A Standard Operating Procedure for Outlier Removal in Large-Sample
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A Review on Outlier/Anomaly Detection in Time Series Data
A review on outlier/anomaly detection in time series data ANE BLÁZQUEZ-GARCÍA and ANGEL CONDE, Ikerlan Technology Research Centre, Basque Research and Technology Alliance (BRTA), Spain USUE MORI, Intelligent Systems Group (ISG), Department of Computer Science and Artificial Intelligence, University of the Basque Country (UPV/EHU), Spain JOSE A. LOZANO, Intelligent Systems Group (ISG), Department of Computer Science and Artificial Intelligence, University of the Basque Country (UPV/EHU), Spain and Basque Center for Applied Mathematics (BCAM), Spain Recent advances in technology have brought major breakthroughs in data collection, enabling a large amount of data to be gathered over time and thus generating time series. Mining this data has become an important task for researchers and practitioners in the past few years, including the detection of outliers or anomalies that may represent errors or events of interest. This review aims to provide a structured and comprehensive state-of-the-art on outlier detection techniques in the context of time series. To this end, a taxonomy is presented based on the main aspects that characterize an outlier detection technique. Additional Key Words and Phrases: Outlier detection, anomaly detection, time series, data mining, taxonomy, software 1 INTRODUCTION Recent advances in technology allow us to collect a large amount of data over time in diverse research areas. Observations that have been recorded in an orderly fashion and which are correlated in time constitute a time series. Time series data mining aims to extract all meaningful knowledge from this data, and several mining tasks (e.g., classification, clustering, forecasting, and outlier detection) have been considered in the literature [Esling and Agon 2012; Fu 2011; Ratanamahatana et al. -
Mean, Median and Mode We Use Statistics Such As the Mean, Median and Mode to Obtain Information About a Population from Our Sample Set of Observed Values
INFORMATION AND DATA CLASS-6 SUB-MATHEMATICS The words Data and Information may look similar and many people use these words very frequently, But both have lots of differences between What is Data? Data is a raw and unorganized fact that required to be processed to make it meaningful. Data can be simple at the same time unorganized unless it is organized. Generally, data comprises facts, observations, perceptions numbers, characters, symbols, image, etc. Data is always interpreted, by a human or machine, to derive meaning. So, data is meaningless. Data contains numbers, statements, and characters in a raw form What is Information? Information is a set of data which is processed in a meaningful way according to the given requirement. Information is processed, structured, or presented in a given context to make it meaningful and useful. It is processed data which includes data that possess context, relevance, and purpose. It also involves manipulation of raw data Mean, Median and Mode We use statistics such as the mean, median and mode to obtain information about a population from our sample set of observed values. Mean The mean/Arithmetic mean or average of a set of data values is the sum of all of the data values divided by the number of data values. That is: Example 1 The marks of seven students in a mathematics test with a maximum possible mark of 20 are given below: 15 13 18 16 14 17 12 Find the mean of this set of data values. Solution: So, the mean mark is 15. Symbolically, we can set out the solution as follows: So, the mean mark is 15. -
Outlier Identification.Pdf
STATGRAPHICS – Rev. 7/6/2009 Outlier Identification Summary The Outlier Identification procedure is designed to help determine whether or not a sample of n numeric observations contains outliers. By “outlier”, we mean an observation that does not come from the same distribution as the rest of the sample. Both graphical methods and formal statistical tests are included. The procedure will also save a column back to the datasheet identifying the outliers in a form that can be used in the Select field on other data input dialog boxes. Sample StatFolio: outlier.sgp Sample Data: The file bodytemp.sgd file contains data describing the body temperature of a sample of n = 130 people. It was obtained from the Journal of Statistical Education Data Archive (www.amstat.org/publications/jse/jse_data_archive.html) and originally appeared in the Journal of the American Medical Association. The first 20 rows of the file are shown below. Temperature Gender Heart Rate 98.4 Male 84 98.4 Male 82 98.2 Female 65 97.8 Female 71 98 Male 78 97.9 Male 72 99 Female 79 98.5 Male 68 98.8 Female 64 98 Male 67 97.4 Male 78 98.8 Male 78 99.5 Male 75 98 Female 73 100.8 Female 77 97.1 Male 75 98 Male 71 98.7 Female 72 98.9 Male 80 99 Male 75 2009 by StatPoint Technologies, Inc. Outlier Identification - 1 STATGRAPHICS – Rev. 7/6/2009 Data Input The data to be analyzed consist of a single numeric column containing n = 2 or more observations. -
