R Notebook
Adhislacy
ARTIFICIAL NEURAL NETWORKS & SUPPORT VECTOR MACHINES.
HOMEWORK 7: MODELLING THE STRENGTH OF CONCRETE.
STEP 1: COLLECTING DATA.
STEP 2: DATA EXPLORATION AND PREPARATION.
- Read in the data.
concrete <- read.csv("http://www.sci.csueastbay.edu/~esuess/classes/Statistics_6620/Presentations/ml11/concrete.csv")
- Examine the structure of the data.
str(concrete)## 'data.frame': 1030 obs. of 9 variables:
## $ cement : num 141 169 250 266 155 ...
## $ slag : num 212 42.2 0 114 183.4 ...
## $ ash : num 0 124.3 95.7 0 0 ...
## $ water : num 204 158 187 228 193 ...
## $ superplastic: num 0 10.8 5.5 0 9.1 0 0 6.4 0 9 ...
## $ coarseagg : num 972 1081 957 932 1047 ...
## $ fineagg : num 748 796 861 670 697 ...
## $ age : int 28 14 28 28 28 90 7 56 28 28 ...
## $ strength : num 29.9 23.5 29.2 45.9 18.3 ...
- Customize the normalization function.
normalize <- function(x) {
return((x - min(x)) / (max(x) - min(x)))
}
- Appling the normalization function to entire data frame.
concrete_norm <- as.data.frame(lapply(concrete, normalize))
- Confirming that the range is now between 0 and 1.
summary(concrete_norm$strength)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000 0.2664 0.4001 0.4172 0.5457 1.0000
- Comparing the original minimum and maximum.
summary(concrete$strength)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.33 23.71 34.44 35.82 46.14 82.60
- Fitting the (training and test data) model by splitting the data frames.
concrete_train <- concrete_norm[1:773, ]concrete_test <- concrete_norm[774:1030, ]STEP 3: TRAINING THE MODEL ON THE DATA.
- Train the neuralnet model.
library(neuralnet)## Warning: package 'neuralnet' was built under R version 3.3.3
- Creating a simple ANN with only a single hidden neuron.
- To guarantee replaucible results, we set a seed, which is essential when we try to optimize a function that involves randomly generated numbers (e.g. in simulation based estimation). If otherwise, the variation due to drawing different random numbers will likely cause the optimization algorithm to fail.
set.seed(12345)concrete_model <- neuralnet(formula = strength ~ cement + slag +
ash + water + superplastic +
coarseagg + fineagg + age,
data = concrete_train)Visualizing the network topology.
plot(concrete_model)
- Here we see the connection between the variables and how the contribute to the strength of the concrete. There’s an error rate of 5.077438, with 4882 steps. Should we add nore steps, there might be a reduced rate of the error.
- Getting an alternative visual plot.
library(NeuralNetTools)## Warning: package 'NeuralNetTools' was built under R version 3.3.3plotnet## function (mod_in, ...)
## UseMethod("plotnet")
## <environment: namespace:NeuralNetTools>par(mar = numeric(4), family = 'serif')plotnet(concrete_model, alpha = 0.6)
STEP 4: EVALUATING MODEL PERFORMANCE.
- Obtaining model results.
model_results <- compute(concrete_model, concrete_test[1:8])
- Obtaining predicted strength values.
predicted_strength <- model_results$net.result
- Examining the correlation between predicted and actual values. This value will be higher than the one stated in the textbook (0.7170368646), thus proving a stronger correlation.
cor(predicted_strength, concrete_test$strength)## [,1]
## [1,] 0.8064655576
- Producing actual predictions.
head(predicted_strength)## [,1]
## 774 0.3258991537
## 775 0.4677425372
## 776 0.2370268181
## 777 0.6718811029
## 778 0.4663428766
## 779 0.4685272270concrete_train_original_strength <- concrete[1:773,"strength"]strength_min <- min(concrete_train_original_strength)strength_max <- max(concrete_train_original_strength)head(concrete_train_original_strength)## [1] 29.89 23.51 29.22 45.85 18.29 21.86
- Customizing the normalization function.
