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Pm_model_runs_NN_density.Rmd
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Pm_model_runs_NN_density.Rmd
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---
title: 'GoMx sperm whale habitat models: Density with neural nets'
author:
- name: Kaitlin Frasier
affiliation: Scripps Institution of Oceanography, UC San Diego
date: "`r format(Sys.time(), '%d %B %Y')`"
output:
html_document:
toc: true
toc_depth: 4
toc_float: true
theme: spacelab
fig_caption: true
bibliography: exportlist.bibtex
csl: plos-computational-biology.csl
---
```{r setup, echo = FALSE}
knitr::opts_chunk$set(echo = TRUE)
```
```{r load packages, echo = FALSE, message = FALSE, warning = FALSE}
library(rgdal)
library(raster)
library(ggplot2)
library(rgeos)
library(mapview)
library(leaflet)
library(psych)
library(broom)
library(plotrix)
library(magrittr)
library(colorRamps)
library(lubridate)
#library(HabitatProject)
library(nnet)
library(caret)
library(parallel)
library(MLmetrics)
library(pracma)
library(grid)
library(knitr)
library(matrixStats)
library(zoo)
library(tmap)
library(scales)
source('E:/NASData/AcoustoVisualDE/AcoustoVisualDE/HabitatProject/R/plot_covarDensity.R')
source('E:/NASData/AcoustoVisualDE/AcoustoVisualDE/HabitatProject/R/weighted_logloss.R')
source('E:/NASData/AcoustoVisualDE/AcoustoVisualDE/HabitatProject/R/multiplot.R')
source('E:/NASData/AcoustoVisualDE/AcoustoVisualDE/HabitatProject/R/plot_missingdata.R')
source('E:/NASData/AcoustoVisualDE/AcoustoVisualDE/HabitatProject/R/plot_cleveland.R')
source('E:/NASData/AcoustoVisualDE/AcoustoVisualDE/HabitatProject/R/plot_timeseries.R')
source('E:/NASData/AcoustoVisualDE/AcoustoVisualDE/HabitatProject/R/transform_covars.R')
source('E:/NASData/AcoustoVisualDE/AcoustoVisualDE/nnet_plot_update.r')
options(stringsAsFactors = FALSE)
# load some preferences
load('E:/NASData/ModelData/Pm/setup_info_Pm.Rdata')
load('E:/NASData/ModelData/Pm/PmMergedData.Rdata')
outDir <- file.path('E:/NASData/ModelData',SP,'log//')
inDir <- file.path('E:/NASData/ModelData',SP,'//')
```
<br>
# 1. Exploratory analysis
<br>
## 1.1 Data Inputs
NOAA SEFSC visual data goes back to 1992, but as shown in the figure below, many predictor variables are only available starting in 2003, therefore earlier visual data is currently excluded from further analyses.
Note: Future work could use monthly climatologies (averages) so that older sightings data could be used. Some dynamic drivers like eddy and front locations would not be able to be considered using that approach.
```{r Missing data, echo = FALSE}
plotCols1 <-c(7:10,14,16,19,22,23)
covarList<-names(mergedSegments[c(plotCols1)])
varUnits <- c("SST (C)","SSH (m)",expression("Chlorophyll A (mg/m"^3*")"),"MLD (m)", "Salinity (ppm)",
"Current Magnitude (m/sec)", "Upwelling (m/sec)",
"Dist. to Anti-Cyclonic Eddy (km)","Dist. to Cyclonic Eddy (km)")
names(varUnits)<-covarList
percFilled <- plot.missingdata(mergedSegments,covarList,
paste0(outDir,'AcousticAndVisual_',SP),varUnits)
percFilled <- plot.missingdata(AcOnlySegments,covarList,
paste0(outDir,'AcousticOnly_',SP),varUnits)
percFilled <- plot.missingdata(VisOnlySegments,covarList,
paste0(outDir,'VisualOnly_',SP),varUnits)
visDataAvailPlot <- paste0(savePath,'/VisualOnly_',SP,'_missingData.png')
```
**Visual data predictor variable availability:**
<br>
### 1.1.1 Splitting into testing and training sets
The data are split into training and testing sets. In this case, visual data from 2009 and acoustic data from 2013 were used only for testing. Only observations from 2003 or later were used for modeling due to covariate limitations.
```{r test train split, echo = FALSE}
# If you decide from the missing data plots that you want to restrict years going forward:
yearListIdx = as.numeric(format(mergedSegments$date,"%Y"))
yearListIdx_AcOnly = as.numeric(format(AcOnlySegments$date,"%Y"))
yearListIdx_VisOnly = as.numeric(format(VisOnlySegments$date,"%Y"))
isVisual <- mergedSegments$Category
keepDates.train <- which(yearListIdx != 2009 &
yearListIdx >= 2003 &
yearListIdx != 2013)
keepDates.test <- which(yearListIdx == 2009 |
yearListIdx == 2013)
keepDates_AcOnly.train <- which(yearListIdx_AcOnly != 2009 &
yearListIdx_AcOnly >= 2003 & yearListIdx_AcOnly <= 2012)
keepDates_AcOnly.test <- which(yearListIdx_AcOnly == 2009 |
yearListIdx_AcOnly == 2013)
keepDatesVisOnly.train <- which(yearListIdx_VisOnly != 2009 &
yearListIdx_VisOnly >= 2003)
keepDatesVisOnly.test <- which(yearListIdx_VisOnly == 2009 |
yearListIdx_VisOnly == 2013)
Train_Joint.set<- mergedSegments[keepDates.train,]
Train_AcOnly.set <- AcOnlySegments[keepDates_AcOnly.train,]
Train_VisOnly.set<- VisOnlySegments[keepDatesVisOnly.train,]
Test_Joint.set<- mergedSegments[keepDates.test,]
Test_AcOnly.set<- AcOnlySegments[keepDates_AcOnly.test,]
Test_VisOnly.set<- VisOnlySegments[keepDatesVisOnly.test,]
```
<br>
### 1.1.2 Map of visual sightings data
The visual data selected for modeling are displayed on the map below. Data from 2009 were held back for testing. Blue markers indicate HARP locations.
