Coursera Practical Machine Learning Course Project
Anne Strader
5/20/2021
Executive Summary
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.
The goal of this project is to use data from accelerometers on the belt, forearm, and dumbbell of six participants to predict the manner in which they did an exercise. The participants performed the exercise six different ways: one correct way and five incorrect ways.
The data for this project come from this source: http://web.archive.org/web/20161224072740/http:/groupware.les.inf.puc-rio.br/har.
Getting and Cleaning the Dataset
In preparation for the analysis, necessary R libraries are loaded:
library(knitr)
library(caret)
library(corrplot)
library(rattle)
library(randomForest)The training and test data are then downloaded:
# define the URLs where the data are stored
trainURL <- "https://d396qusza40orc.cloudfront.net/predmachlearn/pml-training.csv" # training data set
testURL <- "https://d396qusza40orc.cloudfront.net/predmachlearn/pml-testing.csv" # test data set
# define the source data filenames
fileTrainData <- "pml-training.csv" # training data set
fileTestData <- "pml-testing.csv" # test data set
# check if datasets have already been downloaded in working directory, and download them if not
if (!file.exists(fileTrainData)) { # training data set
download.file(trainURL, fileTrainData)
}
if (!file.exists(fileTestData)) { # test data set
download.file(testURL, fileTestData)
}The test data set is considered to be a final “validation” set, whereas the training data set will be subdivided into a smaller training set (70% of the data) and a test set (30% of the data).
# read in both data sets
trainingData <- read.csv(fileTrainData) # training data set
validationSet <- read.csv(fileTestData) # test data set (validation)Let’s look at a summary of the training data set, in order to identify the predicted variable:
str(trainingData)## 'data.frame': 19622 obs. of 160 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 ...
## $ new_window : Factor w/ 2 levels "no","yes": 1 1 1 1 1 1 1 1 1 1 ...
## $ 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 ...
## $ kurtosis_roll_belt : Factor w/ 397 levels "","-0.016850",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ kurtosis_picth_belt : Factor w/ 317 levels "","-0.021887",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ kurtosis_yaw_belt : Factor w/ 2 levels "","#DIV/0!": 1 1 1 1 1 1 1 1 1 1 ...
## $ skewness_roll_belt : Factor w/ 395 levels "","-0.003095",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ skewness_roll_belt.1 : Factor w/ 338 levels "","-0.005928",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ skewness_yaw_belt : Factor w/ 2 levels "","#DIV/0!": 1 1 1 1 1 1 1 1 1 1 ...
## $ max_roll_belt : num NA NA NA NA NA NA NA NA NA NA ...
## $ max_picth_belt : int NA NA NA NA NA NA NA NA NA NA ...
## $ max_yaw_belt : Factor w/ 68 levels "","-0.1","-0.2",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ min_roll_belt : num NA NA NA NA NA NA NA NA NA NA ...
## $ min_pitch_belt : int NA NA NA NA NA NA NA NA NA NA ...
## $ min_yaw_belt : Factor w/ 68 levels "","-0.1","-0.2",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ amplitude_roll_belt : num NA NA NA NA NA NA NA NA NA NA ...
## $ amplitude_pitch_belt : int NA NA NA NA NA NA NA NA NA NA ...
## $ amplitude_yaw_belt : Factor w/ 4 levels "","#DIV/0!","0.00",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ var_total_accel_belt : num NA NA NA NA NA NA NA NA NA NA ...
