Introduction

The goal of this project is to predict the activities (sitting-down, standing-up, standing, walking, and sitting) of 6 participants based on the data from accelerometers placed on the belt, forearm, arm, and dumbell.

The data for this project comes from the following source: Groupware@LES.

Data preparation

First we load the data and remove unnecessary variables.

#Load data
dftrainRaw <- tbl_df(read.csv("pml-training.csv"))
dftest <- tbl_df(read.csv("pml-testing.csv"))

#Remove some unnecessary variables
dftest <- dplyr::select(dftest, -one_of(c("X","problem_id","raw_timestamp_part_1", "num_window",
                                          "raw_timestamp_part_2", "cvtd_timestamp")))
zeroVarIndices <- which(nearZeroVar(dftest, saveMetrics = T)["zeroVar"]==TRUE)
dftest <- dplyr::select(dftest,-zeroVarIndices)

#Now prepare training set to match test set
dftrainDev <- dplyr::select(dftrainRaw, one_of(c("classe",names(dftest))))

Then data is partitioned into training and development set with a factor of 3/1.

Using 14718 observations for training and 4904 observations for development.

Exploratory data analysis

First we check if the 5 different activities are well distributed over time. Looking at the plot in Appendix 1, it seems to be the case.

Using unsupervised clustering with k-means shows that the 5 activities cannot be groups by proximity into 5 centroids. See Appendix 2.

Prediction models

We will fit three models for comparison: a linear model, a random forest model and a stochastic gradient boosting model.

Looking at the scales of the selected variables, we observe that they differ. Hence, in the three models, variables will be standardized (centering and scaling).

Linear model

Some variables are highly correlated: correlation > 0.9, we remove them.

c <- cor(dftrain[,-c(1,2)])
diag(c) <- 0
corCol <- row.names(which(abs(c) > 0.9,arr.ind = T))

dftrainSelected <- dplyr::select(dftrain, -one_of(corCol))
dfdevSelected <- dplyr::select(dfdev, -one_of(corCol))

Then we train a linear model.

#First get the mean and standard deviation for predictors
preObj <- preProcess(dftrainSelected[,-c(1,2)], method=c("center", "scale"))

#Add a numeric factor
map <- c("A"=1,"B"=2,"C"=3,"D"=4, "E"=5)
dftrainSelected$classe2 <- map[dftrainSelected$classe]
dfdevSelected$classe2 <- map[dfdevSelected$classe]

#Train the models
modelFitLinear <- lm(classe2~., data<-predict(preObj,dftrainSelected[,-c(1,2)]))
predLinear <- predict(modelFitLinear, newdata = predict(preObj,dfdevSelected[,-c(1,2)]))

A linear model produce an accuracy of 37.72%.

Random forest model

For the random forest model, we will work with all variables. This is because a random selection of variables is done at each split.

Based on the trace output of the Out Of Bag estimate (OOB), we have selected a value of 27 for the number of variables randomly sampled as candidates at each split and a maximum number of trees in the forest of 100.

We then train using 5-folds cross validation method to get a first estimate of the out of sample performances.

Finally the development set is used to assess out of sample performances.

set.seed(2345)
dftrainSelected$classe2 <- NULL; dfdevSelected$classe2 <- NULL

mtryGrid <- expand.grid(mtry = 27)
modelFitRF <-train(classe~.,data=dftrain[,-c(2)],method="rf", preProcess=c("center","scale"), 
                   trControl=trainControl(method="cv", number=5),
                   prox=TRUE,importance=TRUE,do.trace=FALSE,ntree=100, tuneGrid=mtryGrid)

predRF <- predict(modelFitRF, newdata = dfdev)

The model accuracy using 5-folds cross validation is 98.97%.

The development set accuracy is 99.18%.

Stochastic Gradient Boosting

We have already seen a huge improvement with the random forest algorithm, lets try now the Stochastic Gradient Boosting algorithm.

After running the algorithm without parameters specification and looking at the results across tuning parameters, we choose to use 150 trees and the number of split for each tree will be limited to 3.

set.seed(4567)
params <- data.frame(interaction.depth=3, n.trees=150, shrinkage=0.1, n.minobsinnode=10)
modelFitGBM <-train(classe~.,data=dftrain[,-c(2)],method="gbm", preProcess=c("center","scale"), 
                    trControl=trainControl(method="cv", number=5), tuneGrid=params)

predGBM <- predict(modelFitGBM, newdata = dfdev)

The model accuracy using 5-folds cross validation is 96.39%.

The development set accuracy is 95.94%.

The stochastic gradient boosting algorithm also give us a summary of the most influential variables. In our case the roll_belt and pitch_forearm are the two most influential variables. For a top ten list, see Appendix 3.

Prediction on test set

Lets predict the test set with our random forest model.

cat(as.character(predict(modelFitRF, newdata = dftest)))
## B A B A A E D B A A B C B A E E A B B B

Conclusion

After reviewing three different algorithms, it turns out that our data is best predicted with a random forest algorithm.

The final estimated out of sample accuracy measure is of 99.18% and is more optimistic than the 5 fold accuracy measure that is of 98.97%.

By increasing the number of trees and selecting more precisely variables, we may gain a little bit more accuracy. However this accuracy level should be sufficient for most of the tasks.

Appendixes

Appendix 1: Distribution of activities over time

Appendix 2: Unsupervised clustering with k-means

A B C D E
2230 515 917 449 452
441 396 206 352 602
308 575 253 264 247
743 1016 811 992 1078
463 346 380 355 327

Appendix 3: Most influential variables based on GBM model

Variables Overall
roll_belt 100.00000
pitch_forearm 49.64765
yaw_belt 36.67881
magnet_dumbbell_z 34.26113
magnet_dumbbell_y 27.09485
magnet_belt_z 24.67123
roll_forearm 22.96736
accel_forearm_x 14.28475
pitch_belt 13.72924
gyros_belt_z 13.56751