Training Models From GA selected features for Metalicity Prediction

In previous steps features were selected by using GA technology to assess the suitability of such features.

Differnt GA strategies for fitness evaluation and we have tested nearcenter and randomforest technologies.

Feature selection was prepared acording to document paso2

suppressPackageStartupMessages(library(googleVis))
suppressPackageStartupMessages(library(xtable))
suppressPackageStartupMessages(library(Peaks))
suppressPackageStartupMessages(library(magic))
suppressPackageStartupMessages(library(segmented))
suppressPackageStartupMessages(library(fftw))
suppressPackageStartupMessages(library(FITSio))
suppressPackageStartupMessages(library(stringr))
suppressPackageStartupMessages(library(utils))
suppressPackageStartupMessages(library(e1071))
suppressPackageStartupMessages(library(quantmod))
suppressPackageStartupMessages(library(JADE))
suppressPackageStartupMessages(library(zoo))
suppressPackageStartupMessages(library(plyr))
suppressPackageStartupMessages(library(doMC))
suppressPackageStartupMessages(library(multicore))
suppressPackageStartupMessages(library(parallel))
suppressPackageStartupMessages(library(foreach))
suppressPackageStartupMessages(library(compiler))
suppressPackageStartupMessages(library(galgo))

##Feature extraction as defined by the GA

For feature selection BT-Settl 2012 library from France Allard was selected and wavelength reduction was performed to become compatible with the data coming from the satellite IPAC.

# Procesado del genético de Tª
setwd("~/git/M_sel")
load("nearcenter_ALL_m_5_900.RData")
plot(bb.nc.3, type = "fitness")

plot of chunk lee01

plot(bb.nc.3, type = "fitness", filter = "nosolutions")

plot of chunk lee01

plot(bb.nc.3, type = "confusion")
## Computing confusion from class prediction...
## 5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80% 85% 90% 95% 100%

plot of chunk lee01

cpm <- classPredictionMatrix(bb.nc.3)
cm <- confusionMatrix(bb.nc.3, cpm)
sec <- sensitivityClass(bb.nc.3, cm)
spc <- specificityClass(bb.nc.3, cm)
plot(bb.nc.3, type = "confusion", set = c(1, 0), splits = 1)
## Computing confusion from class prediction...
## 5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80% 85% 90% 95% 100%

plot of chunk lee01

plot(bb.nc.3, type = "confusion", set = c(1, 0), splits = 1, chromosomes = list(bb.nc.3$bestChromosomes[[1]]))
## Computing confusion from class prediction...

plot of chunk lee01

plot(bb.nc.3, type = "generankstability")

