Related papers: Separating Topological Noise from Features using P…
This article investigates the possibility to use the class entropy of the output of a connectionist phoneme recogniser to predict time boundaries between phonetic classes. The rationale is that the value of the entropy should increase in…
Topological data analysis is becoming increasingly relevant to support the analysis of unstructured data sets. A common assumption in data analysis is that the data set is a sample---not necessarily a uniform one---of some high-dimensional…
In topological data analysis, persistent homology is used to study the "shape of data". Persistent homology computations are completely characterized by a set of intervals called a bar code. It is often said that the long intervals…
Polyphonic music files were analyzed using the set of symbols that produced the Minimal Entropy Description which we call the Fundamental Scale. This allowed us to create a novel space to represent music pieces by developing: a) a method to…
This paper proposes to use set features for detecting anomalies in samples that consist of unusual combinations of normal elements. Many leading methods discover anomalies by detecting an unusual part of a sample. For example,…
In this paper, we exploit minimal sensing information gathered from biologically inspired sensor networks to perform exploration and mapping in an unknown environment. A probabilistic motion model of mobile sensing nodes, inspired by motion…
Deep models trained with noisy labels are prone to over-fitting and struggle in generalization. Most existing solutions are based on an ideal assumption that the label noise is class-conditional, i.e., instances of the same class share the…
We explore a novel application of zero-dimensional persistent homology from Topological Data Analysis (TDA) for bracketing zero-crossings of both one-dimensional continuous functions, and uniformly sampled time series. We present an…
This paper introduces an unsupervised method to estimate the class separability of text datasets from a topological point of view. Using persistent homology, we demonstrate how tracking the evolution of embedding manifolds during training…
In this paper we propose a measure of anisotropy as a quality parameter to estimate the amount of noise in noisy images. The anisotropy of an image can be determined through a directional measure, using an appropriate statistical…
We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of…
Biomolecular structure comparison not only reveals evolutionary relationships, but also sheds light on biological functional properties. However, traditional definitions of structure or sequence similarity always involve superposition or…
Persistent homology provides information about the lifetime of homology classes along a filtration of cell complexes. Persistence barcode is a graphical representation of such information. A filtration might be determined by time in a set…
We use Topological Data Analysis tools for studying the inner organization of cells in segmented images of epithelial tissues. More specifically, for each segmented image, we compute different persistence barcodes, which codify lifetime of…
Persistent homology is an area within topological data analysis (TDA) that can uncover different dimensional holes (connected components, loops, voids, etc.) in data. The holes are characterized, in part, by how long they persist across…
This paper aims to discuss a method of quantifying the 'shape' of data, via a methodology called topological data analysis. The main tool within topological data analysis is persistent homology; this is a means of measuring the shape of…
The code base of software projects evolves essentially through inserting and removing information to and from the source code. We can measure this evolution via the elements of information - tokens, words, nodes - of the respective…
We characterize structures such as monotonicity, convexity, and modality in smooth regression curves using persistent homology. Persistent homology is a key tool in topological data analysis that detects higher-dimensional topological…
Understanding the limitations imposed by noise on current and next-generation quantum devices is a crucial step towards demonstrating practical quantum advantage. In this work, we investigate the accumulation of entropy density as a…
Coarse geometry studies metric spaces on the large scale. Our goal here is to study dynamics from a coarse point of view. To this end we introduce a coarse version of topological entropy, suitable for unbounded metric spaces, consistent…