Related papers: Euler Characteristic Tools For Topological Data An…
This work proposes an ensemble clustering method using transfer learning approach. We consider a clustering problem, in which in addition to data under consideration, "similar" labeled data are available. The datasets can be described with…
Interacting, self-propelled particles such as epithelial cells can dynamically self-organize into complex multicellular patterns, which are challenging to classify without a priori information. Classically, different phases and phase…
In a world abundant with diverse data arising from complex acquisition techniques, there is a growing need for new data analysis methods. In this paper we focus on high-dimensional data that are organized into several hierarchical datasets.…
Learning effective high-order feature interactions is very crucial in the CTR prediction task. However, it is very time-consuming to calculate high-order feature interactions with massive features in online e-commerce platforms. Most…
In the evolving domains of Machine Learning and Data Analytics, existing dataset characterization methods such as statistical, structural, and model-based analyses often fail to deliver the deep understanding and insights essential for…
Understanding the topological characteristics of data is important to many areas of research. Recent work has demonstrated that synthetic 4D image-type data can be useful to train 4D convolutional neural network models to see topological…
Assume that the coefficients of a polynomial in a complex variable are Laurent polynomials in some complex parameters. The parameter space (a complex torus) splits into strata corresponding to different combinations of coincidence of the…
Weighing the topological domain over which data can be represented and analysed is a key strategy in many signal processing and machine learning applications, enabling the extraction and exploitation of meaningful data features and their…
Dynamical systems are ubiquitous in science and engineering as models of phenomena that evolve over time. Although complex dynamical systems tend to have important modular structure, conventional modeling approaches suppress this structure.…
Descriptors play an important role in data-driven materials design. While most descriptors of crystalline materials emphasize structure and composition, they often neglect the electron density - a complex yet fundamental quantity that…
Topological Data Analysis (TDA) is an emergent field that aims to discover topological information hidden in a dataset. TDA tools have been commonly used to create filters and topological descriptors to improve Machine Learning (ML)…
Hypergraph is a topological model for networks. In order to study the topology of hypergraphs, the homology of the associated simplicial complexes and the embedded homology have been invented. In this paper, we give some algorithms to…
Topological data analysis has emerged as a powerful tool for extracting the metric, geometric and topological features underlying the data as a multi-resolution summary statistic, and has found applications in several areas where data…
A parameterization is described for quantifying translational motion of a point in three-dimensional Euclidean space. The parameterization is similar to well-known parameterizations such as spherical coordinates in that both position and…
The goal of this paper is to establish the fundamental tools to analyze signals defined over a topological space, i.e. a set of points along with a set of neighborhood relations. This setup does not require the definition of a metric and…
Topological study of existing random simplicial complexes is non-trivial and has led to several seminal works. However, the applicability of such studies is limited since the randomness there is usually governed by a single parameter. With…
In this paper we obtain some explicit expressions for the Euler characteristic of a rank n coherent sheaf F on P^N and of its twists F(t) as polynomials in the Chern classes c_i(F), also giving algorithms for the computation. The employed…
Topological methods, including persistent homology, are powerful tools for analysis of high-dimensional data sets but these methods rely almost exclusively on thresholding techniques. In noisy data sets, thresholding does not always allow…
The Euler scheme is up to date the most important numerical method for ordinary differential inclusions, because the use of the available higher-order methods is prohibited by their enormous complexity after spatial discretization.…
The method of characteristics is a classical method for gaining understanding in the solution of a partial differential equation. It has recently been applied to the adjoint equations of the 2D Euler equations and the first goal of this…