```{r map inputs, warning = FALSE, echo = FALSE}
# Get test visual sightings
sightingsTrain <- Train_VisOnly.set[Train_VisOnly.set$Density>0,c('lat','long','date')]
sightingsTest <- Test_VisOnly.set[Test_VisOnly.set$Density>0,c('lat','long','date')]
HARPsites <- unique(Train_AcOnly.set[c('lat','long')])
pal <-colorFactor(palette = "RdYlGn",
domain = c(2003,2004,2009,2012,2014))
map1 <- leaflet() %>% setView(lng = -89.4, lat = 27.0, zoom = 6)%>%
addProviderTiles(providers$Esri.OceanBasemap) %>%
addCircleMarkers(data = sightingsTrain, lng = ~ long, lat = ~ lat,color = ~pal(year(date)),
stroke = TRUE, fillOpacity = 0.8, group = 'Training Set',radius = 4)%>%
addCircleMarkers(data = sightingsTest, lng = ~ long, lat = ~ lat,color = ~pal(year(date)),
stroke = TRUE, fillOpacity = 0.8, group = 'Test Set',radius = 4)%>%
addMarkers(data = HARPsites, lng = ~ long, lat = ~ lat) %>%
addLegend(pal = pal,values = c(2003,2004,2009,2012,2014),title = 'Year')
map1
```
<br>
### 1.1.3 Time series of acoustic data
The time series below show timeseries of estimated densities from passive acoustic data used for modeling (Densities were calculated following methods detailed in @RN806). Data from 2011 and 2012 were used for training, and 2013 data was held back for testing.
<br>
**Acoustic Timeseries:**
```{r plot timeseries, message = FALSE, echo = FALSE}
plot.timeseries(siteList,outDir,AcOnlySegments)
MCTS <- paste0(outDir,SP,'_Timeseries_Site_MC.png')
GCTS <- paste0(outDir,SP,'_Timeseries_Site_GC.png')
DTTS <- paste0(outDir,SP,'_Timeseries_Site_DT.png')
```
<br>
## 1.2 Examination of covariates
```{r remove outliers, message = FALSE, results = 'hide', echo = FALSE}
### Identify Outliers
# Replace extreme outliers (bad data) with NaNs.
outlierList <-which(Train_Joint.set$CHL< -10)
Train_Joint.set$CHL[outlierList] <- NaN
#outlierList <-which(Train_Joint.set$FrontDist_Cayula>800000)
#Train_Joint.set$FrontDist_Cayula[outlierList] <- NaN
outlierList <-which(Train_Joint.set$Density>100000)
Train_Joint.set$Density[outlierList] <- NaN
outlierList <-which(Test_Joint.set$CHL< -10)
Test_Joint.set$CHL[outlierList] <- NaN
#outlierList <-which(Test_Joint.set$FrontDist_Cayula > 800000)
#Test_Joint.set$FrontDist_Cayula[outlierList] <- NaN
outlierList <-which(Test_Joint.set$Density>100000)
Test_Joint.set$Density[outlierList] <- NaN
outlierList <-which(Train_AcOnly.set$CHL< -10)
Train_AcOnly.set$CHL[outlierList] <- NaN
#outlierList <-which(Train_AcOnly.set$FrontDist_Cayula > 800000)
#Train_AcOnly.set$FrontDist_Cayula[outlierList] <- NaN
outlierList <-which(Train_AcOnly.set$Density > 100000)
Train_AcOnly.set$Density[outlierList] <- NaN
outlierList <-which(Test_AcOnly.set$CHL< -10)
Test_AcOnly.set$CHL[outlierList] <- NaN
#outlierList <-which(Test_AcOnly.set$FrontDist_Cayula>800000)
#Test_AcOnly.set$FrontDist_Cayula[outlierList] <- NaN
outlierList <-which(Test_AcOnly.set$Density>100000)
Test_AcOnly.set$Density[outlierList] <- NaN
outlierList <-which(Train_VisOnly.set$CHL< -10)
Train_VisOnly.set$CHL[outlierList] <- NaN
#outlierList <-which(Train_VisOnly.set$FrontDist_Cayula>800000)
#Train_VisOnly.set$FrontDist_Cayula[outlierList] <- NaN
outlierList <-which(Train_VisOnly.set$Density>100000)
Train_VisOnly.set$Density[outlierList] <- NaN
outlierList <-which(Test_VisOnly.set$CHL< -10)
Test_VisOnly.set$CHL[outlierList] <- NaN
#outlierList <-which(Test_VisOnly.set$FrontDist_Cayula>800000)
#Test_VisOnly.set$FrontDist_Cayula[outlierList] <- NaN
outlierList <-which(Test_VisOnly.set$Density>100000)
Test_VisOnly.set$Density[outlierList] <- NaN
```
<br>
### 1.2.1 Covariate distribution check
<br>
**Distributions of covariates from acoustic observations (training data only):**
```{r dot plots, eval = TRUE, message = FALSE, results = 'hide', echo = FALSE}
plot.cleveland(Train_AcOnly.set,covarList,FALSE,paste0(outDir,'AcousticOnly_',SP),varUnits)
plot.cleveland(Train_VisOnly.set,covarList,FALSE,paste0(outDir,'VisualOnly_',SP),varUnits)
plot.cleveland(Train_Joint.set,covarList,FALSE,paste0(outDir,'AcousticAndVisual_',SP),varUnits)
ACclevelandPlot<-paste0(outDir,'AcousticOnly_',
SP,'_clevelandDots_noTransform.png')
VisclevelandPlot<-paste0(outDir,'VisualOnly_',
SP,'_clevelandDots_noTransform.png')
```
<br>
**Distributions of covariates from the visual observations (training data only):**
<br>
Some of these covariates are more or less interrelated. Correlations are examined in the figure below. Numbers closer to 1 above the diagonal in the figure below represent correlation coefficients. If a pair of covariates is highly-correlated only one should typically be used in the model.
