Related papers: PH-STAT
Two-dimensional (2D) particle systems, such as magnetic skyrmions, exhibit topological phase transitions between unique 2D phases. However, a simple and computationally efficient methodology to capture lattice configurational properties and…
We propose a unified framework based on persistent homology (PH) to characterize both local and global structures in disordered systems. It can simultaneously generate local and global descriptors using the same algorithm and data…
Topological data analysis (TDA) aims to extract noise-robust features from a data set by examining the number and persistence of holes in its topology. We show that a computational problem closely related to a core task in TDA --…
Large Language Models (LLMs) have advanced autonomous agents from deep search, which retrieves concise factual answers, to deep research, which synthesizes scattered evidence into long-form reports. However, verifiable multimodal deep…
We introduce a subsampling method for topological data analysis based on strong collapses of simplicial complexes. Given a point cloud and a scale parameter $\delta$, we construct a subsampling that preserves both global and local…
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…
Persistent homology is currently one of the more widely known tools from computational topology and topological data analysis. We present in this note a brief survey on the evolution of the subject. The goal is to highlight the main ideas,…
Surface roughness plays an important role in analyzing engineering surfaces. It quantifies the surface topography and can be used to determine whether the resulting surface finish is acceptable or not. Nevertheless, while several existing…
As a powerful tool of asynchronous event sequence analysis, point processes have been studied for a long time and achieved numerous successes in different fields. Among various point process models, Hawkes process and its variants attract…
Advances in entity-graph based analysis of histopathology images have brought in a new paradigm to describe tissue composition, and learn the tissue structure-to-function relationship. Entity-graphs offer flexible and scalable…
Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field.…
Prediction and discovery of new materials with desired properties are at the forefront of quantum science and technology research. A major bottleneck in this field is the computational resources and time complexity related to finding new…
In the 20th century, newly invented technical artifacts were connected to form large-scale complex engineering systems. Furthermore, the interactions found within these networked systems has grown in both degree as well as heterogeneity.…
Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…
Persistent homology theory is a relatively new but powerful method in data analysis. Using simplicial complexes, classical persistent homology is able to reveal high dimensional geometric structures of datasets, and represent them as…
We apply topological data analysis (TDA) to speech classification problems and to the introspection of a pretrained speech model, HuBERT. To this end, we introduce a number of topological and algebraic features derived from Transformer…
Tabular data is one of the most common data sources in machine learning. Although a wide range of classical methods demonstrate practical utilities in this field, deep learning methods on tabular data are becoming promising alternatives due…
Persistence diagrams (PDs), often characterized as sets of death and birth of homology class, have been known for providing a topological representation of a graph structure, which is often useful in machine learning tasks. Prior works rely…
Persistent homology (PH) studies the topology of data across multiple scales by building nested collections of topological spaces called filtrations, computing homology and returning an algebraic object that can be vizualised as a…
Topological Data Analysis (TDA) is a novel new and fast growing field of data science providing a set of new topological and geometric tools to derive relevant features out of complex high-dimensional data. In this paper we apply two of…