Prediction of Exercise Class
Justin Rice
Executive Summary
This study was commissioned to predict how a subject performed an exercise. The data used for this project was collected from a range of wireless activity wristbands. The wristbands were worn by the subjects as they performed excercies in 5 different ways. To study the data I broke the source data into a training and testing set. I experimented with 2 training models; Decision Tree and Random Forest. The decision tree performed very poorly which is likely to be caused by a lack of homogeneity in the data. We know that random forest is one of the most accurate models and it proved itself here with this data.
Getting and Cleaning
library(knitr)
library(dplyr)
library(plyr)
library(ggplot2)
library(gridExtra)
library(caret)
library(party)
#library(e1071)
set.seed(2016)
#download the data if it doesn't already exist
if(!file.exists("pml-training.csv")) {
trainURL <- "https://d396qusza40orc.cloudfront.net/predmachlearn/pml-training.csv"
download.file(trainURL, destfile="pml-training.csv")
}
if(!file.exists("pml-testing.csv")) {
trainURL <- "https://d396qusza40orc.cloudfront.net/predmachlearn/pml-testing.csv"
download.file(trainURL, destfile="pml-testing.csv")
}
#Load the data into R
pmlVal <- read.csv("pml-testing.csv")
pmlData <- read.csv("pml-training.csv")
#Remove all the columns that include NA values
NAcols <- colSums(is.na(pmlData)) == 0
Validcolumns <- sum(NAcols == TRUE)
pmlData <- pmlData[, NAcols]
#Remove columns that are not meaningful predictors
nzv <- nearZeroVar(pmlData, saveMetrics = T)
pmlData <- pmlData[, nzv$nzv==F]
#pmlData <- head(pmlData, 1000)
str(pmlData)## 'data.frame': 19622 obs. of 59 variables:
## $ X : int 1 2 3 4 5 6 7 8 9 10 ...
## $ user_name : Factor w/ 6 levels "adelmo","carlitos",..: 2 2 2 2 2 2 2 2 2 2 ...
## $ raw_timestamp_part_1: int 1323084231 1323084231 1323084231 1323084232 1323084232 1323084232 1323084232 1323084232 1323084232 1323084232 ...