A Machine Learning Approach to Outlier Detection and Imputation of Missing Data1
Ninth IFC Conference on “Are post-crisis statistical initiatives completed?” Basel, 30-31 August 2018 A machine learning approach to outlier detection and imputation of missing data1 Nicola Benatti, European Central Bank 1 This paper was prepared for the meeting. The views expressed are those of the authors and do not necessarily reflect the views of the BIS, the IFC or the central banks and other institutions represented at the meeting. A machine learning approach to outlier detection and imputation of missing data Nicola Benatti In the era of ready-to-go analysis of high-dimensional datasets, data quality is essential for economists to guarantee robust results. Traditional techniques for outlier detection tend to exclude the tails of distributions and ignore the data generation processes of specific datasets. At the same time, multiple imputation of missing values is traditionally an iterative process based on linear estimations, implying the use of simplified data generation models. In this paper I propose the use of common machine learning algorithms (i.e. boosted trees, cross validation and cluster analysis) to determine the data generation models of a firm-level dataset in order to detect outliers and impute missing values. Keywords: machine learning, outlier detection, imputation, firm data JEL classification: C81, C55, C53, D22 Contents A machine learning approach to outlier detection and imputation of missing data ... 1 Introduction .............................................................................................................................................. -
Accelerating Raw Data Analysis with the ACCORDA Software and Hardware Architecture
Accelerating Raw Data Analysis with the ACCORDA Software and Hardware Architecture Yuanwei Fang Chen Zou Andrew A. Chien CS Department CS Department University of Chicago University of Chicago University of Chicago Argonne National Laboratory [email protected] [email protected] [email protected] ABSTRACT 1. INTRODUCTION The data science revolution and growing popularity of data Driven by a rapid increase in quantity, type, and number lakes make efficient processing of raw data increasingly impor- of sources of data, many data analytics approaches use the tant. To address this, we propose the ACCelerated Operators data lake model. Incoming data is pooled in large quantity { for Raw Data Analysis (ACCORDA) architecture. By ex- hence the name \lake" { and because of varied origin (e.g., tending the operator interface (subtype with encoding) and purchased from other providers, internal employee data, web employing a uniform runtime worker model, ACCORDA scraped, database dumps, etc.), it varies in size, encoding, integrates data transformation acceleration seamlessly, en- age, quality, etc. Additionally, it often lacks consistency or abling a new class of encoding optimizations and robust any common schema. Analytics applications pull data from high-performance raw data processing. Together, these key the lake as they see fit, digesting and processing it on-demand features preserve the software system architecture, empower- for a current analytics task. The applications of data lakes ing state-of-art heuristic optimizations to drive flexible data are vast, including machine learning, data mining, artificial encoding for performance. ACCORDA derives performance intelligence, ad-hoc query, and data visualization. Fast direct from its software architecture, but depends critically on the processing on raw data is critical for these applications. -
Effects of Outliers with an Outlier
• The mean is a good measure to use to describe data that are close in value. • The median more accurately describes data Effects of Outliers with an outlier. • The mode is a good measure to use when you have categorical data; for example, if each student records his or her favorite color, the color (a category) listed most often is the mode of the data. In the data set below, the value 12 is much less than Additional Example 2: Exploring the Effects of the other values in the set. An extreme value such as Outliers on Measures of Central Tendency this is called an outlier. The data shows Sara’s scores for the last 5 35, 38, 27, 12, 30, 41, 31, 35 math tests: 88, 90, 55, 94, and 89. Identify the outlier in the data set. Then determine how the outlier affects the mean, median, and x mode of the data. x x xx x x x 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 55, 88, 89, 90, 94 outlier 55 1 Additional Example 2 Continued Additional Example 2 Continued With the Outlier Without the Outlier 55, 88, 89, 90, 94 55, 88, 89, 90, 94 outlier 55 mean: median: mode: mean: median: mode: 55+88+89+90+94 = 416 55, 88, 89, 90, 94 88+89+90+94 = 361 88, 89,+ 90, 94 416 5 = 83.2 361 4 = 90.25 2 = 89.5 The mean is 83.2. The median is 89. There is no mode. -
How Significant Is a Boxplot Outlier?