plot of chunk lee01

rchr <- lapply(bb.nc.3$bestChromosomes[1:300], robustGeneBackwardElimination, 
    bb.nc.3, result = "shortest")
fsm <- forwardSelectionModels(bb.nc.3, plot = FALSE)
## 4% 8% 12% 16% 20% 24% 29% 33% 37% 41% 45% 49% 53% 57% 61% 65% 69% 73% 78% 82% 86% 90% 94% 98%
fsm$models
## [[1]]
## [1] 27674 43391
## 
## [[2]]
##  [1] 27674 43391 14555 77120  7253  4736 17002 50196  2372  8133 57171
## [12]  9738  6949   889   895  3109 15275 77119 20750 35778 83871 49075
## [23] 70267  3402 50333 50334 63733  3403 57036 12072 35783 76709 69714
## [34]  6662 36065 43531
## 
## [[3]]
##  [1] 27674 43391 14555 77120  7253  4736 17002 50196  2372  8133 57171
## [12]  9738  6949   889   895  3109 15275 77119 20750 35778 83871 49075
## [23] 70267  3402 50333 50334 63733  3403 57036 12072 35783 76709 69714
## [34]  6662 36065 43531 83330
## 
## [[4]]
##  [1] 27674 43391 14555 77120  7253  4736 17002 50196  2372  8133 57171
## [12]  9738  6949   889   895  3109 15275 77119 20750 35778 83871 49075
## [23] 70267  3402 50333 50334 63733  3403 57036 12072 35783 76709 69714
## [34]  6662 36065 43531 83330   890
## 
## [[5]]
##  [1] 27674 43391 14555 77120  7253  4736 17002 50196  2372  8133 57171
## [12]  9738  6949   889   895  3109 15275 77119 20750 35778 83871 49075
## [23] 70267  3402 50333 50334 63733  3403 57036 12072 35783 76709 69714
## [34]  6662 36065 43531 83330   890 15276
## 
## [[6]]
##  [1] 27674 43391 14555 77120  7253  4736 17002 50196  2372  8133 57171
## [12]  9738  6949   889   895  3109 15275 77119 20750 35778 83871 49075
## [23] 70267  3402 50333 50334 63733  3403 57036 12072 35783 76709 69714
## [34]  6662 36065 43531 83330   890 15276 16717  2806
## 
## [[7]]
##  [1] 27674 43391 14555 77120  7253  4736 17002 50196  2372  8133 57171
## [12]  9738  6949   889   895  3109 15275 77119 20750 35778 83871 49075
## [23] 70267  3402 50333 50334 63733  3403 57036 12072 35783 76709 69714
## [34]  6662 36065 43531 83330   890 15276 16717  2806  7547  9595  2239
## 
## [[8]]
##  [1] 27674 43391 14555 77120  7253  4736 17002 50196  2372  8133 57171
## [12]  9738  6949   889   895  3109 15275 77119 20750 35778 83871 49075
## [23] 70267  3402 50333 50334 63733  3403 57036 12072 35783 76709 69714
## [34]  6662 36065 43531 83330   890 15276 16717  2806  7547  9595  2239
## [45] 69715
## 
## [[9]]
##  [1] 27674 43391 14555 77120  7253  4736 17002 50196  2372  8133 57171
## [12]  9738  6949   889   895  3109 15275 77119 20750 35778 83871 49075
## [23] 70267  3402 50333 50334 63733  3403 57036 12072 35783 76709 69714
## [34]  6662 36065 43531 83330   890 15276 16717  2806  7547  9595  2239
## [45] 69715 10179
## 
## [[10]]
##  [1] 27674 43391 14555 77120  7253  4736 17002 50196  2372  8133 57171
## [12]  9738  6949   889   895  3109 15275 77119 20750 35778 83871 49075
## [23] 70267  3402 50333 50334 63733  3403 57036 12072 35783 76709 69714
## [34]  6662 36065 43531 83330   890 15276 16717  2806  7547  9595  2239
## [45] 69715 10179 17864
## 
## [[11]]
##  [1] 27674 43391 14555 77120  7253  4736 17002 50196  2372  8133 57171
## [12]  9738  6949   889   895  3109 15275 77119 20750 35778 83871 49075
## [23] 70267  3402 50333 50334 63733  3403 57036 12072 35783 76709 69714
## [34]  6662 36065 43531 83330   890 15276 16717  2806  7547  9595  2239
## [45] 69715 10179 17864 65212
## 
## [[12]]
##  [1] 27674 43391 14555 77120  7253  4736 17002 50196  2372  8133 57171
## [12]  9738  6949   889   895  3109 15275 77119 20750 35778 83871 49075
## [23] 70267  3402 50333 50334 63733  3403 57036 12072 35783 76709 69714
## [34]  6662 36065 43531 83330   890 15276 16717  2806  7547  9595  2239
## [45] 69715 10179 17864 65212 17153
## 
## [[13]]
##  [1] 27674 43391 14555 77120  7253  4736 17002 50196  2372  8133 57171
## [12]  9738  6949   889   895  3109 15275 77119 20750 35778 83871 49075
## [23] 70267  3402 50333 50334 63733  3403 57036 12072 35783 76709 69714
## [34]  6662 36065 43531 83330   890 15276 16717  2806  7547  9595  2239
## [45] 69715 10179 17864 65212 17153 70129
rownames(ALL)[fsm$models[[3]]]
##  [1] "145:148_130:144" "19:24_28:37"     "13:16_1:12"     
##  [4] "19:26_28:37"     "156:159_148:155" "93:96_97:104"   
##  [7] "48:51_52:63"     "19:24_25:36"     "60:63_49:56"    
## [10] "28:31_16:25"     "20:25_28:42"     "60:63_49:58"    
## [13] "131:134_142:149" "27:30_19:26"     "33:36_19:26"    
## [16] "72:75_64:71"     "28:31_16:27"     "18:25_28:37"    
## [19] "145:148_130:141" "27:32_19:26"     "19:26_28:39"    
## [22] "13:18_1:12"      "19:26_31:38"     "64:67_70:77"    
## [25] "19:24_28:39"     "20:25_28:39"     "20:25_28:44"    
## [28] "65:68_70:77"     "19:24_25:39"     "93:96_97:106"   
## [31] "32:37_19:26"     "30:37_19:28"     "29:36_19:26"    
## [34] "145:148_136:143" "19:24_25:32"     "20:25_31:40"    
## [37] "29:36_16:27"
# 
features <- list()
features$M <- c("19:26_28:37", "48:51_52:63", "93:96_97:104", "145:148_130:141", 
    "156:159_148:155")
output <- 7
# 