## $ avg_roll_belt : num NA NA NA NA NA NA NA NA NA NA ...
## $ stddev_roll_belt : num NA NA NA NA NA NA NA NA NA NA ...
## $ var_roll_belt : num NA NA NA NA NA NA NA NA NA NA ...
## $ avg_pitch_belt : num NA NA NA NA NA NA NA NA NA NA ...
## $ stddev_pitch_belt : num NA NA NA NA NA NA NA NA NA NA ...
## $ var_pitch_belt : num NA NA NA NA NA NA NA NA NA NA ...
## $ avg_yaw_belt : num NA NA NA NA NA NA NA NA NA NA ...
## $ stddev_yaw_belt : num NA NA NA NA NA NA NA NA NA NA ...
## $ var_yaw_belt : num NA NA NA NA NA NA NA NA NA NA ...
## $ 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 ...
## $ var_accel_arm : num NA NA NA NA NA NA NA NA NA NA ...
## $ avg_roll_arm : num NA NA NA NA NA NA NA NA NA NA ...
## $ stddev_roll_arm : num NA NA NA NA NA NA NA NA NA NA ...
## $ var_roll_arm : num NA NA NA NA NA NA NA NA NA NA ...
## $ avg_pitch_arm : num NA NA NA NA NA NA NA NA NA NA ...
## $ stddev_pitch_arm : num NA NA NA NA NA NA NA NA NA NA ...
## $ var_pitch_arm : num NA NA NA NA NA NA NA NA NA NA ...
## $ avg_yaw_arm : num NA NA NA NA NA NA NA NA NA NA ...
## $ stddev_yaw_arm : num NA NA NA NA NA NA NA NA NA NA ...
## $ var_yaw_arm : num NA NA NA NA NA NA NA NA NA NA ...
## $ 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 ...
## $ kurtosis_roll_arm : Factor w/ 330 levels "","-0.02438",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ kurtosis_picth_arm : Factor w/ 328 levels "","-0.00484",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ kurtosis_yaw_arm : Factor w/ 395 levels "","-0.01548",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ skewness_roll_arm : Factor w/ 331 levels "","-0.00051",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ skewness_pitch_arm : Factor w/ 328 levels "","-0.00184",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ skewness_yaw_arm : Factor w/ 395 levels "","-0.00311",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ max_roll_arm : num NA NA NA NA NA NA NA NA NA NA ...
## $ max_picth_arm : num NA NA NA NA NA NA NA NA NA NA ...
## $ max_yaw_arm : int NA NA NA NA NA NA NA NA NA NA ...
## $ min_roll_arm : num NA NA NA NA NA NA NA NA NA NA ...
## $ min_pitch_arm : num NA NA NA NA NA NA NA NA NA NA ...
## $ min_yaw_arm : int NA NA NA NA NA NA NA NA NA NA ...
## $ amplitude_roll_arm : num NA NA NA NA NA NA NA NA NA NA ...
## $ amplitude_pitch_arm : num NA NA NA NA NA NA NA NA NA NA ...
## $ amplitude_yaw_arm : int NA NA NA NA NA NA NA NA NA NA ...
## $ 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 ...
## $ kurtosis_roll_dumbbell : Factor w/ 398 levels "","-0.0035","-0.0073",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ kurtosis_picth_dumbbell : Factor w/ 401 levels "","-0.0163","-0.0233",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ kurtosis_yaw_dumbbell : Factor w/ 2 levels "","#DIV/0!": 1 1 1 1 1 1 1 1 1 1 ...
## $ skewness_roll_dumbbell : Factor w/ 401 levels "","-0.0082","-0.0096",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ skewness_pitch_dumbbell : Factor w/ 402 levels "","-0.0053","-0.0084",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ skewness_yaw_dumbbell : Factor w/ 2 levels "","#DIV/0!": 1 1 1 1 1 1 1 1 1 1 ...
## $ max_roll_dumbbell : num NA NA NA NA NA NA NA NA NA NA ...
## $ max_picth_dumbbell : num NA NA NA NA NA NA NA NA NA NA ...
## $ max_yaw_dumbbell : Factor w/ 73 levels "","-0.1","-0.2",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ min_roll_dumbbell : num NA NA NA NA NA NA NA NA NA NA ...
## $ min_pitch_dumbbell : num NA NA NA NA NA NA NA NA NA NA ...
## $ min_yaw_dumbbell : Factor w/ 73 levels "","-0.1","-0.2",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ amplitude_roll_dumbbell : num NA NA NA NA NA NA NA NA NA NA ...
