Nothing
## ----echo = FALSE-------------------------------------------------------------
knitr::opts_chunk$set(
fig.width = 5 ,
fig.height = 3.5,
fig.align = 'center'
)
## -----------------------------------------------------------------------------
library("cellWise")
library("gridExtra") # has grid.arrange()
# Default options for DDC:
DDCpars = list(fracNA = 0.5, numDiscrete = 3, precScale = 1e-12,
cleanNAfirst = "automatic", tolProb = 0.99,
corrlim = 0.5, combinRule = "wmean",
returnBigXimp = FALSE, silent = FALSE,
nLocScale = 25000, fastDDC = FALSE,
standType = "1stepM", corrType = "gkwls",
transFun = "wrap", nbngbrs = 100)
# A small list giving the same results:
DDCpars = list(fastDDC = FALSE)
## -----------------------------------------------------------------------------
i = c(1,2,3,4,5,6,7,8,9)
name = c("aa","bb","cc","dd","ee","ff","gg","hh","ii")
logic = c(TRUE, FALSE, TRUE, FALSE, FALSE, TRUE, TRUE, TRUE, FALSE)
V1 = c(1.3,NaN,4.5,2.7,20.0,4.4,-2.1,1.1,-5)
V2 = c(2.3,NA,5,6,7,8,4,-10,0.5)
V3 = c(2,Inf,3,-4,5,6,7,-2,8)
Vna = c(1,-4,2,NaN,3,-Inf,NA,6,5)
Vdis = c(1,1,2,2,3,3,3,1,2)
V0s = c(1,1.5,2,2,2,2,2,3,2.5)
datafr = data.frame(i,name,logic,V1,V2,V3,Vna,Vdis,V0s)
datafr
DDCdatafr = DDC(datafr,DDCpars)
remX = DDCdatafr$remX; dim(remX)
cellMap(DDCdatafr$stdResid)
# Red cells have higher value than predicted, blue cells lower,
# white cells are missing values, all other cells are yellow.
## ----fig.height=6,fig.width=3-------------------------------------------------
set.seed(12345) # for reproducibility
n <- 50; d <- 20
A <- matrix(0.9, d, d); diag(A) = 1
round(A[1:10,1:10],1) # true covariance matrix
library(MASS) # only needed for the following line:
x <- mvrnorm(n, rep(0,d), A)
x[sample(1:(n * d), 50, FALSE)] <- NA
x[sample(1:(n * d), 50, FALSE)] <- 10
x[sample(1:(n * d), 50, FALSE)] <- -10
# When not specifying DDCpars in the call to DDC
# all defaults are used:
DDCx <- DDC(x)
cellMap(DDCx$stdResid)
# Red cells have higher value than predicted, blue cells lower,
# white cells are missing values, all other cells are yellow.
## -----------------------------------------------------------------------------
DDCx$DDCpars # These are the default options:
names(DDCx)
# We will now go through these outputs one by one:
DDCx$colInAnalysis # all columns X1,...,X20 remain:
DDCx$rowInAnalysis # all rows 1,...,50 remain:
DDCx$namesNotNumeric # no non-numeric columns:
DDCx$namesCaseNumber # no column was the case number:
DDCx$namesNAcol # no columns with too many NA's:
DDCx$namesNArow # no columns with too many NA's:
DDCx$namesDiscrete # no discrete columns:
DDCx$namesZeroScale # no columns with scale = 0:
dim(DDCx$remX) # remaining data matrix
round(DDCx$locX,2) # robust location estimates of all 20 columns:
round(DDCx$scaleX,2) # robust scale estimates of all 20 columns:
round(DDCx$Z[1:10,1:10],1)
