of STEM literature, yet finding semantic representations for formulae remains a challenging problem. Because mathematical notation is precise, and its meaning changes significantly with small…

The machinery of topological data analysis becomes increasingly popular in a broad range of machine learning tasks, ranging from anomaly detection and manifold learning to graph classification. Persistent homology is one of the key…

Relational representation learning transforms relational data into continuous and low-dimensional vector representations. However, vector-based representations fall short in capturing crucial properties of relational data that are complex…

Modern representation learning increasingly relies on unsupervised and self-supervised methods trained on large-scale unlabeled data. While these approaches achieve impressive generalization across tasks and domains, evaluating embedding…

Solving different types of optimization models (including parameters fitting) for support vector machines on large-scale training data is often an expensive computational task. This paper proposes a multilevel algorithmic framework that…