## $ raw_timestamp_part_2: int 788290 808298 820366 120339 196328 304277 368296 440390 484323 484434 ...
## $ cvtd_timestamp : Factor w/ 20 levels "02/12/2011 13:32",..: 9 9 9 9 9 9 9 9 9 9 ...
## $ num_window : int 11 11 11 12 12 12 12 12 12 12 ...
## $ roll_belt : num 1.41 1.41 1.42 1.48 1.48 1.45 1.42 1.42 1.43 1.45 ...
## $ pitch_belt : num 8.07 8.07 8.07 8.05 8.07 8.06 8.09 8.13 8.16 8.17 ...
## $ yaw_belt : num -94.4 -94.4 -94.4 -94.4 -94.4 -94.4 -94.4 -94.4 -94.4 -94.4 ...
## $ total_accel_belt : int 3 3 3 3 3 3 3 3 3 3 ...
## $ gyros_belt_x : num 0 0.02 0 0.02 0.02 0.02 0.02 0.02 0.02 0.03 ...
## $ gyros_belt_y : num 0 0 0 0 0.02 0 0 0 0 0 ...
## $ gyros_belt_z : num -0.02 -0.02 -0.02 -0.03 -0.02 -0.02 -0.02 -0.02 -0.02 0 ...
## $ accel_belt_x : int -21 -22 -20 -22 -21 -21 -22 -22 -20 -21 ...
## $ accel_belt_y : int 4 4 5 3 2 4 3 4 2 4 ...
## $ accel_belt_z : int 22 22 23 21 24 21 21 21 24 22 ...
## $ magnet_belt_x : int -3 -7 -2 -6 -6 0 -4 -2 1 -3 ...
## $ magnet_belt_y : int 599 608 600 604 600 603 599 603 602 609 ...
## $ magnet_belt_z : int -313 -311 -305 -310 -302 -312 -311 -313 -312 -308 ...
## $ roll_arm : num -128 -128 -128 -128 -128 -128 -128 -128 -128 -128 ...
## $ pitch_arm : num 22.5 22.5 22.5 22.1 22.1 22 21.9 21.8 21.7 21.6 ...
## $ yaw_arm : num -161 -161 -161 -161 -161 -161 -161 -161 -161 -161 ...
## $ total_accel_arm : int 34 34 34 34 34 34 34 34 34 34 ...
## $ gyros_arm_x : num 0 0.02 0.02 0.02 0 0.02 0 0.02 0.02 0.02 ...
## $ gyros_arm_y : num 0 -0.02 -0.02 -0.03 -0.03 -0.03 -0.03 -0.02 -0.03 -0.03 ...
## $ gyros_arm_z : num -0.02 -0.02 -0.02 0.02 0 0 0 0 -0.02 -0.02 ...
## $ accel_arm_x : int -288 -290 -289 -289 -289 -289 -289 -289 -288 -288 ...
## $ accel_arm_y : int 109 110 110 111 111 111 111 111 109 110 ...
## $ accel_arm_z : int -123 -125 -126 -123 -123 -122 -125 -124 -122 -124 ...
## $ magnet_arm_x : int -368 -369 -368 -372 -374 -369 -373 -372 -369 -376 ...
## $ magnet_arm_y : int 337 337 344 344 337 342 336 338 341 334 ...
## $ magnet_arm_z : int 516 513 513 512 506 513 509 510 518 516 ...
## $ roll_dumbbell : num 13.1 13.1 12.9 13.4 13.4 ...
## $ pitch_dumbbell : num -70.5 -70.6 -70.3 -70.4 -70.4 ...
## $ yaw_dumbbell : num -84.9 -84.7 -85.1 -84.9 -84.9 ...
## $ total_accel_dumbbell: int 37 37 37 37 37 37 37 37 37 37 ...
## $ gyros_dumbbell_x : num 0 0 0 0 0 0 0 0 0 0 ...
## $ gyros_dumbbell_y : num -0.02 -0.02 -0.02 -0.02 -0.02 -0.02 -0.02 -0.02 -0.02 -0.02 ...
## $ gyros_dumbbell_z : num 0 0 0 -0.02 0 0 0 0 0 0 ...
## $ accel_dumbbell_x : int -234 -233 -232 -232 -233 -234 -232 -234 -232 -235 ...
## $ accel_dumbbell_y : int 47 47 46 48 48 48 47 46 47 48 ...
## $ accel_dumbbell_z : int -271 -269 -270 -269 -270 -269 -270 -272 -269 -270 ...
## $ magnet_dumbbell_x : int -559 -555 -561 -552 -554 -558 -551 -555 -549 -558 ...
## $ magnet_dumbbell_y : int 293 296 298 303 292 294 295 300 292 291 ...
## $ magnet_dumbbell_z : num -65 -64 -63 -60 -68 -66 -70 -74 -65 -69 ...
## $ roll_forearm : num 28.4 28.3 28.3 28.1 28 27.9 27.9 27.8 27.7 27.7 ...
## $ pitch_forearm : num -63.9 -63.9 -63.9 -63.9 -63.9 -63.9 -63.9 -63.8 -63.8 -63.8 ...
## $ yaw_forearm : num -153 -153 -152 -152 -152 -152 -152 -152 -152 -152 ...
## $ total_accel_forearm : int 36 36 36 36 36 36 36 36 36 36 ...
## $ gyros_forearm_x : num 0.03 0.02 0.03 0.02 0.02 0.02 0.02 0.02 0.03 0.02 ...
## $ gyros_forearm_y : num 0 0 -0.02 -0.02 0 -0.02 0 -0.02 0 0 ...
