Prediction of physical activity quality from activity monitors/Sensors
Chu Ngwoke
04. September 2020
Synopsis
Using devices such as Jawbone Up, Nike FuelBand, and Fitbit it is now possible to collect a large amount of data about personal activity relatively inexpensively. These type of devices are part of the quantified self movement – a group of enthusiasts who take measurements about themselves regularly to improve their health, to find patterns in their behavior, or because they are tech geeks. One thing that people regularly do is quantify how much of a particular activity they do, but they rarely quantify how well they do it. In this project, your goal will be to use data from accelerometers on the belt, forearm, arm, and dumbell of 6 participants. They were asked to perform barbell lifts correctly and incorrectly in 5 different ways.
The goal of this project is to predict the manner in which they did the exercise. This is the classe variable in the training set.
Data description
The outcome variable is classe, a factor variable with 5 levels. For this data set, participants were asked to perform one set of 10 repetitions of the Unilateral Dumbbell Biceps Curl in 5 different fashions:
- exactly according to the specification (Class A)
- throwing the elbows to the front (Class B)
- lifting the dumbbell only halfway (Class C)
- lowering the dumbbell only halfway (Class D)
- throwing the hips to the front (Class E)
Initial configuration
The initial configuration consists of loading some required packages and initializing some variables.
## Data variables
training.file <- './data/pml-training.csv'
test.cases.file <- './data/pml-testing.csv'
training.url <- 'http://d396qusza40orc.cloudfront.net/predmachlearn/pml-training.csv'
test.cases.url <- 'http://d396qusza40orc.cloudfront.net/predmachlearn/pml-testing.csv'
#Directories
if (!file.exists("data")){
dir.create("data")
}
if (!file.exists("data/submission")){
dir.create("data/submission")
}
# R-Packages
library("caret")
library("randomForest")
library("rpart")
library("rpart.plot")
library(rattle)
# Setting seed for reproducability
set.seed(9999)Data processing
In this section the data is downloaded and processed. Some basic transformations and cleanup will be performed, so that NA values are omitted. Irrelevant columns (columns 1 to 7) will be removed in the subset.
The pml-training.csv data is used to devise training and testing sets. The pml-test.csv data is used to predict and answer the 20 questions based on the trained model.
# Download data
download.file(training.url, training.file)
download.file(test.cases.url,test.cases.file )
# Clean data
training <-read.csv(training.file, na.strings=c("NA","#DIV/0!", ""))
testing <-read.csv(test.cases.file , na.strings=c("NA", "#DIV/0!", ""))
training<-training[,colSums(is.na(training)) == 0]
testing <-testing[,colSums(is.na(testing)) == 0]
# Subset data
training <-training[,-c(1:7)]
testing <-testing[,-c(1:7)]
training$classe <- as.factor(training$classe)Cross-validation
Cross-validation will be performed by splitting the training data in training (75%) and testing (25%) data.
subSamples <- createDataPartition(y=training$classe, p=0.75, list=FALSE)
subTraining <- training[subSamples, ]
subTesting <- training[-subSamples, ]Expected out-of-sample error
The expected out-of-sample error will correspond to the quantity: 1-accuracy in the cross-validation data. Accuracy is the proportion of correct classified observation over the total sample in the subTesting data set. Expected accuracy is the expected accuracy in the out-of-sample data set (i.e. original testing data set). Thus, the expected value of the out-of-sample error will correspond to the expected number of missclassified observations/total observations in the Test data set, which is the quantity: 1-accuracy found from the cross-validation data set.
Exploratory analysis
The variable classe contains 5 levels. The plot of the outcome variable shows the frequency of each levels in the subTraining data.
plot(as.factor(subTraining$classe), col="blue", main="Levels of the variable classe", xlab="classe levels", ylab="Frequency", )
The plot above shows that Level A is the most frequent classe. D appears to be the least frequent one.
Prediction models
In this section a decision tree and random forest will be applied to the data.