```{r correlation plots, eval = TRUE, message = FALSE, warning = FALSE, results = 'hide', echo = FALSE}
covarList2 <- c("Density","SST","SSH","CHL",
"HYCOM_MLD","HYCOM_SALIN_0","HYCOM_MAG_0",
"HYCOM_UPVEL_50",
"Neg_EddyDist","Pos_EddyDist",
"fac1","fac2","EffectiveArea")
# restrict covariates again to limited set
Train_Joint.set2<- Train_Joint.set[,covarList2]
Test_Joint.set2<- Test_Joint.set[,covarList2]
Train_AcOnly.set2<- Train_AcOnly.set[,covarList2]
Test_AcOnly.set2<- Test_AcOnly.set[,covarList2]
Train_VisOnly.set2<- Train_VisOnly.set[,covarList2]
Test_VisOnly.set2<- Test_VisOnly.set[,covarList2]
# without transform
png(paste(outDir,SP,'_correlations_noTransform.png',sep=''), width = 2000, height = 1600)
pairs.panels(Train_Joint.set2[,1:(length(covarList2)-3)], ellipses=FALSE, method = "spearman",cex.cor=.75)
dev.off()
png(paste(outDir,SP,'_correlations_noTransform_AcOnly.png',sep=''), width = 2000, height = 1600)
pairs.panels(Train_AcOnly.set2[,1:(length(covarList2)-3)], ellipses=FALSE, method = "spearman",cex.cor=.75)
dev.off()
png(paste(outDir,SP,'_correlations_noTransform_visOnly.png',sep=''), width = 2000, height = 1600)
pairs.panels(Train_VisOnly.set2[,1:(length(covarList2)-3)], ellipses=FALSE, method = "spearman",cex.cor=.75)
dev.off()
covarPlot <-paste0(outDir,SP,'_correlations_noTransform.png')
```
<br>
**Covariate Correlations:**
<br>
### 1.2.2 Transformation of predictor variables
Some variables, including chlorophyll, mixed layer depth and distance to fronts are highly skewed and were log-transformed for input to GAMs.
```{r transform covars, message = FALSE, results = 'hide', echo = FALSE, warning = FALSE}
# covarList2 <- c("Density","SST","SSH","CHL",
# "HYCOM_MLD","HYCOM_SALIN_0","HYCOM_MAG_0",
# "HYCOM_UPVEL_50",
# "Neg_EddyDist", "PosEddyDist",
# "fac1","fac2")
transformList <- c("none","none","none","log10",
"log10","none","log10",
"none",
"none","none",
"none","none","none")
transformedCovars.train <-
transform.covars(Train_Joint.set2,covarList2,transformList)
transformedCovars.test <-
transform.covars(Test_Joint.set2,covarList2,transformList)
transformedCovars_AcOnly.train <-
transform.covars(Train_AcOnly.set2,covarList2,transformList)
transformedCovars_AcOnly.test <-
transform.covars(Test_AcOnly.set2,covarList2,transformList)
transformedCovars_VisOnly.train <-
transform.covars(Train_VisOnly.set2,covarList2,transformList)
transformedCovars_VisOnly.test <-
transform.covars(Test_VisOnly.set2,covarList2,transformList)
# Generate correlation plots with transform
png(paste(outDir,SP,'_correlations_withTransform.png',sep=''), width = 2000, height = 1600)
pairs.panels(transformedCovars.train[,1:(length(covarList2)-2)],
ellipses=FALSE,
method = "spearman",cex.cor=.75)
dev.off()
png(paste(outDir,SP,'_correlations_withTransform_AcOnly.png',sep=''),
width = 2000, height = 1600)
pairs.panels(transformedCovars_AcOnly.train[,1:(length(covarList2)-2)],
ellipses=FALSE, method = "spearman",cex.cor=.75)
dev.off()
png(paste(outDir,SP,'_correlations_withTransform_visOnly.png',sep=''),
width = 2000, height = 1600)
pairs.panels(transformedCovars_VisOnly.train[,1:(length(covarList2)-2)],
ellipses=FALSE, method = "spearman",cex.cor=.75)
dev.off()
```
```{r transformed dot plots, eval = TRUE, message = FALSE, results = 'hide', echo = FALSE}
# Plotting the transformed variables:
plotCols = colnames(transformedCovars.train)[c(2:10)]
names(varUnits)<-plotCols
varUnits["log10_HYCOM_MAG_0"]<-expression("log"[10]*"(Current Magnitude (m/sec))")
varUnits["log10_HYCOM_MLD"]<- expression("log"[10]*"(MLD (m))")
varUnits["log10_CHL"] <-expression("log"[10]*"(Chorophyll A (mg/m"^3*"))")
plot.cleveland(transformedCovars.train,
plotCols,TRUE,paste0(outDir,'AcousticAndVisual_',SP),varUnits)
plot.cleveland(transformedCovars_AcOnly.train,
plotCols,TRUE,paste0(outDir,'AcousticOnly_',SP),varUnits)
plot.cleveland(transformedCovars_VisOnly.train,
plotCols,TRUE,paste0(outDir,'VisualOnly_',SP),varUnits)
clevlandJointTransformed<-paste0(outDir,'AcousticAndVisual_',
SP,'_clevelandDots_withTransform.png')
```
Below, the two sets of covariates have been combined and transformed:
<br>
### 1.2.3 Preliminary check of predictive power
To get an idea of the basic predictive power of these covariates, we can look at presence/absence relative to each variable. This also provides an opportunity to look at the range of values observed for each covariate in the visual and acoustic datasets. In the plots below dotted lines indicate the distribution of each covariate when `r SPLong` were present, and solid lines indicate the distribution when `r SPLong` were absent. Note that these plots do not account for effort.
```{r presence absence histograms, eval = TRUE, message = FALSE, results = 'hide', echo = FALSE}
plot.covarDensity(transformedCovars.train[,2:10],
colnames(transformedCovars.train[,2:10]),
transformedCovars.train$Density,paste0(outDir,'Both_',SP),varUnits)
plot.covarDensity(transformedCovars_AcOnly.train[,2:10],
colnames(transformedCovars_AcOnly.train[2:10]),
transformedCovars_AcOnly.train$Density,paste0(outDir,'AcousticOnly_',SP),varUnits)
plot.covarDensity(transformedCovars_VisOnly.train[,2:10],
colnames(transformedCovars_VisOnly.train[,2:10]),
transformedCovars_VisOnly.train$Density,paste0(outDir,'VisualOnly_',SP),varUnits)
acKernels <-paste0(savePath,'/AcousticOnly_',SP,'_density_pres_abs.png')
visKernels <- paste0(savePath,'/VisualOnly_',SP,'_density_pres_abs.png')
```
<br>
**Acoustic kernel densities:**
<br>
**Visual kernel densities:**
<br>
### 1.2.4 Estimation of relative weights
```{r load detection prob, echo = FALSE}
visDetProbData<-paste0(inDir,SP,'sightwTrunc_GU.Rdata')
load(visDetProbData)
visDetProb <- detFun[[bestModelIdx]]$fitted[1]
visDetProbFigure <- paste0(inDir,SP,'sightwTrunc_GU.png')
```
To train the model, we need to know how much power the various data points have relative to one another. This is important because the duration, spatial coverage, and detection probabilities are quite different between the visual and acoustic data sets. If an animal is seen or heard, we know for certain that the species was present. However, if it was not heard, then it either wasn't present, or it was present but missed.
