Sparse signal shrinkage and outlier detection in high-dimensional quantile regression with variational Bayes

2020 ◽  
Vol 13 (2) ◽  
pp. 237-249 ◽  
Author(s):  
Daeyoung Lim ◽  
Beomjo Park ◽  
David Nott ◽  
Xueou Wang ◽  
Taeryon Choi
Keyword(s):  
Quantile Regression ◽  
Outlier Detection ◽  
Variational Bayes ◽  
High Dimensional ◽  
Sparse Signal

Subspace rotations for high-dimensional outlier detection

2020 ◽  
pp. 104713
Author(s):  
Hee Cheol Chung ◽  
Jeongyoun Ahn
Keyword(s):  
Outlier Detection ◽  
High Dimensional

Development for modification of Torgerson projection method using cumulative curve analysis in outlier detection problem for high-dimensional data

2020 ◽  
pp. 119-129
Author(s):  
Никита Сергеевич Олейник ◽  
Владислав Юрьевич Щеколдин
Keyword(s):  
Multidimensional Scaling ◽  
Outlier Detection ◽  
High Dimensional Data ◽  
Quality Data ◽  
Multidimensional Data ◽  
High Dimensional ◽  
Detection Problem ◽  
Gravity Center ◽  
Largest Eigenvalues ◽  
Cumulative Curves

Рассмотрена задача выявления аномальных наблюдений в данных больших размерностей на основе метода многомерного шкалирования с учетом возможности построения качественной визуализации данных. Предложен алгоритм модифицированного метода главных проекций Торгерсона, основанный на построении подпространства проектирования исходных данных путем изменения способа факторизации матрицы скалярных произведений при помощи метода анализа кумулятивных кривых. Построено и проанализировано эмпирическое распределение F -меры для разных вариантов проектирования исходных данных Purpose. Purpose of the article. The paper aims at the development of methods for multidimensional data presentation for solving classification problems based on the cumulative curves analysis. The paper considers the outlier detection problem for high-dimensional data based on the multidimensional scaling, in order to construct high-quality data visualization. An abnormal observation (or outlier), according to D. Hawkins, is an observation that is so different from others that it may be assumed as appeared in the sample in a fundamentally different way. Methods. One of the conceptual approaches that allow providing the classification of sample observations is multidimensional scaling, representing by the classical Orlochi method, the Torgerson main projections and others. The Torgerson method assumes that when converting data to construct the most convenient classification, the origin must be placed at the gravity center of the analyzed data, after which the matrix of scalar products of vectors with the origin at the gravity center is calculated, the two largest eigenvalues and corresponding eigenvectors are chosen and projection matrix is evaluated. Moreover, the method assumes the linear partitioning of regular and anomalous observations, which arises rarely. Therefore, it is logical to choose among the possible axes for designing those that allow obtaining more effective results for solving the problem of detecting outlier observations. A procedure of modified CC-ABOD (Cumulative Curves for Angle Based Outlier Detection) to estimate the visualization quality has been applied. It is based on the estimation of the variances of angles assumed by particular observation and remaining observations in multidimensional space. Further the cumulative curves analysis is implemented, which allows partitioning out groups of closely localized observations (in accordance with the chosen metric) and form classes of regular, intermediate, and anomalous observations. Results. A proposed modification of the Torgerson method is developed. The F1-measure distribution is constructed and analyzed for different design options in the source data. An analysis of the empirical distribution showed that in a number of cases the best axes are corresponding to the second, third, or even fourth largest eigenvalues. Findings. The multidimensional scaling methods for constructing visualizations of multi-dimensional data and solving problems of outlier detection have been considered. It was found out that the determination of design is an ambiguous problem.

scholarly journals A Novel Density-based Technique for Outlier Detection of High Dimensional Data Utilizing Full Feature Space

2021 ◽  
Vol 50 (1) ◽  
pp. 138-152
Author(s):  
Mujeeb Ur Rehman ◽  
Dost Muhammad Khan
Keyword(s):  
Data Mining ◽  
Outlier Detection ◽  
High Dimensional Data ◽  
Research Work ◽  
Feature Space ◽  
High Dimensional ◽  
Data Set ◽  
Data Points ◽  
Low Dimensional ◽  
Intrinsic Feature

Recently, anomaly detection has acquired a realistic response from data mining scientists as a graph of its reputation has increased smoothly in various practical domains like product marketing, fraud detection, medical diagnosis, fault detection and so many other fields. High dimensional data subjected to outlier detection poses exceptional challenges for data mining experts and it is because of natural problems of the curse of dimensionality and resemblance of distant and adjoining points. Traditional algorithms and techniques were experimented on full feature space regarding outlier detection. Customary methodologies concentrate largely on low dimensional data and hence show ineffectiveness while discovering anomalies in a data set comprised of a high number of dimensions. It becomes a very difficult and tiresome job to dig out anomalies present in high dimensional data set when all subsets of projections need to be explored. All data points in high dimensional data behave like similar observations because of its intrinsic feature i.e., the distance between observations approaches to zero as the number of dimensions extends towards infinity. This research work proposes a novel technique that explores deviation among all data points and embeds its findings inside well established density-based techniques. This is a state of art technique as it gives a new breadth of research towards resolving inherent problems of high dimensional data where outliers reside within clusters having different densities. A high dimensional dataset from UCI Machine Learning Repository is chosen to test the proposed technique and then its results are compared with that of density-based techniques to evaluate its efficiency.

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