Now, we start to load the original data bp_clean and bq_clean, and we will process the features according to the feature list.

In order to generate features we will use the formula \( \int{\lambda_{1}}{\lambda_{2}}{1-\frac{F_{line}}{F_{cont}} d\lambda} \) as depicted in formula (1) of the above reference.

The band frequences are defined in the previous table but \( F_{cont} \) is not defined. As such a genetic algorithm testing different potential continuum spectra will be tested and looking the best matching to explain spectral parameters by precious feature functions.

Once the signal points and continuous regions were identified, models were setted-up and assessed by crossvalidation procedure. Iedas for the implementation were taken from http://moderntoolmaking.blogspot.com.es/2013/03/caretensemble-classification-example.html

# Cargamos bp_clean (BT_SETTL) & bq_clean (IPAC)
load("~/git/M_prep/M_prep_cleanip_BT-Settl.RData")
rm(xtmp)
# Buscamos las catacterísticas para extraerla del conjunto de train par T
signal <- unlist(lapply(features$M, function(x) {
    a <- strsplit(x, "_")
    return(a[[1]][1])
}))
noise <- unlist(lapply(features$M, function(x) {
    a <- strsplit(x, "_")
    return(a[[1]][2])
}))
sn <- cbind(signal, noise)
int_spec <- function(x, idx, norm = 0) {
    y <- x$data[[1]][eval(parse(text = idx)), ]
    xz <- diff(as.numeric(y[, 1]), 1)
    yz <- as.numeric(y[, 2])
    if (norm > 0) {
        z <- sum(xz)
    } else {
        z <- sum(xz * rollmean(yz, 2))
    }
    return(z)
}
# 
feature_extr <- function(sn, bp) {
    sig <- sn[1]
    noi <- sn[2]
    Fcont <- unlist(lapply(bp, int_spec, noi, 0))/unlist(lapply(bp, int_spec, 
        noi, 1))
    fea <- unlist(lapply(bp, int_spec, sig, 1)) - unlist(lapply(bp, int_spec, 
        sig, 0))/Fcont
    return(fea)
}
xx <- apply(sn, 1, feature_extr, bp_clean)
colnames(xx) <- as.character(sn[, 1])
colnames(xx) <- str_replace(paste("X", colnames(xx), sep = ""), ":", ".")
xx <- cbind(xx, unlist(lapply(bp_clean, function(x) {
    return(x$stellarp[3])
})))
colnames(xx)[ncol(xx)] <- "G"