"Zero inflation" or an excess of false zeros more common in the visual survey data because each data point represents a 10km transect section, traversed at survey speed (>10 knots) or approximately 30 minutes of observation effort. In contrast, the acoustic data are binned by day with a stationary instrument, therefore the probability of missing a group over the course of a day is lower.
For each data type, we estimated the probability of a missed detection to account for differences in zero-inflation, downweighting zeros according to the probability of a recording false negative.
The visual data represent wether or not `r SPLong` were seen during each transect segment. The probability of missing a sighting of `r SPLong` was estimated as
\[P_{V}(detect|present) = \mu_{det} * g0\ = `r round(visDetProb*100)/100` * `r round(visG0*100)/100` = `r round(visDetProb* visG0*100)/100`\]
where \mu_{det} is the mean detection probability as estimated by a model fit using the mrds package, and g0 is the probability of observing an animal on the transect line [@RN862]. We assume that reported absences are likely to be true absences `r round(visDetProb* visG0*100)` % of the time, therefore zeros are given a weight of `r round(visDetProb* visG0*100)/100` on a scale of [0,1].
The acoustic data represent presence or absence of `r SPLong` in one day bins. Given that a group of animals is present near the sensor, the probability of detecting them in a 5 minute period within a `r r_sp` km range is estimated at `r Ac_pDet`, therefore the probability of missing an encounter is 1 - `r Ac_pDet` = `r 1-Ac_pDet` [@RN806; @RN506]. Given that animals were present, the probability of missing a group for a full day (288 5-minute periods) is estimated as
\[P_{A}(detect|present) = (1-`r Ac_pDet`)^{288} \approx 1\]
Therefore we assume that there are no false negative days in the passive acoustic timeseries, and all acoustic observations are given weight = 1.
<br>
**Best visual detection probability model for `r SPLong`:**
<br>
# 2. Model Fitting
Models were fit using avnnet from the caret package in R.
```{r load starting data, echo = FALSE,message = FALSE, results = 'hide'}
pOccur <- read.csv(pOccurenceFile, header = TRUE,na.strings=c('',' ','NA','NaN'))
```
```{r model setup, echo = FALSE, message = FALSE, results = 'hide'}
# set up weighting
yAcOnly <- transformedCovars_AcOnly.train$Density
yVisOnly <- transformedCovars_VisOnly.train$Density
y <- transformedCovars.train$Density
visDetProb <- detFun[[bestModelIdx]]$fitted[1]
transformedCovars_AcOnly.train$yAcOnly<- transformedCovars_AcOnly.train$Density
transformedCovars_VisOnly.train$yVisOnly<-transformedCovars_VisOnly.train$Density
transformedCovars.train$y <- transformedCovars.train$Density
transformedCovars_AcOnly.train$yAcOnlySqrt <-sqrt(transformedCovars_AcOnly.train$Density)
transformedCovars_VisOnly.train$yVisOnlySqrt <-sqrt(transformedCovars_VisOnly.train$Density)
transformedCovars.train$ySqrt <-sqrt(transformedCovars.train$Density)
transformedCovars_AcOnly.test$yAcOnly <- transformedCovars_AcOnly.test$Density
transformedCovars_VisOnly.test$yVisOnly <- transformedCovars_VisOnly.test$Density
transformedCovars.test$y <- transformedCovars.test$Density
transformedCovars_AcOnly.test$yAcOnlySqrt <-sqrt(transformedCovars_AcOnly.test$Density)
transformedCovars_VisOnly.test$yVisOnlySqrt <-sqrt(transformedCovars_VisOnly.test$Density)
transformedCovars.test$ySqrt <-sqrt(transformedCovars.test$Density)
# make some factors and calculate introduce column of g0 weights
joint_train_weightsG0<- array(data = 1, dim = c(length(transformedCovars.train$fac1),1))
joint_test_weightsG0<- array(data = 1, dim = c(length(transformedCovars.test$fac1),1))
for (iFac in 1:length(transformedCovars.train$fac1)) {
if (!is.na(transformedCovars.train$fac1[iFac]) & !is.na(transformedCovars.train$Density[iFac])){
if (transformedCovars.train$fac1[iFac]>5) {
if (transformedCovars.train$Density[iFac]==0){
# if it's visual data and it's a zero, adjust by g0 ie, only a X% chance it was a true zero.
joint_train_weightsG0[iFac,1] <- visG0*visDetProb
}
}
}
}
maxEffectiveAreaJoint <- max(c(transformedCovars.train$EffectiveArea,
transformedCovars.test$EffectiveArea))
# do additional adjustment for effective area
joint_train_weightsG0 <- joint_train_weightsG0*
(transformedCovars.train$EffectiveArea/maxEffectiveAreaJoint)
for (iFac in 1:length(transformedCovars.test$fac1)) {
if (!is.na(transformedCovars.test$fac1[iFac]) & !is.na(transformedCovars.test$Density[iFac])){
if (transformedCovars.test$fac1[iFac]>5) {
if (transformedCovars.test$Density[iFac]==0){
# if it's visual data and it's a zero, adjust by g0 ie, only a X% chance it was a true zero.
joint_test_weightsG0[iFac,1] <- visG0*visDetProb
}
}
}
}
# do additional adjustment for effective area
joint_test_weightsG0 <- joint_test_weightsG0*
(transformedCovars.test$EffectiveArea/maxEffectiveAreaJoint)
VisOnly.train_weightsG0<- array(data = 1, dim = c(length(transformedCovars_VisOnly.train$fac1),1))
VisOnly.test_weightsG0<- array(data = 1, dim = c(length(transformedCovars_VisOnly.test$fac1),1))
