Data pre-processing for k- means clustering
Customer Segmentation in Python. Data Symmetric distribution of variables (not skewed) ... Logarithmic transformation (positive values only).
chapter
Data Analysis Toolkit #3: Tools for Transforming Data Page 1
data are right-skewed (clustered at lower values) move down the ladder of powers (that is try square root
Toolkit
Transformations for Left Skewed Data
skewed Beta data to normality: reflect then logarithm with base 10 transformation reflect then square root transformation
WCE pp
Linear Regression Models with Logarithmic Transformations
17 mars 2011 distribution defined as a distribution whose logarithm is normally distributed – but whose untrans- formed scale is skewed.).
logmodels
Access Free Outlier Detection Method In Linear Regression Based
il y a 2 jours Anomaly Detection With Time Series Data: How to Know if. Something is Terribly Wrong Log Transformation for Outliers
LambertW: Probabilistic Models to Analyze and Gaussianize Heavy
The transformed RV Y has a Lambert W x F distribution. This package contains functions to model and analyze skewed heavy-tailed data the Lambert Way:.
LambertW
Download Ebook Outlier Detection Method In Linear Regression
il y a 24 heures IQR is first to transform raw data into Z-s- ... Wrong Log Transformation for Outliers
Modelling skewed data with many zeros: A simple approach
elling the log-abundance data using ordinary regression. use a general linear model in conjunction with a ln(y+c) transformation
Fletcher et al
Too many zeros and/or highly skewed? A tutorial on modelling
22 juin 2020 strategies for this data involve explicit (or implied) transformations. (smoker v. non-smoker log transformations). However
Introduction to Non-Gaussian Random Fields: a Journey Beyond
Skew-Normal Random Fields. Introduction to Non-Gaussian Random Fields: Transformed Multigaussian Random Fields ... Compute log-data Yi = ln Zi i ∈ I.
AllardToledo
Copyright © 1995, 2001 Prof. James Kirchner
Reasons to transform data
-to more closely approximate a theoretical distribution that has nice statistical properties -to spread data out more evenly -to make data distributions more symmetrical -to make relationships between variables more linear -to make data more constant in variance (homoscedastic)Ladder of powers
A useful organizing concept for data transformations is the ladder of powers (P.F. Velleman and D.C.Hoaglin, Applications, Basics, and Computing of Exploratory Data Analysis, 354 pp., Duxbury Press, 1981).
Data transformations are commonly power transformations, x'=xθ (where x' is the transformed x). One can visualize these as a continuous series of transformations:θ transformation
3 x 3 cube 2 x 2 square 1 x 1 identity (no transformation)1/2 x0.5
square root 1/3 x 1/3 cube root0 log(x) logarithmic (holds the place of zero)
-1/2 -1/x 0.5 reciprocal root -1 -1/x reciprocal -2 -1/x2 reciprocal squareNote: -higher and lower powers can be used
-fractional powers (other than those shown) can be used -minus sign in reciprocal transformations can (optionally) be used to preserve the order (relative ranking) of the data, which would otherwise be inverted by transformations for θ<0.To use the ladder of powers, visualize the original, untransformed data as starting at θ=1. Then if the
data are right-skewed (clustered at lower values) move down the ladder of powers (that is, try square root,
cube root, logarithmic, etc. transformations). If the data are left-skewed (clustered at higher values) move
up the ladder of powers (cube, square, etc).Special transformations
x'=log(x+1) -often used for transforming data that ar e right-skewed, but also include zero values. -note that the shape of the resulting distribution will depend on how big x is compared to the constant 1. Therefore the shape of the resulting distribution depends on the units in which x was measured. One way to deal with this problem is to use x'=log(x/mean(x)+k), where k is a small constant (k <<1). In this transformation, the mean x will be transformed to near x'=0 and k will function as a shape factor (small k will make x' more left-skewed, larger k will make it less so). But most importantly, changing the units of measure will not change the shape of the distribution. Data Analysis Toolkit #3: Tools for Transforming Data Page 2Copyright © 1995, 2001 Prof. James Kirchner
50.xx+=′ -sometimes used where data are taken from a Poisson distribution (for example,