unnormalize <- function(x, min, max) {
return( (max - min)*x + min )
}strength_pred <- unnormalize(predicted_strength, strength_min, strength_max)strength_pred## [,1]
## 774 28.212910787
## 775 39.478112301
## 776 21.154669896
## 777 55.690797192
## 778 39.366951260
## 779 39.540432369
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## 999 38.388908212
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## 1001 44.736636088
## 1002 20.515435999
## 1003 43.646913655
## 1004 53.414481990
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## 1011 15.938227741
## 1012 31.463715541
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## 1029 55.704290534
## 1030 46.250018028STEP 5: IMPROVING MODEL PERFORMANCE.*
- Creating a more complex neural network topology with five hidden neurons. *This will result in more steps..**
- We set a seed to guarante replausible results.
set.seed(12345)
- The commonly used link is the logit, with its inverse being the logistic, which we will use in this second model. This is best preferred for a binomial model.
concrete_model2 <- neuralnet(strength ~ cement + slag +
ash + water + superplastic +
coarseagg + fineagg + age,
data = concrete_train, hidden = 5, act.fct = "logistic")
- Plotting the network. With the second model and much more steps taken, the error rate has reduced from 5.077438 to 1.626684, making it a much better model for the predicion of the strength.
plot(concrete_model2)
- Plotting using ‘plotnet’.
par(mar = numeric(4), family = 'serif')plotnet(concrete_model2, alpha = 0.6)
- Evaluating the results.
model_results2 <- compute(concrete_model2, concrete_test[1:8])predicted_strength2 <- model_results2$net.result
- We get a higher correlation in the second model compared to the first one. Therefore this is a good model for our data.
cor(predicted_strength2, concrete_test$strength)## [,1]
## [1,] 0.9244533426
- Trying a different activation function: a complex neural network topology with five hidden neurons.
set.seed(12345)concrete_model2 <- neuralnet(strength ~ cement + slag +
ash + water + superplastic +
coarseagg + fineagg + age,
data = concrete_train, hidden = 5, act.fct = "tanh")
- Evaluating the results.
model_results2 <- compute(concrete_model2, concrete_test[1:8])predicted_strength2 <- model_results2$net.result
- We see a strong correlation here.
cor(predicted_strength2, concrete_test$strength)## [,1]
## [1,] 0.5741729322USE OF H20
library(h2o)## Warning: package 'h2o' was built under R version 3.3.3##
## ----------------------------------------------------------------------
##
## Your next step is to start H2O:
## > h2o.init()
##
## For H2O package documentation, ask for help:
## > ??h2o
##
## After starting H2O, you can use the Web UI at http://localhost:54321
## For more information visit http://docs.h2o.ai
##
## ----------------------------------------------------------------------##
## Attaching package: 'h2o'## The following objects are masked from 'package:stats':
##
## cor, sd, var## The following objects are masked from 'package:base':
##
## %*%, %in%, &&, ||, apply, as.factor, as.numeric, colnames,
## colnames<-, ifelse, is.character, is.factor, is.numeric, log,
## log10, log1p, log2, round, signif, trunch2o.init(nthreads=4, max_mem_size="2G")## Connection successful!
##
## R is connected to the H2O cluster:
## H2O cluster uptime: 2 hours 58 minutes
## H2O cluster version: 3.10.4.6
## H2O cluster version age: 27 days
## H2O cluster name: H2O_started_from_R_annmo_fgl344
## H2O cluster total nodes: 1
## H2O cluster total memory: 1.61 GB
## H2O cluster total cores: 4
## H2O cluster allowed cores: 4
## H2O cluster healthy: TRUE
## H2O Connection ip: localhost
## H2O Connection port: 54321
## H2O Connection proxy: NA
## H2O Internal Security: FALSE
## R Version: R version 3.3.2 (2016-10-31)h2o.removeAll() ## clean slate - just in case the cluster was already running
h2o.init()## Connection successful!
