Related papers: Pointwise Data Depth for Univariate and Multivaria…

There has been extensive work on data depth-based methods for robust multivariate data analysis. Recent developments have moved to infinite-dimensional objects such as functional data. In this work, we propose a new notion of depth, the…

We consider functional outlier detection from a geometric perspective, specifically: for functional data sets drawn from a functional manifold which is defined by the data's modes of variation in amplitude and phase. Based on this manifold,…

This paper considers the problem of outlier detection in functional data analysis focusing particularly on the more difficult case of shape outliers. We present an inductive conformal anomaly detection method based on elastic functional…

We propose a new method to visualize and detect shape outliers in samples of curves. In functional data analysis we observe curves defined over a given real interval and shape outliers are those curves that exhibit a different shape from…

Distributional data analysis, concerned with statistical analysis and modeling for data objects consisting of random probability density functions (PDFs) in the framework of functional data analysis (FDA), has received considerable interest…

This article proposes a new graphical tool, the magnitude-shape (MS) plot, for visualizing both the magnitude and shape outlyingness of multivariate functional data. The proposed tool builds on the recent notion of functional directional…

Smart metering infrastructures collect data almost continuously in the form of fine-grained long time series. These massive data series often have common daily patterns that are repeated between similar days or seasons and shared among…

The classification of multivariate functional data is an important task in scientific research. Unlike point-wise data, functional data are usually classified by their shapes rather than by their scales. We define an outlyingness matrix by…

Functional data analysis can be seriously impaired by abnormal observations, which can be classified as either magnitude or shape outliers based on their way of deviating from the bulk of data. Identifying magnitude outliers is relatively…

We propose a novel procedure for outlier detection in functional data, in a semi-supervised framework. As the data is functional, we consider the coefficients obtained after projecting the observations onto orthonormal bases (wavelet, PCA).…

Data depth is a powerful nonparametric tool originally proposed to rank multivariate data from center outward. In this context, one of the most archetypical depth notions is Tukey's halfspace depth. In the last few decades notions of depth…

We propose a new family of depth measures called the elastic depths that can be used to greatly improve shape anomaly detection in functional data. Shape anomalies are functions that have considerably different geometric forms or features…

Functional data covers a wide range of data types. They all have in common that the observed objects are functions of of a univariate argument (e.g. time or wavelength) or a multivariate argument (say, a spatial position). These functions…

The direction of outlyingness is crucial to describing the centrality of multivariate functional data. Motivated by this idea, we generalize classical depth to directional outlyingness for functional data. We investigate theoretical…

Outlier detection can serve as an extremely important tool for researchers from a wide range of fields. From the sectors of banking and marketing to the social sciences and healthcare sectors, outlier detection techniques are very useful…

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)…

This article introduces trimmed estimators for the mean and covariance function of general functional data. The estimators are based on a new measure of outlyingness or data depth that is well defined on any metric space, although this…

High-dimensional data poses unique challenges in outlier detection process. Most of the existing algorithms fail to properly address the issues stemming from a large number of features. In particular, outlier detection algorithms perform…

Surface, image and video data can be considered as functional data with a bivariate domain. To detect outlying surfaces or images, a new method is proposed based on the mean and the variability of the degree of outlyingness at each grid…

We propose two new outlier detection methods, for identifying and classifying different types of outliers in (big) functional data sets. The proposed methods are based on an existing method called Massive Unsupervised Outlier Detection…