# Robustly standardized dataset. Due to the high correlations,
# cells in the same row look similar (except for outlying cells).
DDCx$nbngbrs
# For each column the code looked for up to 19 non-self neighbors (highly correlated columns).
# It goes through all of them, unless fastDDC is set to TRUE.
DDCx$ngbrs[1:3,]
# Shows the neighbors, e.g. the nearest non-self neighbor of X1 is X11, then X2,...
round(DDCx$robcors[1:3,],2)
# Robust correlations with these neighbors. In each row the correlations
# are sorted by decreasing absolute value.
round(DDCx$robslopes[1:3,],2)
# For each column, the slope of each neighbor predicting it.
# For instance, X1 is predicted by its first neighbor with
# slope 0.97 and by its second neighbor with slope 0.81 .
round(DDCx$deshrinkage,2)
# For each column, the factor by which its prediction is multiplied.
## -----------------------------------------------------------------------------
round(DDCx$Xest[1:12,1:10],2) # the estimated cells of remX:
round(DDCx$stdResid[1:12,1:10],1)
# The standardized residuals of the cells. Note the NA's and some
# large positive and negative cell residuals.
qqnorm(as.vector(DDCx$stdResid)) # Note the far outliers on both sides:
as.vector(DDCx$indcells) # indices of the cells that were flagged by DDC:
plot(DDCx$Ti) # the Ti values of the rows. None are high.
qqnorm(DDCx$Ti)
DDCx$medTi # median of the raw Ti (used to standardize Ti):
DDCx$madTi # median absolute deviation of the raw Ti (used to standardize Ti):
DDCx$indrows # numeric(0) means no rows are flagged:
as.vector(DDCx$indall) # indices of the flagged cells, including those in flagged rows:
as.vector(DDCx$indNAs) # indices of the missing cells:
round(DDCx$Ximp[1:10,1:10],2)
# The imputed matrix. Both the cellwise outliers and the missing values
# are replaced by their predicted values.
round((DDCx$Ximp - DDCx$remX)[1:10,1:10],2)
# The nonzero values and the NA's correspond to imputed cells.
## ----results='hide',message=FALSE,warning=FALSE-------------------------------
library(robustHD)
data(TopGear)
## -----------------------------------------------------------------------------
dim(TopGear)
rownames(TopGear)[1:13] # "1" to "297" are not useful names
rownames(TopGear) = paste(TopGear[,1],TopGear[,2])
# Now the rownames are make and model of the cars.
rownames(TopGear)[165] = "Mercedes-Benz G" # name was too long
myTopGear = TopGear[,-31] # removes the subjective variable `Verdict'
# Transform some variables to get roughly gaussianity in the center:
transTG = myTopGear
transTG$Price = log(myTopGear$Price)
transTG$Displacement = log(myTopGear$Displacement)
transTG$BHP = log(myTopGear$BHP)
transTG$Torque = log(myTopGear$Torque)
transTG$TopSpeed = log(myTopGear$TopSpeed)
# Run the DDC method:
DDCpars = list(fastDDC = FALSE, silent = TRUE)
DDCtransTG = DDC(transTG,DDCpars)