for (iFac in 1:length(transformedCovars_VisOnly.train$fac1)) {
if (!is.na(transformedCovars_VisOnly.train$Density[iFac]) &
transformedCovars_VisOnly.train$Density[iFac]==0){
# if it's visual data and it's a zero, adjust by g0 ie, only a X% chance it was a true zero.
VisOnly.train_weightsG0[iFac,1] <- visG0*visDetProb
}
}
maxEffectiveAreaVis <- max(c(transformedCovars_VisOnly.train$EffectiveArea,
transformedCovars_VisOnly.test$EffectiveArea))
# do additional adjustment for effective area
VisOnly.train_weightsG0 <- VisOnly.train_weightsG0*
(transformedCovars_VisOnly.train$EffectiveArea/maxEffectiveAreaVis)
for (iFac in 1:length(transformedCovars_VisOnly.test$fac1)) {
if (!is.na(transformedCovars_VisOnly.test$Density[iFac]) &
transformedCovars_VisOnly.test$Density[iFac]==0){
# if it's visual data and it's a zero, adjust by g0 ie, only a X% chance it was a true zero.
VisOnly.test_weightsG0[iFac,1] <- visG0*visDetProb
}
}
# do additional adjustment for effective area
VisOnly.test_weightsG0 <- VisOnly.test_weightsG0*
(transformedCovars_VisOnly.test$EffectiveArea/maxEffectiveAreaVis)
# Remove NaNs
goodData_Ac <- which(!is.na(rowSums(transformedCovars_AcOnly.train)))
AcOnly.train.NoNa <- transformedCovars_AcOnly.train[goodData_Ac,]
goodData_Vis <- which(!is.na(rowSums(transformedCovars_VisOnly.train)))
VisOnly.train.NoNa <- transformedCovars_VisOnly.train[goodData_Vis,]
goodData_Joint <- which(!is.na(rowSums(transformedCovars.train)))
Joint.train.NoNa <- transformedCovars.train[goodData_Joint,]
goodData_Ac_test <- which(!is.na(rowSums(transformedCovars_AcOnly.test)))
AcOnly.test.NoNa <- transformedCovars_AcOnly.test[goodData_Ac_test,]
goodData_Vis_test <- which(!is.na(rowSums(transformedCovars_VisOnly.test)))
VisOnly.test.NoNa <- transformedCovars_VisOnly.test[goodData_Vis_test,]
goodData_Joint_test <- which(!is.na(rowSums(transformedCovars.test)))
Joint.test.NoNa <- transformedCovars.test[goodData_Joint_test,]
```
<br>
Case weights:
```{r plot weights, echo = FALSE}
png(paste(outDir,SP,'_caseWeights_NNet_density.png',sep=''), width = 4, height = 4, units = 'in',res = 300)
# par(mar = c(5.1, 4.1, 4.1, 3.1))
visIdx <-length(VisOnly.train_weightsG0)
jointN <- length(joint_train_weightsG0)
plot(c(1:visIdx), joint_train_weightsG0[c(1:visIdx)],pch = 1,col = "red",
ylim =c(0,1 ),ylab='Case Weight',xlab = 'Case Index',cex = 1,xlim= c(0,jointN+1))
points(c((1+visIdx):jointN),
joint_train_weightsG0[c((1+visIdx):jointN)],pch = 4,
ylim =c(0,1 ),ylab = 'Case Weight',xlab = 'Case Index',cex = 1,xlim= c(0,jointN+1))
abline(v = visIdx+.5,col = "darkgrey",lty = 2, lwd = 3)
dev.off()
wghtFig <-paste0(outDir,SP,'_caseWeights_NNet_density.png')
```
```{r Scale all the data, echo = FALSE}
# NNs don't do well with unscaled data. Scale it and then unscale it at the end.
# Scale Joint training data for the NN
covars_Joint_max.train <- apply(Joint.train.NoNa, 2, max, na.rm = TRUE)
covars_Joint_min.train <- apply(Joint.train.NoNa, 2, min, na.rm = TRUE)
Joint_train_scaled <- as.data.frame(scale(Joint.train.NoNa,
center = covars_Joint_min.train,
scale = covars_Joint_max.train-covars_Joint_min.train))
Joint_train_scaled$y<- log(Joint.train.NoNa$y+1)/log(covars_Joint_max.train['y'])
Joint_train_scaled$y[is.infinite(Joint_train_scaled$y)]<-0
Joint_train_scaled$ySqrt <- Joint.train.NoNa$ySqrt
Joint_train_scaled$weightsG0<-joint_train_weightsG0[goodData_Joint]
# Scale Ac only training data for the NN
AcOnly_train_scaled <- as.data.frame(scale(AcOnly.train.NoNa,
center = covars_Joint_min.train,
scale = covars_Joint_max.train-covars_Joint_min.train))
AcOnly_train_scaled$yAcOnly<-log(AcOnly.train.NoNa$yAcOnly+1)/log(covars_Joint_max.train['y'])
AcOnly_train_scaled$yAcOnly[is.infinite(AcOnly_train_scaled$yAcOnly )]<-0
AcOnly_train_scaled$yAcOnlySqrt <- AcOnly.train.NoNa$yAcOnlySqrt
# Scale Vis only training data for the NN
VisOnly_train_scaled <- as.data.frame(scale(VisOnly.train.NoNa,
center = covars_Joint_min.train,
scale = covars_Joint_max.train-covars_Joint_min.train))
VisOnly_train_scaled$yVisOnly <- log(VisOnly.train.NoNa$yVisOnly+1)/log(covars_Joint_max.train['y'])
VisOnly_train_scaled$yVisOnly[is.infinite(VisOnly_train_scaled$yVisOnly)]<-0
VisOnly_train_scaled$yVisOnlySqrt <- VisOnly.train.NoNa$yVisOnlySqrt
VisOnly_train_scaled$weightsG0<-VisOnly.train_weightsG0[goodData_Vis]
# Scale Ac only test data for the NN
AcOnly_test_scaled <- as.data.frame(scale(AcOnly.test.NoNa,
center = covars_Joint_min.train,
scale = covars_Joint_max.train-covars_Joint_min.train))
AcOnly_test_scaled$yAcOnly <- log(AcOnly.test.NoNa$yAcOnly+1)/log(covars_Joint_max.train['y'])
AcOnly_test_scaled$yAcOnly[is.infinite(AcOnly_test_scaled$yAcOnly)]<-0
AcOnly_test_scaled$yAcOnlySqrt <- AcOnly.test.NoNa$yAcOnlySqrt
# Scale Vis only test data for the NN
VisOnly_test_scaled <- as.data.frame(scale(VisOnly.test.NoNa,
center = covars_Joint_min.train,
scale = covars_Joint_max.train-covars_Joint_min.train))
VisOnly_test_scaled$yVisOnly <- log(VisOnly.test.NoNa$yVisOnly+1)/log(covars_Joint_max.train['y'])
VisOnly_test_scaled$yVisOnly[is.infinite(VisOnly_test_scaled$yVisOnly )]<-0
VisOnly_test_scaled$yVisOnlySqrt <- VisOnly.test.NoNa$yVisOnlySqrt
VisOnly_test_scaled$weightsG0<-VisOnly.test_weightsG0[goodData_Vis_test]