counts of random events that occur in a fixed time period), or used for right- skewed data that include some x values that are very small or zero. As above, the resulting distribution of x' depends on the units used to measure x.xarcsinx=′ -used for data that are proportions (for example, fraction of eggs in a clutch that fail to
hatch); converts the binomial distribution that often characterizes such data into an approximate normal distribution.Important note
-in general, parameters (means, standard deviations, regression slopes, etc.) that are calculated on the transformed data and then are transformed back to the original units, will not equal the same parameters calculated on the original, untransformed data. Symmetry plots (a precise visual tool for displaying departures from symmetry)How to: -sort the data set x
i , i=1..n into ascending order, and find the median -for each pair of points surrounding the median (which will be the the points x i and x (n+1-i) , plot: -on the horizontal axis, the distance x median -x i -on the vertical axis, the distance x (n+1-i) -x median -if the points lie consistently above the 1:1 line, then the data are right-skewed. -if the points lie consistently below the 1:1 line, then the data are left-skewed. -if the points lie close to the 1:1 line, then x median -x i ≈ x (n+1-i) -x median and the distribution is approximately symmetrical. Reference: Chambers, J. M., W. S. Cleveland, B. Kleiner and P. A. Tukey, Graphical Methods forData Anal
ysis, 395 pp., Wadsworth & Brooks/Cole Publishing Co., 1983. Data Analysis Toolkit #3: Tools for Transforming Data Page 1Copyright © 1995, 2001 Prof. James Kirchner
Reasons to transform data
-to more closely approximate a theoretical distribution that has nice statistical properties -to spread data out more evenly -to make data distributions more symmetrical -to make relationships between variables more linear -to make data more constant in variance (homoscedastic)Ladder of powers
A useful organizing concept for data transformations is the ladder of powers (P.F. Velleman and D.C.Hoaglin, Applications, Basics, and Computing of Exploratory Data Analysis, 354 pp., Duxbury Press, 1981).
Data transformations are commonly power transformations, x'=xθ (where x' is the transformed x). One can visualize these as a continuous series of transformations:θ transformation
3 x 3 cube 2 x 2 square 1 x 1 identity (no transformation)1/2 x0.5
square root 1/3 x 1/3 cube root0 log(x) logarithmic (holds the place of zero)
-1/2 -1/x 0.5 reciprocal root -1 -1/x reciprocal -2 -1/x2 reciprocal squareNote: -higher and lower powers can be used
-fractional powers (other than those shown) can be used -minus sign in reciprocal transformations can (optionally) be used to preserve the order (relative ranking) of the data, which would otherwise be inverted by transformations for θ<0.To use the ladder of powers, visualize the original, untransformed data as starting at θ=1. Then if the
data are right-skewed (clustered at lower values) move down the ladder of powers (that is, try square root,
cube root, logarithmic, etc. transformations). If the data are left-skewed (clustered at higher values) move
up the ladder of powers (cube, square, etc).Special transformations
x'=log(x+1) -often used for transforming data that ar e right-skewed, but also include zero values. -note that the shape of the resulting distribution will depend on how big x is compared to the constant 1. Therefore the shape of the resulting distribution depends on the units in which x was measured. One way to deal with this problem is to use x'=log(x/mean(x)+k), where k is a small constant (k <<1). In this transformation, the mean x will be transformed to near x'=0 and k will function as a shape factor (small k will make x' more left-skewed, larger k will make it less so). But most importantly, changing the units of measure will not change the shape of the distribution. Data Analysis Toolkit #3: Tools for Transforming Data Page 2Copyright © 1995, 2001 Prof. James Kirchner
50.xx+=′ -sometimes used where data are taken from a Poisson distribution (for example,
counts of random events that occur in a fixed time period), or used for right- skewed data that include some x values that are very small or zero. As above, the resulting distribution of x' depends on the units used to measure x.xarcsinx=′ -used for data that are proportions (for example, fraction of eggs in a clutch that fail to
hatch); converts the binomial distribution that often characterizes such data into an approximate normal distribution.