# With DDCpars = list(fastDDC = FALSE, silent = FALSE) we obtain more information:
#
# The input data has 297 rows and 31 columns.
#
# The input data contained 19 non-numeric columns (variables).
# Their column names are:
#
# [1] Maker Model Type Fuel
# [5] DriveWheel AdaptiveHeadlights AdjustableSteering AlarmSystem
# [9] Automatic Bluetooth ClimateControl CruiseControl
# [13] ElectricSeats Leather ParkingSensors PowerSteering
# [17] SatNav ESP Origin
#
# These columns will be ignored in the analysis.
# We continue with the remaining 12 numeric columns:
#
# [1] Price Cylinders Displacement BHP Torque Acceleration TopSpeed
# [8] MPG Weight Length Width Height
#
# The data contained 1 rows with over 50% of NAs.
# Their row names are:
#
# [1] Citroen C5 Tourer
#
# These rows will be ignored in the analysis.
# We continue with the remaining 296 rows:
#
# [1] Alfa Romeo Giulietta Alfa Romeo MiTo
# .......
# [295] Volvo XC70 Volvo XC90
#
# The data contained 1 columns with zero or tiny median absolute deviation.
# Their column names are:
#
# [1] Cylinders
#
# These columns will be ignored in the analysis.
# We continue with the remaining 11 columns:
#
# [1] Price Displacement BHP Torque Acceleration TopSpeed MPG
# [8] Weight Length Width Height
#
# The final data set we will analyze has 296 rows and 11 columns.
## ----fig.height=8,fig.width=6-------------------------------------------------
remX = DDCtransTG$remX # the remaining part of the dataset
dim(remX)
colSums(is.na(remX)) # There are still NAs, mainly in `Weight':
# Analyze the data by column:
standX = scale(remX,apply(remX,2,median,na.rm = TRUE),
apply(remX,2,mad,na.rm = TRUE))
dim(standX)
round(standX[1:5,],1) # has NAs where remX does
transTGcol = remX
transTGcol[abs(standX) > sqrt(qchisq(0.99,1))] = NA
round(transTGcol[1:5,],1) # has NAs in outlying cells as well:
# Make untransformed submatrix of X for labeling the cells in the plot:
tempX = myTopGear[DDCtransTG$rowInAnalysis,DDCtransTG$colInAnalysis]
tempX$Price = tempX$Price/1000 # to avoid printing long numbers
dim(tempX)
# Show the following 17 cars in the cellmap:
showrows = c(12,42,56,73,81,94,99,135,150,164,176,198,209,215,234,241,277)
# Make two ggplot2 objects:
ggpcol = cellMap(standX, showcellvalues="D", D=tempX,
mTitle="By column", showrows=showrows,
sizecellvalues = 0.6, adjustrowlabels=0.5)
plot(ggpcol)
## ----fig.height=10,fig.width=8------------------------------------------------
ggpDDC = cellMap(DDCtransTG$stdResid, showcellvalues="D", D=tempX,
mTitle="DetectDeviatingCells", showrows=showrows,
sizecellvalues = 0.6, adjustrowlabels=0.5)
plot(ggpDDC)
# Creating the pdf:
# pdf("cellMap_TopGear.pdf", width = 12, height = 10)
# gridExtra::grid.arrange(ggpcol,ggpDDC,nrow=1) # combines 2 plots in a figure
# dev.off()
## ----fig.height=8,fig.width=6-------------------------------------------------
# Top Gear dataset: prediction of "new" data
############################################
# For comparison we first remake the cell map of the entire dataset, but now
# showing the values of the residuals instead of the data values:
dim(remX) # 296 11
ggpDDC = cellMap(DDCtransTG$stdResid, showcellvalues="R",
sizecellvalues = 0.7, mTitle="DetectDeviatingCells",
showrows=showrows, adjustrowlabels=0.5)
plot(ggpDDC)
## -----------------------------------------------------------------------------
initX = remX[-showrows,]
dim(initX) # 279 11
# Fit initX:
DDCinitX = DDC(initX,DDCpars=DDCpars)
## -----------------------------------------------------------------------------
newX = remX[showrows,]
dim(newX) # 17 11
# Make predictions by DDCpredict.
# Its inputs are:
# Xnew : the new data (test data)
# InitialDDC : Must be provided.
# DDCpars : the input options to be used for the prediction.
# By default the options of InitialDDC are used.
predictDDC = DDCpredict(newX,DDCinitX)
names(DDCinitX)
# For comparison with:
names(predictDDC) # Fewer, since DDCpredict does not call checkDataSet:
# If you specify the parameters the result is the same:
predictDDC2 = DDCpredict(newX,DDCinitX,DDCpars=DDCpars)
all.equal(predictDDC,predictDDC2) # TRUE
## ----fig.height=10,fig.width=8------------------------------------------------
ggpnew = cellMap(predictDDC$stdResid, showcellvalues="R",
sizecellvalues = 0.7, mTitle="DDCpredict",
adjustrowlabels=0.5)
plot(ggpnew) # Looks quite similar to the result using the entire dataset:
# Creating the pdf:
# pdf("TopGear_DDCpredict.pdf",width=12,height=10)
# gridExtra::grid.arrange(ggpDDC,ggpnew,nrow=1)
# dev.off()
## -----------------------------------------------------------------------------
data(data_philips)
dim(data_philips)
colnames(data_philips) = c("X1","X2","X3","X4","X5","X6","X7","X8","X9")
DDCphilips = DDC(data_philips)
qqnorm(as.vector(DDCphilips$Z)) # rather gaussian, here we only see 2 outliers:
round(DDCphilips$stdResid[1:12,],1) # the standardized residuals:
DDCphilips$indcells # indices of the cells that were flagged:
DDCphilips$indrows # flagged rows:
## ----results='hide',message=FALSE,warning=FALSE-------------------------------
library(robustbase) # for covMcd
## ----fig.height=4,fig.width=8-------------------------------------------------
MCDphilips = robustbase::covMcd(data_philips)
indrowsMCD = which(mahalanobis(data_philips,MCDphilips$center,
MCDphilips$cov) > qchisq(0.975,df=9))
plot(sqrt(mahalanobis(data_philips,MCDphilips$center,MCDphilips$cov)),
main="Philips data",ylab="Robust distances",xlab="",pch=20)
abline(h=sqrt(qchisq(0.975,df=9))) # this horizontal line is the cutoff.
