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This paper proposes a novel approach for detecting the topology of distribution networks based on the analysis of time series measurements. The time-based analysis approach draws on data from high-precision phasor measurement units (PMUs or…
We propose a novel method for topological analysis of unweighted graphs which is based on \textit{persistent homology}. The proposed method maps the input graph to a complete weighted graph where the weighting function maps each edge to a…
In artificial-intelligence-aided signal processing, existing deep learning models often exhibit a black-box structure, and their validity and comprehensibility remain elusive. The integration of topological methods, despite its relatively…
Topological data analysis (TDA) is an emerging mathematical concept for characterizing shapes in complex data. In TDA, persistence diagrams are widely recognized as a useful descriptor of data, and can distinguish robust and noisy…
The objective of this study is to detect and quantify the periodic behavior of the signals using topological methods. We propose to use delay-coordinate embeddings as a tool to measure the periodicity of signals. Moreover, we use persistent…
Traditional error detection and correction codes focus on bit-level fidelity, which is insufficient for emerging technologies like eXtended Reality (XR) and holographic communications requiring high-data-rate, low-latency systems. Bit-level…
We develop in this paper a theoretical framework for the topological study of time series data. Broadly speaking, we describe geometrical and topological properties of sliding window (or time-delay) embeddings, as seen through the lens of…
Persistent homology is a natural tool for probing the topological characteristics of weighted graphs, essentially focusing on their $0$-dimensional homology. While this area has been substantially studied, we present a new approach to…
This work presents a framework for studying temporal networks using zigzag persistence, a tool from the field of Topological Data Analysis (TDA). The resulting approach is general and applicable to a wide variety of time-varying graphs. For…
The study of topology is strictly speaking, a topic in pure mathematics. However in only a few years, Topological Data Analysis (TDA), which refers to methods of utilizing topological features in data (such as connected components, tunnels,…
This paper tackles the problem of detecting abrupt changes in the mean of a heteroscedastic signal by model selection, without knowledge on the variations of the noise. A new family of change-point detection procedures is proposed, showing…
Clustering consists of grouping together samples giving their similar properties. The problem of modeling simultaneously groups of samples and features is known as Co-Clustering. This paper introduces ROCCO - a Robust Continuous…
In this paper we present a novel methodology based on a topological entropy, the so-called persistent entropy, for addressing the comparison between discrete piecewise linear functions. The comparison is certified by the stability theorem…
In this paper we present a novel algorithm and efficient data structure for anomaly detection based on temporal data. Time-series data are represented by a sequence of symbolic time intervals, describing increasing and decreasing trends, in…
Dynamic community detection methods often lack effective mechanisms to ensure temporal consistency, hindering the analysis of network evolution. In this paper, we propose a novel deep graph clustering framework with temporal consistency…
We present a way to use Topological Data Analysis (TDA) for machine learning tasks on grayscale images. We apply persistent homology to generate a wide range of topological features using a point cloud obtained from an image, its natural…
Many multi-variate time series obtained in the natural sciences and engineering possess a repetitive behavior, as for instance state-space trajectories of industrial machines in discrete automation. Recovering the times of recurrence from…
In this article, we introduce a Topological Data Analysis (TDA) pipeline for neural spike train data. Understanding how the brain transforms sensory information into perception and behavior requires analyzing coordinated neural population…
This paper introduces advanced techniques of Topological Data Analysis (TDA) for unsupervised anomaly detection and customer segmentation in banking data. Using the Mapper algorithm and persistent homology, we develop unsupervised…
This survey provides a comprehensive exploration of applications of Topological Data Analysis (TDA) within neural network analysis. Using TDA tools such as persistent homology and Mapper, we delve into the intricate structures and behaviors…