## $ gyros_forearm_z : num -0.02 -0.02 0 0 -0.02 -0.03 -0.02 0 -0.02 -0.02 ...
## $ accel_forearm_x : int 192 192 196 189 189 193 195 193 193 190 ...
## $ accel_forearm_y : int 203 203 204 206 206 203 205 205 204 205 ...
## $ accel_forearm_z : int -215 -216 -213 -214 -214 -215 -215 -213 -214 -215 ...
## $ magnet_forearm_x : int -17 -18 -18 -16 -17 -9 -18 -9 -16 -22 ...
## $ magnet_forearm_y : num 654 661 658 658 655 660 659 660 653 656 ...
## $ magnet_forearm_z : num 476 473 469 469 473 478 470 474 476 473 ...
## $ classe : Factor w/ 5 levels "A","B","C","D",..: 1 1 1 1 1 1 1 1 1 1 ...In this section, the data was downloaded and loaded into Data Frames. It was important to remove the NA columns as they could mislead the results. I also removed the columns that did not contribute any variance to the prediction model.
Setup Cross-Validation
partition <- createDataPartition(pmlData$classe, p=0.8, list=F)
inTrain <- pmlData[partition, ]
inTest <- pmlData[-partition, ]
i <- data.frame("Total"=c(nrow(inTrain), nrow(inTest)))
DT <- matrix(NA, nrow=2, ncol=5)
TR <- as.data.frame(table(inTrain$classe))
TE <- as.data.frame(table(inTest$classe))
DT[1, ] <- TR[,2]
DT[2, ] <- TE[,2]
g <- as.data.frame(DT)
colnames(g) <- c("A", "B", "C", "D", "E")
e<- cbind(g, i)
f <- colSums(e)
r <- rbind(e, f)
rownames(r) <- c('Training Data','Testing Data','Total')
kable(r)| A | B | C | D | E | Total | |
|---|---|---|---|---|---|---|
| Training Data | 4464 | 3038 | 2738 | 2573 | 2886 | 15699 |
| Testing Data | 1116 | 759 | 684 | 643 | 721 | 3923 |
| Total | 5580 | 3797 | 3422 | 3216 | 3607 | 19622 |
This shows the break-down of the dependent variable. 80% of the data was used for model building and the remaining 20% was reservered for validation. One may observe that exercise A was performed most by the participants. The graph below also provides further illustration.
qplot(user_name, data=inTrain, fill=classe)
Build Decision Tree Model
treeFit <- train(classe ~., method="rpart", data=inTrain)
treePred <- predict(treeFit, newdata=inTest)
treeMatrix <- confusionMatrix(inTest$classe, treePred)
treeMatrix$overall['Accuracy']## Accuracy
## 0.6614836treeMatrix$table## Reference
## Prediction A B C D E
## A 1116 0 0 0 0
## B 1 758 0 0 0
## C 0 0 0 0 684
## D 0 0 0 0 643
## E 0 0 0 0 721The decision tree model provided 66% accuracy, however the model failed to predict exercises of class C and D as illustrated in the confusion matrix.
Random Forest
I’ll try the Random Forest model since it is considered one of the most accurate models. This model uses bootstrap samples and variables which should resolve the issues we encountered with predicting C and D in the previous model.
ctrl <- trainControl(allowParallel = T, method="cv", number=4)
rfFit <- train(classe ~., method="rf", data=inTrain, trControl=ctrl)
rfPred <- predict(rfFit, newdata=inTest)
rfMatrix <- confusionMatrix(inTest$classe, rfPred)
rfMatrix$overall['Accuracy']## Accuracy
## 0.9997451rfMatrix$table## Reference
## Prediction A B C D E
## A 1116 0 0 0 0
## B 1 758 0 0 0
## C 0 0 684 0 0
## D 0 0 0 643 0
## E 0 0 0 0 721Out of Sample Error
err <- 1-rfMatrix$overall['Accuracy']
err## Accuracy
## 0.000254907If a random forest model is used for predictions, the expected Out of Sample Error is 0.02%. The recommendation is to proceed using the random forest model created.