# Just informing for the features
newfea <- cbind(t(apply(sn, 1, function(x) {
    return(range(bp_clean[[1]]$data[[1]][eval(parse(text = x[1])), 1]))
})), t(apply(sn, 1, function(x) {
    return(range(bp_clean[[1]]$data[[1]][eval(parse(text = x[2])), 1]))
})))
colnames(newfea) <- c("Signal_from", "Signal_To", "Cont_From", "Cont_To")

print(xtable(newfea), type = "html")
Signal_from Signal_To Cont_From Cont_To
1 8525.80 8551.00 8558.20 8590.60
2 8630.20 8641.00 8644.60 8684.20
3 8792.20 8803.00 8806.60 8831.80
4 8979.40 8990.20 8925.40 8965.00
5 9019.00 9029.80 8990.20 9015.40
# 

Regression and modeling

Let's build up several models and compare their performance. Generally speaking we split randomly the learning set and we will learn by ten folder cross validation. Then we will test the models against the unseen data and we will test the ensamble technology, even.

# Setup
gc(reset = TRUE)
##             used   (Mb) gc trigger   (Mb)  max used   (Mb)
## Ncells   2149623  114.9    4953636  264.6   2149623  114.9
## Vcells 566078000 4318.9  732821450 5591.0 566078000 4318.9
set.seed(42)  #From random.org

# Libraries
library(caret)
## Loading required package: lattice
## 
## Attaching package: 'lattice'
## 
## The following object is masked from 'package:multicore':
## 
##     parallel
## 
## Loading required package: ggplot2
## 
## Attaching package: 'caret'
## 
## The following objects are masked from 'package:galgo':
## 
##     best, confusionMatrix
library(devtools)
## 
## Attaching package: 'devtools'
## 
## The following objects are masked from 'package:R.oo':
## 
##     check, unload
# Solo una vez: install_github('caretEnsemble', 'zachmayer') #Install zach's
# caretEnsemble package Code gathered from the author's post.
library(caretEnsemble)

# Data
library(mlbench)
xx <- as.data.frame(xx)
X <- xx[, -ncol(xx)]
rownames(X) <- 1:nrow(X)
X <- data.frame(X)
Y <- xx[, ncol(xx)]

