Related papers: Spectral learning of multivariate extremes

The extremal dependence structure of a regularly varying random vector Xis fully described by its limiting spectral measure. In this paper, we investigate how torecover characteristics of the measure, such as extremal coefficients, from the…

Extremes play a special role in Anomaly Detection. Beyond inference and simulation purposes, probabilistic tools borrowed from Extreme Value Theory (EVT), such as the angular measure, can also be used to design novel statistical learning…

In spectral clustering and spectral image segmentation, the data is partioned starting from a given matrix of pairwise similarities S. the matrix S is constructed by hand, or learned on a separate training set. In this paper we show how to…

In the context of clustering, we assume a generative model where each cluster is the result of sampling points in the neighborhood of an embedded smooth surface; the sample may be contaminated with outliers, which are modeled as points…

Extremes occur in stationary regularly varying time series as short periods with several large observations, known as extremal blocks. We study cluster statistics summarizing the behavior of functions acting on these extremal blocks.…

This study introduces a novel estimation method for the entries and structure of a matrix $A$ in the linear factor model $\mathbf{X} = A\textbf{Z} + \textbf{E}$. This is applied to an observable vector $\mathbf{X} \in \mathbb{R}^d$ with…

Spectral clustering is a popular and versatile clustering method based on a relaxation of the normalised graph cut objective. Despite its popularity, however, there is no single agreed upon method for tuning the important scaling parameter,…

In many practical applications, evaluating the joint impact of combinations of environmental variables is important for risk management and structural design analysis. When such variables are considered simultaneously, non-stationarity can…

The angular measure on the unit sphere characterizes the first-order dependence structure of the components of a random vector in extreme regions and is defined in terms of standardized margins. Its statistical recovery is an important step…

Recursive max-linear vectors model causal dependence between its components by expressing each node variable as a max-linear function of its parental nodes in a directed acyclic graph and some exogenous innovation. Motivated by extreme…

This paper presents and analyzes an approach to cluster-based inference for dependent data. The primary setting considered here is with spatially indexed data in which the dependence structure of observed random variables is characterized…

Spectral clustering is a leading and popular technique in unsupervised data analysis. Two of its major limitations are scalability and generalization of the spectral embedding (i.e., out-of-sample-extension). In this paper we introduce a…

Graph clustering is a fundamental task in unsupervised learning with broad real-world applications. While spectral clustering methods for undirected graphs are well-established and guided by a minimum cut optimization consensus, their…

Extremal graphical models encode the conditional independence structure of multivariate extremes. Key statistics for learning extremal graphical structures are empirical extremal variograms, for which we prove non-asymptotic concentration…

We present a new framework for modelling multivariate extremes, based on an angular-radial representation of the probability density function. Under this representation, the problem of modelling multivariate extremes is transformed to that…

Spectral clustering is one of the most popular clustering methods for finding clusters in a graph, which has found many applications in data mining. However, the input graph in those applications may have many missing edges due to error in…

We propose a spectral clustering method based on local principal components analysis (PCA). After performing local PCA in selected neighborhoods, the algorithm builds a nearest neighbor graph weighted according to a discrepancy between the…

Spectral clustering is widely used in practice due to its flexibility, computational efficiency, and well-understood theoretical performance guarantees. Recently, spectral clustering has been studied to find balanced clusters under…

Spectral clustering is a fast and popular algorithm for finding clusters in networks. Recently, Chaudhuri et al. (2012) and Amini et al.(2012) proposed inspired variations on the algorithm that artificially inflate the node degrees for…

There is an increasing interest to understand the dependence structure of a random vector not only in the center of its distribution but also in the tails. Extreme-value theory tackles the problem of modelling the joint tail of a…