# Scale Joint test data for the NN
Joint_test_scaled <- as.data.frame(scale(Joint.test.NoNa,
center = covars_Joint_min.train,
scale = covars_Joint_max.train-covars_Joint_min.train))
Joint_test_scaled$y <-log(Joint.test.NoNa$y)/log(covars_Joint_max.train['y'])
Joint_test_scaled$y[is.infinite(Joint_test_scaled$y+1)]<-0
Joint_test_scaled$ySqrt <- Joint.test.NoNa$ySqrt
Joint_test_scaled$weightsG0<-joint_test_weightsG0[goodData_Joint_test]
n <- names(Joint_test_scaled)
# save ranges of each scaled covariate in training set (max and min)
JointRangesMax <- apply(Joint_train_scaled, MARGIN = 2,
function(x) max(x, na.rm =TRUE))
JointRangesMin <- apply(Joint_train_scaled, MARGIN = 2,
function(x) min(x, na.rm =TRUE))
AcOnlyRangesMax <- apply(AcOnly_train_scaled, MARGIN = 2,
function(x) max(x, na.rm =TRUE))
AcOnlyRangesMin <- apply(AcOnly_train_scaled, MARGIN = 2,
function(x) min(x, na.rm =TRUE))
VisOnlyRangesMax <- apply(VisOnly_train_scaled, MARGIN = 2,
function(x) max(x, na.rm =TRUE))
VisOnlyRangesMin <- apply(VisOnly_train_scaled, MARGIN = 2,
function(x) min(x, na.rm=TRUE))
```
<br>
## 2.1 Run Models
```{r, echo = FALSE}
# set up model params
model1.indices <- c(2:10)
nMax1 <- length(model1.indices)
layerSizeList <- c(4,6,8,10,12,14)
trainRepeats <- 25
```
Run NNs Acoustic only, Visual only, and joint Acoustic/Visual datasets.
Models have the following characteristics:
* `R trainRepeats` averaged repeats with random node initalization
* Include `r length(model1.indices)` covariates
* One hidden layer
* Weighted training data
* Hidden node layer sizes from `r min(layerSizeList)` to `r max(layerSizeList)` were tested in 2 node increments to search for optimal network size.
<br>
```{r, echo = FALSE}
# initialize empty structure for model storage
nn_AcOnly<-NULL
nn_VisOnly<-NULL
nn_Joint<-NULL
# initialize empty structure for error scores and predictions
MSE <- NULL
pr <- NULL
```
```{r Ac. only Model 1, results = 'hide', message = FALSE, eval = TRUE, echo = FALSE}
## ACOUSTIC ONLY
AcCounter <- 0
f.AcOnly_NN1 <- as.formula(paste("yAcOnly ~", paste(n[model1.indices], collapse = " + ")))
# Iterate over a range of hidden layer sizes between 2 and 14 nodes.
for (layerSize in layerSizeList){
AcCounter <- AcCounter + 1
# put together the formula
# train network
nn_AcOnly[[AcCounter]] <- avNNet(f.AcOnly_NN1, data = AcOnly_train_scaled,
size = layerSize,
repeats = trainRepeats,
na.action = na.omit,
rang = 0.7,
decay = 0.0001,
maxit = 500,
trace = FALSE)
# predict on train data and estimate Mean Squared Error (MSE)
pr$nn_AcOnly_train[[AcCounter]] <- predict(nn_AcOnly[[AcCounter]],
AcOnly_train_scaled[,model1.indices])
pr$nn_AcOnly_train[[AcCounter]][pr$nn_AcOnly_train[[AcCounter]] <0]<-0
MSE$nn_AcOnly_train[[AcCounter]] <- mean(abs(AcOnly_train_scaled$yAcOnly -
pr$nn_AcOnly_train[[AcCounter]]),na.rm = TRUE)
# predict on test data and estimate MSE
pr$nn_AcOnly_test[[AcCounter]] <- predict(nn_AcOnly[[AcCounter]],
AcOnly_test_scaled[,model1.indices])
pr$nn_AcOnly_test[[AcCounter]][pr$nn_AcOnly_test[[AcCounter]] <0]<-0
MSE$nn_AcOnly_test[[AcCounter]] <- mean(abs(exp(log(covars_Joint_max.train['y'])*
(AcOnly_test_scaled$yAcOnly -
pr$nn_AcOnly_test[[AcCounter]]))),na.rm = TRUE)
## how well does the model predict joint test data?
pr$nn_AcOnly_test_allData[[AcCounter]] <- predict(nn_AcOnly[[AcCounter]],
Joint_test_scaled[,model1.indices])
pr$nn_AcOnly_test_allData[[AcCounter]][pr$nn_AcOnly_test_allData[[AcCounter]]<0]<-0
MSE$nn_AcOnly_test_allData[[AcCounter]] <- mean(Joint_test_scaled$weightsG0*
abs(exp(log(covars_Joint_max.train['y'])*(Joint_test_scaled$y -
pr$nn_AcOnly_test_allData[[AcCounter]]))),na.rm = TRUE)
cat(paste("Done with AcOnly model iteration ",
AcCounter, " of ", length(layerSizeList),
": Layer Size = ", layerSize, "\n"))
}
```
```{r other models 1, eval = TRUE, echo = FALSE}
## VISUAL ONLY
modelCounter <- 0
# put together the formula
f.VisOnly_NN1 <- as.formula(paste("yVisOnly ~", paste(n[model1.indices], collapse = " + ")))
f.Joint_NN1 <- as.formula(paste("y ~", paste(n[model1.indices], collapse = " + ")))
for (layerSize in layerSizeList){
modelCounter <- modelCounter + 1
# train network
nn_VisOnly[[modelCounter]] <- avNNet(f.VisOnly_NN1, VisOnly_train_scaled,
weights = VisOnly_train_scaled$weightsG0,
size = layerSize,
repeats = trainRepeats,
na.action = na.omit,
rang = 0.7,
decay = 0.0001,
maxit = 500,
trace = FALSE)
# weights =
# predict on train data and estimate MSE
pr$nn_VisOnly_train[[modelCounter]] <- predict(nn_VisOnly[[modelCounter]],
VisOnly_train_scaled[,model1.indices])
pr$nn_VisOnly_train[[modelCounter]][ pr$nn_VisOnly_train[[modelCounter]]<0]<-0
MSE$nn_VisOnly_train[[modelCounter]] <- mean(VisOnly_train_scaled$weightsG0*
abs(exp(log(covars_Joint_max.train['y'])*
(VisOnly_train_scaled$yVisOnly -
pr$nn_VisOnly_train[[modelCounter]]))),na.rm = TRUE)
# predict on test data and estimate MSE
pr$nn_VisOnly_test[[modelCounter]] <- predict(nn_VisOnly[[modelCounter]],
VisOnly_test_scaled[,model1.indices])
pr$nn_VisOnly_test[[modelCounter]][ pr$nn_VisOnly_test[[modelCounter]]<0]<-0
MSE$nn_VisOnly_test[[modelCounter]] <- mean(VisOnly_test_scaled$weightsG0*
abs(exp(log(covars_Joint_max.train['y'])*
(VisOnly_test_scaled$yVisOnly -
pr$nn_VisOnly_test[[modelCounter]]))),na.rm = TRUE)