# Split train/test
train <- runif(nrow(X)) <= 0.66

# Setup CV Folds returnData=FALSE saves some space
folds = 10
repeats = 1
myControl <- trainControl(method = "cv", number = folds, repeats = repeats, 
    returnResamp = "none", returnData = FALSE, savePredictions = TRUE, verboseIter = FALSE, 
    allowParallel = TRUE, index = createMultiFolds(Y[train], k = folds, times = repeats))
# Train some models
model1 <- train(X[train, ], Y[train], method = "gbm", trControl = myControl, 
    tuneGrid = expand.grid(.n.trees = 500, .interaction.depth = 15, .shrinkage = 0.01), 
    verbose = FALSE)
## Loading required package: gbm
## Loading required package: survival
## Loading required package: splines
## 
## Attaching package: 'survival'
## 
## The following object is masked from 'package:caret':
## 
##     cluster
## 
## Loaded gbm 2.1
model2 <- train(X[train, ], Y[train], method = "blackboost", trControl = myControl)
## Loading required package: party
## Loading required package: grid
## Loading required package: sandwich
## Loading required package: strucchange
## Loading required package: modeltools
## Loading required package: stats4
## 
## Attaching package: 'modeltools'
## 
## The following objects are masked from 'package:R.oo':
## 
##     clone, dimension
## 
## The following object is masked from 'package:plyr':
## 
##     empty
## 
## Loading required package: mboost
## This is mboost 2.2-3. See 'package?mboost' and the NEWS file
## for a complete list of changes.
## Note: The default for the computation of the degrees of freedom has changed.
##       For details see section 'Global Options' of '?bols'.
## 
## Attaching package: 'mboost'
## 
## The following object is masked from 'package:ggplot2':
## 
##     %+%
model3 <- train(X[train, ], Y[train], method = "rf", trControl = myControl)
## Loading required package: randomForest
## randomForest 4.6-7
## Type rfNews() to see new features/changes/bug fixes.
model4 <- train(X[train, ], Y[train], method = "mlpWeightDecay", trControl = myControl, 
    trace = FALSE)
## Loading required package: RSNNS
## Loading required package: Rcpp
## 
## Attaching package: 'RSNNS'
## 
## The following objects are masked from 'package:caret':
## 
##     confusionMatrix, train
## 
## The following object is masked from 'package:galgo':
## 
##     confusionMatrix
model5 <- train(X[train, ], Y[train], method = "ppr", trControl = myControl)
model6 <- train(X[train, ], Y[train], method = "earth", trControl = myControl)
## Loading required package: earth
## Loading required package: plotmo
## Loading required package: plotrix
model7 <- train(X[train, ], Y[train], method = "glm", trControl = myControl)
model8 <- train(X[train, ], Y[train], method = "svmRadial", trControl = myControl)
## Loading required package: kernlab
## 
## Attaching package: 'kernlab'
## 
## The following object is masked from 'package:modeltools':
## 
##     prior
## 
## The following object is masked from 'package:galgo':
## 
##     scaling
model9 <- train(X[train, ], Y[train], method = "gam", trControl = myControl)
## Loading required package: mgcv
## Loading required package: nlme
## This is mgcv 1.7-28. For overview type 'help("mgcv-package")'.
## 
## Attaching package: 'mgcv'
## 
## The following object is masked from 'package:magic':
## 
##     magic
model10 <- train(X[train, ], Y[train], method = "glmnet", trControl = myControl)
## Loading required package: glmnet
## Loading required package: Matrix
## Loaded glmnet 1.9-5
model11 <- train(X[train, ], Y[train], method = "nnet", trControl = myControl, 
    trace = FALSE, maxit = 10000, reltol = 1e-11, abstol = 1e-06)
## Loading required package: nnet

# Make a list of all the models
all.models <- list(model1, model2, model3, model4, model5, model6, model7, model8, 
    model9, model10)
names(all.models) <- sapply(all.models, function(x) x$method)
sort(sapply(all.models, function(x) min(x$results$RMSE)))
##      svmRadial            gbm             rf            gam mlpWeightDecay 
##         0.2156         0.2517         0.2621         0.3175         0.3220 
##            ppr     blackboost          earth            glm         glmnet 
##         0.3257         0.3303         0.3535         0.4921         0.5071

# Make a greedy ensemble - currently can only use RMSE
greedy <- caretEnsemble(all.models, iter = 1000L)
## Loading required package: pbapply
sort(greedy$weights, decreasing = TRUE)
## svmRadial        rf       gam 
##     0.842     0.093     0.065
greedy$error
##   RMSE 
## 0.2392

# Make a linear regression ensemble
linear <- caretStack(all.models, method = "glm", trControl = trainControl(method = "cv"))
summary(linear$ens_model$finalModel)
## 
## Call:
## NULL
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -0.6170  -0.1152  -0.0094   0.0865   2.2094  
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     0.00284    0.02776    0.10   0.9185    
## gbm            -0.12431    0.16983   -0.73   0.4650    
## blackboost     -0.37121    0.12659   -2.93   0.0037 ** 
## rf              0.52004    0.17073    3.05   0.0026 ** 
## mlpWeightDecay -0.02802    0.09800   -0.29   0.7752    
## ppr             0.06173    0.08864    0.70   0.4869    
## earth          -0.10917    0.09789   -1.12   0.2660    
## glm             0.03883    0.16056    0.24   0.8091    
## svmRadial       0.83710    0.11905    7.03  2.5e-11 ***
## gam             0.19951    0.12518    1.59   0.1124    
## glmnet         -0.05006    0.17832   -0.28   0.7792    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for gaussian family taken to be 0.05578)
## 
##     Null deviance: 164.234  on 230  degrees of freedom
## Residual deviance:  12.272  on 220  degrees of freedom
## AIC: 1.542
## 
## Number of Fisher Scoring iterations: 2
linear$error
##   parameter   RMSE Rsquared RMSESD RsquaredSD
## 1      none 0.2357   0.8997 0.1281     0.1317

