Related papers: Topological Data Analysis for Unsupervised Anomaly…
Nowadays, Machine Learning and Deep Learning methods have become the state-of-the-art approach to solve data classification tasks. In order to use those methods, it is necessary to acquire and label a considerable amount of data; however,…
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…
Deep topological data analysis (TDA) offers a principled framework for capturing structural invariants such as connectivity and cycles that persist across scales, making it a natural fit for anomaly segmentation (AS). Unlike thresholdbased…
Topological data analysis (TDA) offers novel mathematical tools for deep learning. Inspired by Carlsson et al., this study designs topology-aware convolutional kernels that significantly improve speech recognition networks. Theoretically,…
Dealing with atypical traffic scenarios remains a challenging task in autonomous driving. However, most anomaly detection approaches cannot be trained on raw sensor data but require exposure to outlier data and powerful semantic…
Topological Machine Learning (TML) is an emerging field that leverages techniques from algebraic topology to analyze complex data structures in ways that traditional machine learning methods may not capture. This tutorial provides a…
Large time-varying graphs are increasingly common in financial, social and biological settings. Feature extraction that efficiently encodes the complex structure of sparse, multi-layered, dynamic graphs presents computational and…
In a variety of applications, one desires to detect groups of anomalous data samples, with a group potentially manifesting its atypicality (relative to a reference model) on a low-dimensional subset of the full measured set of features.…
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 --…
Anomaly detection on dynamic graphs refers to detecting entities whose behaviors obviously deviate from the norms observed within graphs and their temporal information. This field has drawn increasing attention due to its application 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…
Anomaly detection is a branch of data analysis and machine learning which aims at identifying observations that exhibit abnormal behaviour. Be it measurement errors, disease development, severe weather, production quality default(s) (items)…
The rapid growth in stored time-oriented data necessitates the development of new methods for handling, processing, and interpreting large amounts of temporal data. One important example of such processing is detecting anomalies in…
Anomaly detection is a well-known task that involves the identification of abnormal events that occur relatively infrequently. Methods for improving anomaly detection performance have been widely studied. However, no studies utilizing…
Real-world graphs are complex to process for performing effective analysis, such as anomaly detection. However, recently, there have been several research efforts addressing the issues surrounding graph-based anomaly detection. In this…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
We propose a hybrid approach to temporal anomaly detection in access data of users to databases --- or more generally, any kind of subject-object co-occurrence data. We consider a high-dimensional setting that also requires fast computation…
Traditional Time-series Anomaly Detection (TAD) methods often struggle with the composite nature of complex time-series data and a diverse array of anomalies. We introduce TADNet, an end-to-end TAD model that leverages Seasonal-Trend…
In the present article we describe and discuss a framework for applying different topological data analysis (TDA) techniques to a music fragment given as a score in traditional Western notation. We first consider different sets of points in…
Detecting anomalous edges in dynamic graphs is an important task in many applications over evolving triple-based data, such as social networks, transaction management, and epidemiology. A major challenge with this task is the absence of…