Related papers: A Survey of Vectorization Methods in Topological D…

Parameter prediction is essential for many applications, facilitating insightful interpretation and decision-making. However, in many real life domains, such as power systems, medicine, and engineering, it can be very expensive to acquire…

Vectorized high-definition (HD) map is essential for autonomous driving, providing detailed and precise environmental information for advanced perception and planning. However, current map vectorization methods often exhibit deviations, and…

Learnable embedding vector is one of the most important applications in machine learning, and is widely used in various database-related domains. However, the high dimensionality of sparse data in recommendation tasks and the huge volume of…

Graphs are a natural abstraction for many problems where nodes represent entities and edges represent a relationship across entities. An important area of research that has emerged over the last decade is the use of graphs as a vehicle for…

Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…

Persistent homology is a technique recently developed in algebraic and computational topology well-suited to analysing structure in complex, high-dimensional data. In this paper, we exposit the theory of persistent homology from first…

We introduce the first unified theory for target tracking using Multiple Hypothesis Tracking, Topological Data Analysis, and machine learning. Our string of innovations are 1) robust topological features are used to encode behavioral…

Vectorization is a powerful optimization technique that significantly boosts the performance of high performance computing applications operating on large data arrays. Despite decades of research on auto-vectorization, compilers frequently…

We discuss and review recent developments in the area of applied algebraic topology, such as persistent homology and barcodes. In particular, we discuss how these are related to understanding more about manifold learning from random point…

The increasing prevalence of graph-structured data across various domains has intensified greater interest in graph classification tasks. While numerous sophisticated graph learning methods have emerged, their complexity often hinders…

With the widespread use of information technologies, information networks are becoming increasingly popular to capture complex relationships across various disciplines, such as social networks, citation networks, telecommunication networks,…

In this work, we develop a pipeline that associates Persistence Diagrams to digital data via the most appropriate filtration for the type of data considered. Using a grid search approach, this pipeline determines optimal representation…

An Important tool in the field topological data analysis is known as persistent Homology (PH) which is used to encode abstract representation of the homology of data at different resolutions in the form of persistence diagram (PD). In this…

Graph-based multi-view clustering has achieved better performance than most non-graph approaches. However, in many real-world scenarios, the graph structure of data is not given or the quality of initial graph is poor. Additionally,…

Graph representation learning aims to effectively encode high-dimensional sparse graph-structured data into low-dimensional dense vectors, which is a fundamental task that has been widely studied in a range of fields, including machine…

The increasing ubiquity of smartphones and resurgence of VR/AR techniques, it is expected that our everyday environment may soon be decorating with objects connecting with virtual elements. Alerting to the presence of these objects is…

Machine learning on graphs is an important and ubiquitous task with applications ranging from drug design to friendship recommendation in social networks. The primary challenge in this domain is finding a way to represent, or encode, graph…

Topology optimization is computationally demanding that requires the assembly and solution to a finite element problem for each material distribution hypothesis. As a complementary alternative to the traditional physics-based topology…

Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning. We present a differentiable topology layer that computes persistent homology based on level set…

With automated measurements, large data sets can be assembled with relative ease. Often these data sets have a large degree of variance. Nonetheless, we hope to find groups within the data set with shared distinguishing characteristics.…