Decision tree
# Fiting the model
modFitDT <- rpart(classe ~ ., data=subTraining, method="class")
# Performing prediction
predictDT <- predict(modFitDT, subTesting, type = "class")
fancyRpartPlot(modFitDT, main="Classification Tree")## Warning: labs do not fit even at cex 0.15, there may be some overplotting
The following confusion matrix shows the errors of the decision tree prediction.
confusionMatrix(predictDT, subTesting$classe)## Confusion Matrix and Statistics
##
## Reference
## Prediction A B C D E
## A 1247 212 23 83 30
## B 32 530 73 23 73
## C 35 96 695 112 121
## D 60 66 46 532 46
## E 21 45 18 54 631
##
## Overall Statistics
##
## Accuracy : 0.7412
## 95% CI : (0.7287, 0.7534)
## No Information Rate : 0.2845
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.6712
##
## Mcnemar's Test P-Value : < 2.2e-16
##
## Statistics by Class:
##
## Class: A Class: B Class: C Class: D Class: E
## Sensitivity 0.8939 0.5585 0.8129 0.6617 0.7003
## Specificity 0.9008 0.9492 0.9101 0.9468 0.9655
## Pos Pred Value 0.7818 0.7250 0.6563 0.7093 0.8205
## Neg Pred Value 0.9553 0.8996 0.9584 0.9345 0.9347
## Prevalence 0.2845 0.1935 0.1743 0.1639 0.1837
## Detection Rate 0.2543 0.1081 0.1417 0.1085 0.1287
## Detection Prevalence 0.3252 0.1491 0.2159 0.1529 0.1568
## Balanced Accuracy 0.8974 0.7538 0.8615 0.8043 0.8329Random forest
# Fiting the model
modFitRF <- randomForest(classe ~ ., data=subTraining, method="class")
# Perform prediction
predictRF <- predict(modFitRF, subTesting, type = "class")The following confusion matrix shows the errors of random forest prediction.
confusionMatrix(predictRF, subTesting$classe)## Confusion Matrix and Statistics
##
## Reference
## Prediction A B C D E
## A 1393 5 0 0 0
## B 2 943 2 0 0
## C 0 1 853 8 0
## D 0 0 0 795 2
## E 0 0 0 1 899
##
## Overall Statistics
##
## Accuracy : 0.9957
## 95% CI : (0.9935, 0.9973)
## No Information Rate : 0.2845
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.9946
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: A Class: B Class: C Class: D Class: E
## Sensitivity 0.9986 0.9937 0.9977 0.9888 0.9978
## Specificity 0.9986 0.9990 0.9978 0.9995 0.9998
## Pos Pred Value 0.9964 0.9958 0.9896 0.9975 0.9989
## Neg Pred Value 0.9994 0.9985 0.9995 0.9978 0.9995
## Prevalence 0.2845 0.1935 0.1743 0.1639 0.1837
## Detection Rate 0.2841 0.1923 0.1739 0.1621 0.1833
## Detection Prevalence 0.2851 0.1931 0.1758 0.1625 0.1835
## Balanced Accuracy 0.9986 0.9963 0.9977 0.9942 0.9988Conclusion
Result
The confusion matrices show, that the Random Forest algorithm performens better than decision trees. The accuracy for the Random Forest model was 0.995 (95% CI: (0.993, 0.997)) compared to 0.739 (95% CI: (0.727, 0.752)) for Decision Tree model. The random Forest model is choosen.
Expected out-of-sample error
The expected out-of-sample error is estimated at 0.005, or 0.5%. The expected out-of-sample error is calculated as 1 - accuracy for predictions made against the cross-validation set. Our Test data set comprises 20 cases. With an accuracy above 99% on our cross-validation data, we can expect that very few, or none, of the test samples will be missclassified.
Submission
In this section the files for the project submission are generated using the random forest algorithm on the testing data.
# Performing prediction
predictSubmission <- predict(modFitRF, testing, type="class")
predictSubmission## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
## B A B A A E D B A A B C B A E E A B B B
## Levels: A B C D E