Journal of Statistics Education, Volume 19, Number 2(2011) How Significant Is A Boxplot Outlier? Robert Dawson Saint Mary’s University Journal of Statistics Education Volume 19, Number 2(2011), www.amstat.org/publications/jse/v19n2/dawson.pdf Copyright © 2011 by Robert Dawson all rights reserved. This text may be freely shared among individuals, but it may not be republished in any medium without express written consent from the author and advance notification of the editor. Key Words: Boxplot; Outlier; Significance; Spreadsheet; Simulation. Abstract It is common to consider Tukey’s schematic (“full”) boxplot as an informal test for the existence of outliers. While the procedure is useful, it should be used with caution, as at least 30% of samples from a normally-distributed population of any size will be flagged as containing an outlier, while for small samples (N<10) even extreme outliers indicate little. This fact is most easily seen using a simulation, which ideally students should perform for themselves. The majority of students who learn about boxplots are not familiar with the tools (such as R) that upper-level students might use for such a simulation. This article shows how, with appropriate guidance, a class can use a spreadsheet such as Excel to explore this issue. 1. Introduction Exploratory data analysis suddenly got a lot cooler on February 4, 2009, when a boxplot was featured in Randall Munroe's popular Webcomic xkcd. 1 Journal of Statistics Education, Volume 19, Number 2(2011) Figure 1 “Boyfriend” (Feb. 4 2009, http://xkcd.com/539/) Used by permission of Randall Munroe But is Megan justified in claiming “statistical significance”? We shall explore this intriguing question using Microsoft Excel. -
Lecture 14 Testing for Kurtosis
9/8/2016 CHE384, From Data to Decisions: Measurement, Kurtosis Uncertainty, Analysis, and Modeling • For any distribution, the kurtosis (sometimes Lecture 14 called the excess kurtosis) is defined as Testing for Kurtosis 3 (old notation = ) • For a unimodal, symmetric distribution, Chris A. Mack – a positive kurtosis means “heavy tails” and a more Adjunct Associate Professor peaked center compared to a normal distribution – a negative kurtosis means “light tails” and a more spread center compared to a normal distribution http://www.lithoguru.com/scientist/statistics/ © Chris Mack, 2016Data to Decisions 1 © Chris Mack, 2016Data to Decisions 2 Kurtosis Examples One Impact of Excess Kurtosis • For the Student’s t • For a normal distribution, the sample distribution, the variance will have an expected value of s2, excess kurtosis is and a variance of 6 2 4 1 for DF > 4 ( for DF ≤ 4 the kurtosis is infinite) • For a distribution with excess kurtosis • For a uniform 2 1 1 distribution, 1 2 © Chris Mack, 2016Data to Decisions 3 © Chris Mack, 2016Data to Decisions 4 Sample Kurtosis Sample Kurtosis • For a sample of size n, the sample kurtosis is • An unbiased estimator of the sample excess 1 kurtosis is ∑ ̅ 1 3 3 1 6 1 2 3 ∑ ̅ Standard Error: • For large n, the sampling distribution of 1 24 2 1 approaches Normal with mean 0 and variance 2 1 of 24/n 3 5 • For small samples, this estimator is biased D. N. Joanes and C. A. Gill, “Comparing Measures of Sample Skewness and Kurtosis”, The Statistician, 47(1),183–189 (1998). -
Big Data and Open Data As Sustainability Tools a Working Paper Prepared by the Economic Commission for Latin America and the Caribbean
Big data and open data as sustainability tools A working paper prepared by the Economic Commission for Latin America and the Caribbean Supported by the Project Document Big data and open data as sustainability tools A working paper prepared by the Economic Commission for Latin America and the Caribbean Supported by the Economic Commission for Latin America and the Caribbean (ECLAC) This paper was prepared by Wilson Peres in the framework of a joint effort between the Division of Production, Productivity and Management and the Climate Change Unit of the Sustainable Development and Human Settlements Division of the Economic Commission for Latin America and the Caribbean (ECLAC). Some of the imput for this document was made possible by a contribution from the European Commission through the EUROCLIMA programme. The author is grateful for the comments of Valeria Jordán and Laura Palacios of the Division of Production, Productivity and Management of ECLAC on the first version of this paper. He also thanks the coordinators of the ECLAC-International Development Research Centre (IDRC)-W3C Brazil project on Open Data for Development in Latin America and the Caribbean (see [online] www.od4d.org): Elisa Calza (United Nations University-Maastricht Economic and Social Research Institute on Innovation and Technology (UNU-MERIT) PhD Fellow) and Vagner Diniz (manager of the World Wide Web Consortium (W3C) Brazil Office). The European Commission support for the production of this publication does not constitute endorsement of the contents, which reflect the views of the author only, and the Commission cannot be held responsible for any use which may be made of the information obtained herein. -
Have You Seen the Standard Deviation?