##
## R is connected to the H2O cluster:
## H2O cluster uptime: 2 hours 58 minutes
## H2O cluster version: 3.10.4.6
## H2O cluster version age: 27 days
## H2O cluster name: H2O_started_from_R_annmo_fgl344
## H2O cluster total nodes: 1
## H2O cluster total memory: 1.61 GB
## H2O cluster total cores: 4
## H2O cluster allowed cores: 4
## H2O cluster healthy: TRUE
## H2O Connection ip: localhost
## H2O Connection port: 54321
## H2O Connection proxy: NA
## H2O Internal Security: FALSE
## R Version: R version 3.3.2 (2016-10-31)
- Feeding in the data.
concrete.hex <- h2o.importFile("http://www.sci.csueastbay.edu/~esuess/classes/Statistics_6620/Presentations/ml11/concrete.csv")##
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- Getting the summary of the data.
summary(concrete.hex)## Warning in summary.H2OFrame(concrete.hex): Approximated quantiles
## computed! If you are interested in exact quantiles, please pass the
## `exact_quantiles=TRUE` parameter.## cement slag ash water
## Min. :102.0 Min. : 0.00 Min. : 0.00 Min. :121.8
## 1st Qu.:192.1 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.:164.9
## Median :272.6 Median : 21.92 Median : 0.00 Median :184.9
## Mean :281.2 Mean : 73.90 Mean : 54.19 Mean :181.6
## 3rd Qu.:349.9 3rd Qu.:142.68 3rd Qu.:118.26 3rd Qu.:191.9
## Max. :540.0 Max. :359.40 Max. :200.10 Max. :247.0
## superplastic coarseagg fineagg age
## Min. : 0.000 Min. : 801.0 Min. :594.0 Min. : 1.00
## 1st Qu.: 0.000 1st Qu.: 931.7 1st Qu.:730.8 1st Qu.: 7.00
## Median : 6.376 Median : 967.8 Median :779.1 Median : 28.00
## Mean : 6.205 Mean : 972.9 Mean :773.6 Mean : 45.66
## 3rd Qu.:10.175 3rd Qu.:1029.1 3rd Qu.:824.0 3rd Qu.: 56.00
## Max. :32.200 Max. :1145.0 Max. :992.6 Max. :365.00
## strength
## Min. : 2.33
## 1st Qu.:23.68
## Median :34.40
## Mean :35.82
## 3rd Qu.:46.10
## Max. :82.60splits <- h2o.splitFrame(concrete.hex, 0.75, seed=1234)dl <- h2o.deeplearning(x=1:8,y="strength",training_frame=splits[[1]],activation = "Tanh", hidden = c(200,200), distribution = "gaussian")##
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|=================================================================| 100%dl.predict <- h2o.predict (dl, splits[[2]])##
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|=================================================================| 100%cor(as.vector(dl.predict), as.vector(splits[[2]]$strength))## [1] 0.9112169447dl@parameters## $model_id
## [1] "DeepLearning_model_R_1495667882195_5"
##
## $training_frame
## [1] "RTMP_sid_a748_2"
##
## $activation
## [1] "Tanh"
##
## $seed
## [1] 8908975863228854272
##
## $distribution
## [1] "gaussian"
##
## $x
## [1] "cement" "slag" "ash" "water"
## [5] "superplastic" "coarseagg" "fineagg" "age"
##
## $y
## [1] "strength"h2o.performance(dl)## H2ORegressionMetrics: deeplearning
## ** Reported on training data. **
## ** Metrics reported on full training frame **
##
## MSE: 44.87359936
## RMSE: 6.69877596
## MAE: 5.415179694
## RMSLE: 0.2430829426
## Mean Residual Deviance : 44.87359936h2o.shutdown(prompt = TRUE)## Are you sure you want to shutdown the H2O instance running at http://localhost:54321/ (Y/N)?