## how well does the model predict joint test data?
pr$nn_VisOnly_test_allData[[modelCounter]] <- predict(nn_VisOnly[[modelCounter]],
Joint_test_scaled[,model1.indices],
na.action = na.omit)
pr$nn_VisOnly_test_allData[[modelCounter]][pr$nn_VisOnly_test_allData[[modelCounter]]<0]<-0
MSE$nn_VisOnly_test_allData[[modelCounter]] <- mean(Joint_test_scaled$weightsG0*
abs(exp(log(covars_Joint_max.train['y'])*(Joint_test_scaled$y -
pr$nn_VisOnly_test_allData[[modelCounter]]))),na.rm = TRUE)
## JOINT
nn_Joint[[modelCounter]] <- avNNet(f.Joint_NN1, Joint_train_scaled,
weights = Joint_train_scaled$weightsG0,
size = layerSize,
repeats = trainRepeats,
na.action = na.omit,
rang = 0.7,
decay = 0.0001,
maxit = 10000,
trace = FALSE)
pr$nn_Joint_train[[modelCounter]] <- predict(nn_Joint[[modelCounter]],
Joint_train_scaled[,model1.indices],
na.action=na.omit)
pr$nn_Joint_train[[modelCounter]][pr$nn_Joint_train[[modelCounter]]<0]<-0
MSE$nn_Joint_train[[modelCounter]] <- mean(Joint_train_scaled$weightsG0*
abs(covars_Joint_max.train['y']*(Joint_train_scaled$y -
pr$nn_Joint_train[[modelCounter]])),na.rm = TRUE)
pr$nn_Joint_test[[modelCounter]] <- predict(nn_Joint[[modelCounter]],
Joint_test_scaled[,model1.indices],
na.action=na.omit)
pr$nn_Joint_test[[modelCounter]][pr$nn_Joint_test[[modelCounter]]<0]<-0
MSE$nn_Joint_test[[modelCounter]] <- mean(Joint_test_scaled$weightsG0*
abs(covars_Joint_max.train['y']*(Joint_test_scaled$y -
pr$nn_Joint_test[[modelCounter]])),na.rm = TRUE)
cat(paste("Done with VisOnly and Joint model iteration ",
modelCounter, " of ", length(layerSizeList),
": Layer Size = ", layerSize, "\n"))
}
```
<br>
```{r save models, eval = TRUE, echo = FALSE}
# Save models if re-calculating everything
save(nn_AcOnly,MSE,pr,
file = paste(outDir,SP,'_AcOnly_NN_density.Rdata',sep=''))
save(nn_VisOnly,MSE,pr,
file = paste(outDir,SP,'_VisOnly_NN_density.Rdata',sep=''))
save(nn_Joint,MSE,pr,
file = paste(outDir,SP,'_Joint_NN_density.Rdata',sep=''))
```
```{r load models, eval = TRUE, echo = FALSE}
# alternative if models are already calculated
load(paste0(outDir,SP,'_AcOnly_NN_density.Rdata'))
load(paste0(outDir,SP,'_VisOnly_NN_density.Rdata'))
load(paste0(outDir,SP,'_Joint_NN_density.Rdata'))
```
<br>
## 2.2 Model Comparisons
Models were compared using mean absolute error (MAE) to compare predicted and observed density in the test data.
```{r Model comparison, echo = FALSE}
XEntropy.AcOnly_train <- NULL
XEntropy.AcOnly_test <- NULL
XEntropy.VisOnly_train <- NULL
XEntropy.VisOnly_test <- NULL
XEntropy.Joint_train <- NULL
XEntropy.Joint_test <- NULL
for (iM in 1: length(nn_AcOnly)){
XEntropy.AcOnly_train[[iM]] <- LogLoss(round(pr$nn_AcOnly_train[[iM]],digits = 0),AcOnly_train_scaled$yAcOnly)
XEntropy.AcOnly_test[[iM]] <- LogLoss(round(pr$nn_AcOnly_test[[iM]],digits = 0),AcOnly_test_scaled$yAcOnly)
XEntropy.VisOnly_train[[iM]] <- weighted_logloss(round(pr$nn_VisOnly_train[[iM]],
digits = 0),VisOnly_train_scaled$yVisOnly,
VisOnly_train_scaled$weightsG0)
XEntropy.VisOnly_test[[iM]] <- weighted_logloss(round(pr$nn_VisOnly_test[[iM]],digits = 0),
VisOnly_test_scaled$yVisOnly,
VisOnly_test_scaled$weightsG0)
XEntropy.Joint_train[[iM]] <- weighted_logloss(round(pr$nn_Joint_train[[iM]], digits = 0),
Joint_train_scaled$y,
Joint_train_scaled$weightsG0)
XEntropy.Joint_test[[iM]] <- weighted_logloss(round(pr$nn_Joint_test[[iM]], digits = 0),
Joint_test_scaled$y,
Joint_test_scaled$weightsG0)
}
KSStat <- NULL
for (iM in 1: length(nn_AcOnly)){
KSStat$AcOnly_train[[iM]] <- KS_Stat(round(pr$nn_AcOnly_train[[iM]],digits = 0),AcOnly_train_scaled$yAcOnly)
KSStat$AcOnly_test[[iM]] <- KS_Stat(round(pr$nn_AcOnly_test[[iM]],digits = 0),AcOnly_test_scaled$yAcOnly)
KSStat$VisOnly_train[[iM]] <- KS_Stat(round(pr$nn_VisOnly_train[[iM]],digits = 0),VisOnly_train_scaled$yVisOnly)
KSStat$VisOnly_test[[iM]] <- KS_Stat(round(pr$nn_VisOnly_test[[iM]],digits = 0),VisOnly_test_scaled$yVisOnly)
KSStat$Joint_train[[iM]] <- KS_Stat(round(pr$nn_Joint_train[[iM]],digits = 0),Joint_train_scaled$y)