# Predict for test set:
preds <- data.frame(sapply(all.models, predict, newdata = X[!train, ]))
preds$ENS_greedy <- predict(greedy, newdata = X[!train, ])
preds$ENS_linear <- predict(linear, newdata = X[!train, ])
sort(sqrt(colMeans((preds - Y[!train])^2)))
##      svmRadial     ENS_greedy     ENS_linear            gbm             rf 
##         0.1642         0.1647         0.1696         0.2218         0.2255 
##            gam          earth mlpWeightDecay            ppr     blackboost 
##         0.2604         0.2706         0.2863         0.3047         0.3142 
##            glm         glmnet 
##         0.5427         0.5556

plot(Y[!train], preds$ENS_greedy)
lines(c(-5, 10), c(-5, 10), col = 2)

plot of chunk lee02.1

IPAC validation

After having the models built as well as the ensamble of them it is time to predict for the IPAC dataset. Thus we start to prepare the data,

# Cargamos bq_clean (IPAC)
yy <- apply(sn, 1, feature_extr, bq_clean)
yy <- as.data.frame(yy)
colnames(yy) <- as.character(sn[, 1])
colnames(yy) <- str_replace(paste("X", colnames(yy), sep = ""), ":", ".")
# Predict for new dataset:
predf <- data.frame(sapply(all.models, predict, newdata = yy))
predf$ENS_greedy <- predict(greedy, newdata = yy)
predf$ENS_linear <- predict(linear, newdata = yy)

Neighbourhood Analysis

In order to realize how close or isolated the both sets (BT-SETTL and IPAC) are a PCA analysis is performed:

# Cargamos bq_clean (IPAC)
zz <- rbind(X, yy)
pcaz <- prcomp(zz)
plot(pcaz$x[, 1], pcaz$x[, 2], pch = ".")
points(pcaz$x[(nrow(X) + 1):nrow(zz), 1], pcaz$x[(nrow(X) + 1):nrow(zz), 2], 
    pch = "x", col = 3)
points(pcaz$x[1:nrow(X), 1], pcaz$x[1:nrow(X), 2], pch = "+", col = 2)

plot of chunk lee04

rownames(yy)[896 - nrow(X)]
## [1] "LP_799-3.7512.txt"

According to the obtained predictions, some comparison will be performed against the prediction carried out by using spectrafull projection by means of ICA/JADE technology. This was carried out by Miss Prendes Gero at http://innova.uned.es, so we will download her prediction datasets and just compare them.

# Cargamos bq_clean (IPAC)
load("~/git/M_sel/IPAC_Belen_M.RData")
load("~/git/M_sel/belen_resul_T.RData")
rownames(dM) = rownames(dd)
lnm <- unlist(lapply(bq_clean, function(x) {
    return(x$name)
}))
idx = apply(data.frame(rownames(dM)), 1, function(x, y) {
    return(which(x == y))
}, lnm)
XY = cbind(dM[, ncol(dM)], predf$ENS_greedy[idx])
plot(XY)

plot of chunk lee05

plot(XY, xlim = c(-5, 5), ylim = c(-5, 5))
lines(c(-5, 5), c(-5, 5), col = 2)

plot of chunk lee05

hist((XY[, 1] - XY[, 2])/sd(XY[, 1] - XY[, 2]), breaks = 20)

plot of chunk lee05

mer1 = mean(XY[, 1] - XY[, 2])
sder1 = sd(XY[, 1] - XY[, 2])