# dev.copy(pdf,"Figure_philips_left.pdf",width=10,height=4)
# dev.off()
## ----fig.height=8,fig.width=6-------------------------------------------------
# cellMaps with rectangular blocks:
ggpMCDphilips = cellMap(data_philips, indrows=indrowsMCD,
mTitle="MCD", nrowsinblock=15,
ncolumnsinblock=1, drawCircles = TRUE)
plot(ggpMCDphilips)
ggpDDCphilips = cellMap(DDCphilips$stdResid, indrows=DDCphilips$indrows,
mTitle="DetectDeviatingCells", nrowsinblock=15,
ncolumnsinblock=1, drawCircles = TRUE)
plot(ggpDDCphilips)
# dev.copy(pdf,"Figure_philips_right.pdf",width=6,height=12)
# dev.off()
## -----------------------------------------------------------------------------
data(data_mortality)
dim(data_mortality)
# 198 91
rownames(data_mortality)[1:5]
colnames(data_mortality)[1:5]
DDCpars = list(fastDDC = FALSE, silent = TRUE)
DDCmortality = DDC(data_mortality,DDCpars) # 1 second
remX = DDCmortality$remX
dim(remX)
## ----results='hide',message=FALSE,warning=FALSE-------------------------------
library(rrcov) # contains ROBPCA
## ----fig.height=8,fig.width=6-------------------------------------------------
PCAmortality = rrcov::PcaHubert(data_mortality,alpha=0.75,scale=FALSE)
ggpROBPCA = cellMap(remX, indrows=which(PCAmortality@flag==FALSE),
mTitle="By row", nrowsinblock=5,
ncolumnsinblock=5, rowtitle = "Years",
columntitle = "Age", sizetitles = 1.5,
drawCircles = TRUE)
plot(ggpROBPCA)
ggpDDC = cellMap(DDCmortality$stdResid,
mTitle="DetectDeviatingCells", nrowsinblock=5,
ncolumnsinblock=5, rowtitle = "Years",
columntitle = "Age", sizetitles = 1.5)
plot(ggpDDC) # Leads to a detailed interpretation:
# pdf("cellmap_mortality.pdf",width=9,height=8)
# gridExtra::grid.arrange(ggpROBPCA,ggpDDC,nrow=1)
# dev.off()
## ----fig.height=8,fig.width=6-------------------------------------------------
rowblocksizes = c(84,14,5,21,6,35,33)
rowlabels = c("19th century","1900-1913","WW1","1919-1939",
"WW2","1946-1980","recent")
colblocksizes = c(5,5,10,10,10,10,10,10,10,10,1)
collabels = c("upto 4","5 to 9","10 to 19","20 to 29","30 to 39","40 to 49","50 to 59","60 to 69","70 to 79","80 to 89","90+")
ggpDDC = cellMap(DDCmortality$stdResid,
mTitle = "Cellmap with manual blocks",
manualrowblocksizes = rowblocksizes,
rowblocklabels = rowlabels,
manualcolumnblocksizes = colblocksizes,
columnblocklabels = collabels,
rowtitle = "Epochs",
columntitle = "Age groups",
sizetitles = 1.2)
# pdf("cellmap_mortality_manual_blocks.pdf",width=5,height=3)
plot(ggpDDC)
# dev.off()
## -----------------------------------------------------------------------------
data(data_glass)
DDCpars = list(fastDDC = FALSE, silent = TRUE)
