Related papers: Separating Topological Noise from Features using P…

Sample selection improves the efficiency and effectiveness of machine learning models by providing informative and representative samples. Typically, samples can be modeled as a sample graph, where nodes are samples and edges represent…

We develop a method that we call \emph{omission of intervals}, for establishing topological properties of subsets of the real line based on their combinatorial structure. Using this method, we obtain conceptual proofs of the fundamental…

Superpixel is widely used in image processing. And among the methods for superpixel generation, clustering-based methods have a high speed and a good performance at the same time. However, most clustering-based superpixel methods are…

In this paper we present a new approach to computing homology (with field coefficients) and persistent homology. We use concepts from discrete Morse theory, to provide an algorithm which can be expressed solely in terms of simple graph…

There has been little to no work in the area of spectroscopy noise in order to create data sets for analytical algorithms to be challenged on the ability to separate chemicals. We present a framework on how to build off of a sparse about of…

We introduce an algorithm to locate contours of functions that are expensive to evaluate. The problem of locating contours arises in many applications, including classification, constrained optimization, and performance analysis of…

Spectral measurements of boundary localized in-gap modes are commonly used to identify topological insulators via the bulk-boundary correspondence. This can be extended to high-order topological insulators for which the most striking…

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…

Persistent homology is one of the most popular methods in topological data analysis. An initial step in its use involves constructing a nested sequence of simplicial complexes. There is an abundance of different complexes to choose from,…

This work presents a study on label noise in medical image segmentation by considering a noise model based on Gaussian field deformations. Such noise is of interest because it yields realistic looking segmentations and because it is…

We propose a new way to measure the balance between freedom and coherence in a dynamical system and a new measure of its internal variability. Based on the concept of entropy and ideas from neuroscience and information theory, we define…

We aim to solve a topology optimization problem where the distribution of material in the design domain is represented by a density function. To obtain candidates for local minima, we want to solve the first order optimality system via…

Segmentation algorithms are prone to make topological errors on fine-scale structures, e.g., broken connections. We propose a novel method that learns to segment with correct topology. In particular, we design a continuous-valued loss…

Label noise is a common problem in real-world datasets, affecting both model training and validation. Clean data are essential for achieving strong performance and ensuring reliable evaluation. While various techniques have been proposed to…

Feature selection is an important tool to deal with high dimensional data. In unsupervised case, many popular algorithms aim at maintaining the structure of the original data. In this paper, we propose a simple and effective feature…

Classifying images often requires manual identification of qualitative features. Machine learning approaches including convolutional neural networks can achieve accuracy comparable to human classifiers, but require extensive data and…

We consider endomorphisms of a compact manifold which are expanding except for a finite number of points and prove the existence and uniqueness of a physical measure and its stochastical stability. We also characterize the zero-noise limit…

Large datasets in NLP suffer from noisy labels, due to erroneous automatic and human annotation procedures. We study the problem of text classification with label noise, and aim to capture this noise through an auxiliary noise model over…

As the size of the dataset used in deep learning tasks increases, the noisy label problem, which is a task of making deep learning robust to the incorrectly labeled data, has become an important task. In this paper, we propose a method of…

Decoherence-free subsystems have been successfully developed as a tool to preserve fragile quantum information against noises. In this letter, we develop a structure theory for decoherence-free subsystems. Based on it, we present an…