Related papers: Directional Outlyingness for Multivariate Function…

Classical multivariate statistics measures the outlyingness of a point by its Mahalanobis distance from the mean, which is based on the mean and the covariance matrix of the data. A multivariate depth function is a function which, given a…

The use of quantiles to obtain insights about multivariate data is addressed. It is argued that incisive insights can be obtained by considering directional quantiles, the quantiles of projections. Directional quantile envelopes are…

The problem of universal outlying sequence detection is studied, where the goal is to detect outlying sequences among $M$ sequences of samples. A sequence is considered as outlying if the observations therein are generated by a distribution…

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…

An outlier is an observation or a data point that is far from rest of the data points in a given dataset or we can be said that an outlier is away from the center of mass of observations. Presence of outliers can skew statistical measures…

The notion of data depth has long been in use to obtain robust location and scale estimates in a multivariate setting. The depth of an observation is a measure of its centrality, with respect to a data set or a distribution. The data depths…

The detection of outliers is of critical importance in the assurance of data quality. Outliers may exist in observed data or in data derived from these observed data, such as estimates and forecasts. An outlier may indicate a problem with…

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…

Imaging genetic research has essentially focused on discovering unique and co-association effects, but typically ignoring to identify outliers or atypical objects in genetic as well as non-genetics variables. Identifying significant…

Functional data clustering is to identify heterogeneous morphological patterns in the continuous functions underlying the discrete measurements/observations. Application of functional data clustering has appeared in many publications across…

The outlying property detection problem is the problem of discovering the properties distinguishing a given object, known in advance to be an outlier in a database, from the other database objects. In this paper, we analyze the problem…

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…

This paper introduces the sparse functional boxplot and the intensity sparse functional boxplot as practical exploratory tools. Besides being available for complete functional data, they can be used in sparse univariate and multivariate…

A median-radius framework for assessing centrality in multivariate data using median distances is proposed. Based on the proposed framework, a scale invariant measure of radial dispersion is defined and used to establish a depth function…

Data depth is a well-known and useful nonparametric tool for analyzing functional data. It provides a novel way of ranking a sample of curves from the center outwards and defining robust statistics, such as the median or trimmed means. It…

In statistics and machine learning, the traditional meaning of the terms `outlier' and `anomaly' is a case in the dataset that behaves differently from the bulk of the data. This raises suspicion that it may belong to a different…

Functional depth is the functional data analysis technique that orders a functional data set. Unlike the case of data on the real line, defining this order is non-trivial, and particularly, with functional data, there are a number of…

Statistical analysis of functional data is challenging due to their complex patterns, for which functional depth provides an effective means of reflecting their ordering structure. In this work, we investigate practical aspects of the…

Shape-constrained functional data encompass a wide array of application fields, such as activity profiling, growth curves, healthcare and mortality. Most existing methods for general functional data analysis often ignore that such data are…

Outlier detection plays a significant role in various real world applications such as intrusion, malfunction, and fraud detection. Traditionally, outlier detection techniques are applied to find outliers in the context of the whole dataset.…