Related papers: Geometric anomaly detection in data

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)…

Datasets in high-dimension do not typically form clusters in their original space; the issue is worse when the number of points in the dataset is small. We propose a low-computation method to find statistically significant clustering…

Topological Data Analysis (TDA) allows us to extract powerful topological and higher-order information on the global shape of a data set or point cloud. Tools like Persistent Homology or the Euler Transform give a single complex description…

We propose a novel and efficient method, that we shall call TopRank in the following paper, for detecting change-points in high-dimensional data. This issue is of growing concern to the network security community since network anomalies…

We study anomaly clustering, grouping data into coherent clusters of anomaly types. This is different from anomaly detection that aims to divide anomalies from normal data. Unlike object-centered image clustering, anomaly clustering is…

Random projection is widely used as a method of dimension reduction. In recent years, its combination with standard techniques of regression and classification has been explored. Here we examine its use with principal component analysis…

In recent years, there has been a growing interest in identifying anomalous structure within multivariate data streams. We consider the problem of detecting collective anomalies, corresponding to intervals where one or more of the data…

Industrial anomaly detection is an important task within computer vision with a wide range of practical use cases. The small size of anomalous regions in many real-world datasets necessitates processing the images at a high resolution. This…

The knowledge that data lies close to a particular submanifold of the ambient Euclidean space may be useful in a number of ways. For instance, one may want to automatically mark any point far away from the submanifold as an outlier or to…

Relationships between entities in datasets are often of multiple nature, like geographical distance, social relationships, or common interests among people in a social network, for example. This information can naturally be modeled by a set…

Clustering methods seek to partition data such that elements are more similar to elements in the same cluster than to elements in different clusters. The main challenge in this task is the lack of a unified definition of a cluster,…

In this paper we explore the use of spatial clustering algorithms as a new computational approach for modeling the cosmic web. We demonstrate that such algorithms are efficient in terms of computing time needed. We explore three distinct…

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)…

Identifying anomalies in multi-dimensional datasets is an important task in many real-world applications. A special case arises when anomalies are occluded in a small set of attributes, typically referred to as a subspace, and not…

The language and methods of algebraic topology, particularly homotopy theory, have been extensively used in the study of the identification, the classification and the evolution of defects. Topological methods provide the means for the…

To address the dual challenges of the curse of dimensionality and the difficulty in separating intra-cluster and inter-cluster structures in high-dimensional manifold embedding, we proposes an Adaptive Multi-Scale Manifold Embedding (AMSME)…

This study introduces SECODA, a novel general-purpose unsupervised non-parametric anomaly detection algorithm for datasets containing continuous and categorical attributes. The method is guaranteed to identify cases with unique or sparse…

Finding densely connected subsets of vertices in an unsupervised setting, called clustering or community detection, is one of the fundamental problems in network science. The edge clustering approach instead detects communities by…

Detection of interesting (e.g., coherent or anomalous) clusters has been studied extensively on plain or univariate networks, with various applications. Recently, algorithms have been extended to networks with multiple attributes for each…

We present a new technique that enables manifold learning to accurately embed data manifolds that contain holes, without discarding any topological information. Manifold learning aims to embed high dimensional data into a lower dimensional…