Related papers: An Outlyingness Matrix for Multivariate Functional…
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…
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…
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…
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,…
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 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…
Data depth is an efficient tool for robustly summarizing the distribution of functional data and detecting potential magnitude and shape outliers. Commonly used functional data depth notions, such as the modified band depth and extremal…
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…
Outlier detection is an important data mining tool that becomes particularly challenging when dealing with nominal data. First and foremost, flagging observations as outlying requires a well-defined notion of nominal outlyingness. This…
A multivariate dataset consists of $n$ cases in $d$ dimensions, and is often stored in an $n$ by $d$ data matrix. It is well-known that real data may contain outliers. Depending on the situation, outliers may be (a) undesirable errors which…
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…
We construct classifiers for multivariate and functional data. Our approach is based on a kind of distance between data points and classes. The distance measure needs to be robust to outliers and invariant to linear transformations of the…
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…
Classification is the basis of cognition. Unlike other solutions, this study approaches it from the view of outliers. We present an expanding algorithm to detect outliers in univariate datasets, together with the underlying foundation. The…
Functional data present unique challenges for clustering due to their infinite-dimensional nature and potential sensitivity to outliers. An extension of the OCLUST algorithm to the functional setting is proposed to address these issues. The…
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…
Support Vector Machines are a widely used classification technique. They are computationally efficient and provide excellent predictions even for high-dimensional data. Moreover, Support Vector Machines are very flexible due to the…
Two frameworks for multivariate functional depth based on multivariate depths are introduced in this paper. The first framework is multivariate functional integrated depth, and the second framework involves multivariate functional extremal…