DDCglass = DDC(data_glass,DDCpars) # takes 8 seconds
remX = DDCglass$remX
# With DDCpars$silent = FALSE we obtain more information:
#
# The input data has 180 rows and 750 columns.
#
# The data contained 11 discrete columns with 3 or fewer values.
# Their column names are:
#
# [1] V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11
#
# These columns will be ignored in the analysis.
# We continue with the remaining 739 columns:
#
# [1] V12 V13 V14 V15 V16 V17 V18 V19 V20 V21 V22 V23 V24 V25
# ......
# [729] V740 V741 V742 V743 V744 V745 V746 V747 V748 V749 V750
#
# The data contained 2 columns with zero or tiny median absolute deviation.
# Their column names are:
#
# [1] V12 V13
#
# These columns will be ignored in the analysis.
# We continue with the remaining 737 columns:
#
# [1] V14 V15 V16 V17 V18 V19 V20 V21 V22 V23 V24 V25 V26 V27
# ......
# [729] V742 V743 V744 V745 V746 V747 V748 V749 V750
#
# The final data set we will analyze has 180 rows and 737 columns.
dim(remX)
## -----------------------------------------------------------------------------
fastDDCpars = list(fastDDC = TRUE, silent = TRUE)
fastDDCglass = DDC(data_glass, fastDDCpars) # takes 2 seconds
remXfast = fastDDCglass$remX
all.equal(remX,remXfast) # The remaining data is the same:
## ----results='hide',message=FALSE,warning=FALSE-------------------------------
library(rrcov) # contains ROBPCA
## ----fig.height=4,fig.width=8-------------------------------------------------
PCAglass = rrcov::PcaHubert(remX,alpha=0.75,scale=FALSE)
n = nrow(remX)
nrowsinblock = 5
rowtitle = "glass samples"
rowlabels = rep("",floor(n/nrowsinblock));
rowlabels[1] = "1"
rowlabels[floor(n/nrowsinblock)] = "n";
d = ncol(remX)
ncolumnsinblock = 5
columntitle = "wavelengths"
columnlabels = rep("",floor(d/ncolumnsinblock));
columnlabels[1] = "1";
columnlabels[floor(d/ncolumnsinblock)] = "d"
ggpROBPCA = cellMap(matrix(0,n,d),
indrows=which(PCAglass@flag==FALSE),
rowblocklabels=rowlabels,
columnblocklabels=columnlabels,
mTitle="By row", nrowsinblock=5,
ncolumnsinblock=5,
rowtitle="glass samples",
columntitle="wavelengths",
sizetitles=1.2,
columnangle=0,
drawCircles = TRUE)
plot(ggpROBPCA)
ggpDDC = cellMap(DDCglass$stdResid,
indrows=DDCglass$indrows,
rowblocklabels=rowlabels,
columnblocklabels=columnlabels,
mTitle="DDC", nrowsinblock=5,
ncolumnsinblock=5,
rowtitle="glass samples",
columntitle="wavelengths",
sizetitles=1.2,
columnangle=0,
drawCircles = TRUE)
plot(ggpDDC)
# pdf("cellmap_glass_ROBPCA_DDC.pdf",width=8,height=6)
# gridExtra::grid.arrange(ggpROBPCA,ggpDDC,ncol=1)
# dev.off()
ggpfastDDC = cellMap(fastDDCglass$stdResid,
indrows=fastDDCglass$indrows,
rowblocklabels=rowlabels,
columnblocklabels=columnlabels,
mTitle="fastDDC", nrowsinblock=5,
ncolumnsinblock=5,
rowtitle="glass samples",
columntitle="wavelengths",
sizetitles=1.2,
columnangle=0,
drawCircles = TRUE)
plot(ggpfastDDC)
# pdf("cellmap_glass_DDC_fastDDC.pdf",width=8,height=6)
# gridExtra::grid.arrange(ggpDDC,ggpfastDDC,ncol=1)
# dev.off()
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