Nepalese Journal of Statistics, Vol. 3, 1-10 J. Sarkar & M. Rashid _________________________________________________________________ Have You Seen the Standard Deviation? Jyotirmoy Sarkar 1 and Mamunur Rashid 2* Submitted: 28 August 2018; Accepted: 19 March 2019 Published online: 16 September 2019 DOI: https://doi.org/10.3126/njs.v3i0.25574 ___________________________________________________________________________________________________________________________________ ABSTRACT Background: Sarkar and Rashid (2016a) introduced a geometric way to visualize the mean based on either the empirical cumulative distribution function of raw data, or the cumulative histogram of tabular data. Objective: Here, we extend the geometric method to visualize measures of spread such as the mean deviation, the root mean squared deviation and the standard deviation of similar data. Materials and Methods: We utilized elementary high school geometric method and the graph of a quadratic transformation. Results: We obtain concrete depictions of various measures of spread. Conclusion: We anticipate such visualizations will help readers understand, distinguish and remember these concepts. Keywords: Cumulative histogram, dot plot, empirical cumulative distribution function, histogram, mean, standard deviation. _______________________________________________________________________ Address correspondence to the author: Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, Indianapolis, IN 46202, USA, E-mail: [email protected] 1; -
A SYSTEMATIC REVIEW of OUTLIERS DETECTION TECHNIQUES in MEDICAL DATA Preliminary Study
A SYSTEMATIC REVIEW OF OUTLIERS DETECTION TECHNIQUES IN MEDICAL DATA Preliminary Study Juliano Gaspar1,2, Emanuel Catumbela1,2, Bernardo Marques1,2 and Alberto Freitas1,2 1Department of Biostatistics and Medical Informatics, Faculty of Medicine, University of Porto, Porto, Portugal 2CINTESIS - Center for Research in Health Technologies and Information Systems University of Porto, Porto, Portugal Keywords: Outliers detection, Data mining, Medical data. Abstract: Background: Patient medical records contain many entries relating to patient conditions, treatments and lab results. Generally involve multiple types of data and produces a large amount of information. These databases can provide important information for clinical decision and to support the management of the hospital. Medical databases have some specificities not often found in others non-medical databases. In this context, outlier detection techniques can be used to detect abnormal patterns in health records (for instance, problems in data quality) and this contributing to better data and better knowledge in the process of decision making. Aim: This systematic review intention to provide a better comprehension about the techniques used to detect outliers in healthcare data, for creates automatisms for those methods in the order to facilitate the access to information with quality in healthcare. Methods: The literature was systematically reviewed to identify articles mentioning outlier detection techniques or anomalies in medical data. Four distinct bibliographic databases were searched: Medline, ISI, IEEE and EBSCO. Results: From 4071 distinct papers selected, 80 were included after applying inclusion and exclusion criteria. According to the medical specialty 32% of the techniques are intended for oncology and 37% of them using patient data. -
Recommended Methods for Outlier Detection and Calculations Of
Recommended Methods for Outlier Detection and Calculations of Tolerance Intervals and Percentiles – Application to RMP data for Mercury-, PCBs-, and PAH-contaminated Sediments Final Report May 27th, 2011 Prepared for: Regional Monitoring Program for Water Quality in San Francisco Bay, Oakland CA Prepared by: Dr. Don L. Stevens, Jr. Principal Statistician Stevens Environmental Statistics, LLC 6200 W. Starr Road Wasilla, AK 99654 Introduction This report presents results of a review of existing methods for outlier detection and for calculation of percentiles and tolerance intervals. Based on the review, a simple method of outlier detection that could be applied annually as new data becomes available is recommended along with a recommendation for a method for calculating tolerance intervals for population percentiles. The recommended methods are applied to RMP probability data collected in the San Francisco Estuary from 2002 through 2009 for Hg, PCB, and PAH concentrations. Outlier detection There is a long history in statistics of attempts to identify outliers, which are in some sense data points that are unusually high or low . Barnett and Lewis (1994) define an outlier in a set of data as “an observation (or subset of observations) which appears to be inconsistent with the remainder of that set of data. This captures the intuitive notion, but does not provide a constructive pathway. Hawkins (1980) defined outliers as data points which are generated by a different distribution than the bulk observations. Hawkins definition suggests something like using a mixture distribution to separate the data into one or more distributions, or, if outliers are few relative to the number of data points, to fit the “bulk” distribution with a robust/resistant estimation procedure, and then determine which points do not conform to the bulk distribution.