Related papers: Directional Outlyingness for Multivariate Function…
The Projection Congruent Subset (PCS) Outlyingness is a new index of multivariate outlyingness obtained by considering univariate projections of the data. Like many other outlier detection procedures, PCS searches for a subset which…
In a recent article, we showed that trigonometric shearlets are able to detect directional step discontinuities along edges of periodic characteristic functions. In this paper, we extend these results to multivariate periodic functions…
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…
The task of outlier detection is to find small groups of data objects that are exceptional when compared with rest large amount of data. Detection of such outliers is important for many applications such as fraud detection and customer…
Discovering causal relationship using multivariate functional data has received a significant amount of attention very recently. In this article, we introduce a functional linear structural equation model for causal structure learning when…
Nowadays many real-world datasets can be considered as functional, in the sense that the processes which generate them are continuous. A fundamental property of this type of data is that in theory they belong to an infinite-dimensional…
The characterization of local regularity is a fundamental issue in signal and image processing, since it contains relevant information about the underlying systems. The 2-microlocal frontier, a monotone concave downward curve in $\mathbb…
Outlier detection and cluster number estimation is an important issue for clustering real data. This paper focuses on spectral clustering, a time-tested clustering method, and reveals its important properties related to outliers. The…
Sources of bias in empirical studies can be separated in those coming from the modelling domain (e.g. multicollinearity) and those coming from outliers. We propose a two-step approach to counter both issues. First, by decontaminating data…
Based on the framework of the directional distance function, we conduct a systematic analysis on the measurement of super-efficiency in order to achieve two main objectives. Our primary purpose is developing two generalized directional…
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…
Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and…
In a multiple linear regression model, the algebraic formula of the decomposition theorem explains the relationship between the univariate regression coefficient and partial regression coefficient using geometry. It was found that…
Random projection is a common technique for designing algorithms in a variety of areas, including information retrieval, compressive sensing and measuring of outlyingness. In this work, the original random projection outlyingness measure is…
This paper introduces two novel, outlyingness scores (OSs) based on Cluster Catch Digraphs (CCDs): Outbound Outlyingness Score (OOS) and Inbound Outlyingness Score (IOS). These scores enhance the interpretability of outlier detection…
Data depth proves successful in the analysis of multivariate data sets, in particular deriving an overall center and assigning ranks to the observed units. Two key features are: the directions of the ordering, from the center towards the…
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)…
Outlier detection is a core task in data mining with a plethora of algorithms that have enjoyed wide scale usage. Existing algorithms are primarily focused on detection, that is the identification of outliers in a given dataset. In this…
Heterogeneous data pose serious challenges to data analysis tasks, including exploration and visualization. Current techniques often utilize dimensionality reductions, aggregation, or conversion to numerical values to analyze heterogeneous…
Motivated by extending the functional stochastic calculus, to important functionals to which it does not apply, a notion of functional derivative along a curve is introduced. This new setting is developed by incorporating path-dependent…