KSStat$Joint_test[[iM]] <- KS_Stat(round(pr$nn_Joint_test[[iM]],digits = 0),Joint_test_scaled$y)
}
RMSE <- NULL
MAE <- NULL
wRMSE <- NULL
wMAE <- NULL
modelCounter <-1
for (modelCounter in 1:length(nn_AcOnly)){
pr$nn_VisOnly_test_allData[[modelCounter]] <-(exp(log(covars_Joint_max.train['y'])*
predict(nn_VisOnly[[modelCounter]],
Joint_test_scaled[,model1.indices],
na.action = na.omit)))-1
pr$nn_VisOnly_test_allData[[modelCounter]][pr$nn_VisOnly_test_allData[[modelCounter]]<0]<-0
MAE$nn_VisOnly_test_allData[[modelCounter]] <- mean(
abs(Joint.test.NoNa$y -
pr$nn_VisOnly_test_allData[[modelCounter]]),na.rm = TRUE)
RMSE$nn_VisOnly_test_allData[[modelCounter]] <- sqrt(mean(
(Joint.test.NoNa$y -
pr$nn_VisOnly_test_allData[[modelCounter]])^2,na.rm = TRUE))
wMAE$nn_VisOnly_test_allData[[modelCounter]] <- mean(Joint_test_scaled$weightsG0*
abs(Joint.test.NoNa$y -
pr$nn_VisOnly_test_allData[[modelCounter]]),na.rm = TRUE)
wRMSE$nn_VisOnly_test_allData[[modelCounter]] <- sqrt(mean(Joint_test_scaled$weightsG0*
(Joint.test.NoNa$y -
pr$nn_VisOnly_test_allData[[modelCounter]])^2,na.rm = TRUE))
## how well does the Acoustic only model predict joint test data?
pr$nn_AcOnly_test_allData[[modelCounter]] <- (exp(log(covars_Joint_max.train['y'])*
predict(nn_AcOnly[[modelCounter]],
Joint_test_scaled[,model1.indices],
na.action = na.omit)))-1
pr$nn_AcOnly_test_allData[[modelCounter]][pr$nn_AcOnly_test_allData[[modelCounter]]<0]<-0
MAE$nn_AcOnly_test_allData[[modelCounter]] <- mean(
abs(Joint.test.NoNa$y -
pr$nn_AcOnly_test_allData[[modelCounter]]),na.rm = TRUE)
RMSE$nn_AcOnly_test_allData[[modelCounter]] <- sqrt(mean(
(Joint.test.NoNa$y -
pr$nn_AcOnly_test_allData[[modelCounter]])^2,na.rm = TRUE))
wMAE$nn_AcOnly_test_allData[[modelCounter]] <- mean(Joint_test_scaled$weightsG0*
abs(Joint.test.NoNa$y -
pr$nn_AcOnly_test_allData[[modelCounter]]),na.rm = TRUE)
wRMSE$nn_AcOnly_test_allData[[modelCounter]] <- sqrt(mean((Joint_test_scaled$weightsG0*
(Joint.test.NoNa$y -
pr$nn_AcOnly_test_allData[[modelCounter]]))^2,na.rm = TRUE))
## how well does the Joint only model predict joint test data?
pr$nn_Joint_test_allData[[modelCounter]] <- (exp(log(covars_Joint_max.train['y'])*
predict(nn_Joint[[modelCounter]],
Joint_test_scaled[,model1.indices],
na.action = na.omit)))-1
pr$nn_Joint_test_allData[[modelCounter]][pr$nn_Joint_test_allData[[modelCounter]]<0]<-0
MAE$nn_Joint_test_allData[[modelCounter]] <- mean(
abs(Joint.test.NoNa$y -
pr$nn_Joint_test_allData[[modelCounter]]),na.rm = TRUE)
RMSE$nn_Joint_test_allData[[modelCounter]] <- sqrt(mean(
(Joint.test.NoNa$y -
pr$nn_Joint_test_allData[[modelCounter]])^2,na.rm = TRUE))
wMAE$nn_Joint_test_allData[[modelCounter]] <- mean(Joint_test_scaled$weightsG0*
abs(Joint.test.NoNa$y -
pr$nn_Joint_test_allData[[modelCounter]]),na.rm = TRUE)
wRMSE$nn_Joint_test_allData[[modelCounter]] <- sqrt(mean((Joint_test_scaled$weightsG0*
(Joint.test.NoNa$y -
pr$nn_Joint_test_allData[[modelCounter]]))^2,na.rm = TRUE))
}
RMSEtable <- rbind(RMSE$nn_AcOnly_test_allData,RMSE$nn_VisOnly_test_allDat,RMSE$nn_Joint_test_allData)
wRMSEtable <- rbind(wRMSE$nn_AcOnly_test_allData,wRMSE$nn_VisOnly_test_allDat,wRMSE$nn_Joint_test_allData)
MAEtable <- rbind(MAE$nn_AcOnly_test_allData,MAE$nn_VisOnly_test_allDat,MAE$nn_Joint_test_allData)
wMAEtable <- rbind(wMAE$nn_AcOnly_test_allData,wMAE$nn_VisOnly_test_allDat,wMAE$nn_Joint_test_allData)
colnames(RMSEtable)<- layerSizeList
rownames(RMSEtable)<- c("Acoustic - Joint test data","Visual - Joint test data","Joint - Test")
colnames(wRMSEtable)<- layerSizeList
rownames(wRMSEtable)<- c("Acoustic - Joint test data","Visual - Joint test data","Joint - Test")
colnames(MAEtable)<- layerSizeList
rownames(MAEtable)<- c("Acoustic - Joint test data","Visual - Joint test data","Joint - Test")
colnames(wMAEtable)<- layerSizeList
rownames(wMAEtable)<- c("Acoustic - Joint test data","Visual - Joint test data","Joint - Test")
print('RMSE (lower is better)')
print(RMSEtable, digits = 3)