## [list output truncated]head(trainingData)## X user_name raw_timestamp_part_1 raw_timestamp_part_2 cvtd_timestamp
## 1 1 carlitos 1323084231 788290 05/12/2011 11:23
## 2 2 carlitos 1323084231 808298 05/12/2011 11:23
## 3 3 carlitos 1323084231 820366 05/12/2011 11:23
## 4 4 carlitos 1323084232 120339 05/12/2011 11:23
## 5 5 carlitos 1323084232 196328 05/12/2011 11:23
## 6 6 carlitos 1323084232 304277 05/12/2011 11:23
## new_window num_window roll_belt pitch_belt yaw_belt total_accel_belt
## 1 no 11 1.41 8.07 -94.4 3
## 2 no 11 1.41 8.07 -94.4 3
## 3 no 11 1.42 8.07 -94.4 3
## 4 no 12 1.48 8.05 -94.4 3
## 5 no 12 1.48 8.07 -94.4 3
## 6 no 12 1.45 8.06 -94.4 3
## kurtosis_roll_belt kurtosis_picth_belt kurtosis_yaw_belt skewness_roll_belt
## 1
## 2
## 3
## 4
## 5
## 6
## skewness_roll_belt.1 skewness_yaw_belt max_roll_belt max_picth_belt
## 1 NA NA
## 2 NA NA
## 3 NA NA
## 4 NA NA
## 5 NA NA
## 6 NA NA
## max_yaw_belt min_roll_belt min_pitch_belt min_yaw_belt amplitude_roll_belt
## 1 NA NA NA
## 2 NA NA NA
## 3 NA NA NA
## 4 NA NA NA
## 5 NA NA NA
## 6 NA NA NA
## amplitude_pitch_belt amplitude_yaw_belt var_total_accel_belt avg_roll_belt
## 1 NA NA NA
## 2 NA NA NA
## 3 NA NA NA
## 4 NA NA NA
## 5 NA NA NA
## 6 NA NA NA
## stddev_roll_belt var_roll_belt avg_pitch_belt stddev_pitch_belt
## 1 NA NA NA NA
## 2 NA NA NA NA
## 3 NA NA NA NA
## 4 NA NA NA NA
## 5 NA NA NA NA
## 6 NA NA NA NA
## var_pitch_belt avg_yaw_belt stddev_yaw_belt var_yaw_belt gyros_belt_x
## 1 NA NA NA NA 0.00
## 2 NA NA NA NA 0.02
## 3 NA NA NA NA 0.00
## 4 NA NA NA NA 0.02
## 5 NA NA NA NA 0.02
## 6 NA NA NA NA 0.02
## gyros_belt_y gyros_belt_z accel_belt_x accel_belt_y accel_belt_z
## 1 0.00 -0.02 -21 4 22
## 2 0.00 -0.02 -22 4 22
## 3 0.00 -0.02 -20 5 23
## 4 0.00 -0.03 -22 3 21
## 5 0.02 -0.02 -21 2 24
## 6 0.00 -0.02 -21 4 21
## magnet_belt_x magnet_belt_y magnet_belt_z roll_arm pitch_arm yaw_arm
## 1 -3 599 -313 -128 22.5 -161
## 2 -7 608 -311 -128 22.5 -161
## 3 -2 600 -305 -128 22.5 -161
## 4 -6 604 -310 -128 22.1 -161
## 5 -6 600 -302 -128 22.1 -161
## 6 0 603 -312 -128 22.0 -161
## total_accel_arm var_accel_arm avg_roll_arm stddev_roll_arm var_roll_arm
## 1 34 NA NA NA NA
## 2 34 NA NA NA NA
## 3 34 NA NA NA NA
## 4 34 NA NA NA NA
## 5 34 NA NA NA NA
## 6 34 NA NA NA NA
## avg_pitch_arm stddev_pitch_arm var_pitch_arm avg_yaw_arm stddev_yaw_arm
## 1 NA NA NA NA NA
## 2 NA NA NA NA NA
## 3 NA NA NA NA NA
## 4 NA NA NA NA NA
## 5 NA NA NA NA NA
## 6 NA NA NA NA NA
## var_yaw_arm gyros_arm_x gyros_arm_y gyros_arm_z accel_arm_x accel_arm_y
## 1 NA 0.00 0.00 -0.02 -288 109
## 2 NA 0.02 -0.02 -0.02 -290 110
## 3 NA 0.02 -0.02 -0.02 -289 110
## 4 NA 0.02 -0.03 0.02 -289 111
## 5 NA 0.00 -0.03 0.00 -289 111
## 6 NA 0.02 -0.03 0.00 -289 111
## accel_arm_z magnet_arm_x magnet_arm_y magnet_arm_z kurtosis_roll_arm
## 1 -123 -368 337 516
## 2 -125 -369 337 513
## 3 -126 -368 344 513
## 4 -123 -372 344 512
## 5 -123 -374 337 506
## 6 -122 -369 342 513
## kurtosis_picth_arm kurtosis_yaw_arm skewness_roll_arm skewness_pitch_arm
## 1
## 2
## 3
## 4
## 5
## 6
## skewness_yaw_arm max_roll_arm max_picth_arm max_yaw_arm min_roll_arm
## 1 NA NA NA NA
## 2 NA NA NA NA
## 3 NA NA NA NA
## 4 NA NA NA NA
## 5 NA NA NA NA
## 6 NA NA NA NA
## min_pitch_arm min_yaw_arm amplitude_roll_arm amplitude_pitch_arm
## 1 NA NA NA NA
## 2 NA NA NA NA
## 3 NA NA NA NA
## 4 NA NA NA NA
## 5 NA NA NA NA
## 6 NA NA NA NA
## amplitude_yaw_arm roll_dumbbell pitch_dumbbell yaw_dumbbell
## 1 NA 13.05217 -70.49400 -84.87394
## 2 NA 13.13074 -70.63751 -84.71065
## 3 NA 12.85075 -70.27812 -85.14078
## 4 NA 13.43120 -70.39379 -84.87363
## 5 NA 13.37872 -70.42856 -84.85306
## 6 NA 13.38246 -70.81759 -84.46500
## kurtosis_roll_dumbbell kurtosis_picth_dumbbell kurtosis_yaw_dumbbell
## 1
## 2
## 3
## 4
## 5
## 6
## skewness_roll_dumbbell skewness_pitch_dumbbell skewness_yaw_dumbbell
## 1
## 2
## 3
## 4
## 5
## 6
## max_roll_dumbbell max_picth_dumbbell max_yaw_dumbbell min_roll_dumbbell
## 1 NA NA NA
## 2 NA NA NA
## 3 NA NA NA
## 4 NA NA NA
## 5 NA NA NA
## 6 NA NA NA
## min_pitch_dumbbell min_yaw_dumbbell amplitude_roll_dumbbell
## 1 NA NA
## 2 NA NA
## 3 NA NA
## 4 NA NA
## 5 NA NA
## 6 NA NA
## amplitude_pitch_dumbbell amplitude_yaw_dumbbell total_accel_dumbbell
## 1 NA 37
## 2 NA 37
## 3 NA 37
## 4 NA 37
## 5 NA 37
## 6 NA 37
## var_accel_dumbbell avg_roll_dumbbell stddev_roll_dumbbell var_roll_dumbbell
## 1 NA NA NA NA
## 2 NA NA NA NA
## 3 NA NA NA NA
## 4 NA NA NA NA
## 5 NA NA NA NA
## 6 NA NA NA NA
## avg_pitch_dumbbell stddev_pitch_dumbbell var_pitch_dumbbell avg_yaw_dumbbell
## 1 NA NA NA NA
## 2 NA NA NA NA
## 3 NA NA NA NA
## 4 NA NA NA NA
## 5 NA NA NA NA
## 6 NA NA NA NA
## stddev_yaw_dumbbell var_yaw_dumbbell gyros_dumbbell_x gyros_dumbbell_y
## 1 NA NA 0 -0.02
## 2 NA NA 0 -0.02
## 3 NA NA 0 -0.02
## 4 NA NA 0 -0.02
## 5 NA NA 0 -0.02
## 6 NA NA 0 -0.02
## gyros_dumbbell_z accel_dumbbell_x accel_dumbbell_y accel_dumbbell_z
## 1 0.00 -234 47 -271
## 2 0.00 -233 47 -269
## 3 0.00 -232 46 -270
## 4 -0.02 -232 48 -269
## 5 0.00 -233 48 -270
## 6 0.00 -234 48 -269
## magnet_dumbbell_x magnet_dumbbell_y magnet_dumbbell_z roll_forearm
## 1 -559 293 -65 28.4
## 2 -555 296 -64 28.3
## 3 -561 298 -63 28.3
## 4 -552 303 -60 28.1
## 5 -554 292 -68 28.0
## 6 -558 294 -66 27.9
## pitch_forearm yaw_forearm kurtosis_roll_forearm kurtosis_picth_forearm
## 1 -63.9 -153
## 2 -63.9 -153
## 3 -63.9 -152
## 4 -63.9 -152
## 5 -63.9 -152
## 6 -63.9 -152
## kurtosis_yaw_forearm skewness_roll_forearm skewness_pitch_forearm
## 1
## 2
## 3
## 4
## 5
## 6
## skewness_yaw_forearm max_roll_forearm max_picth_forearm max_yaw_forearm
## 1 NA NA
## 2 NA NA
## 3 NA NA
## 4 NA NA
## 5 NA NA
## 6 NA NA
## min_roll_forearm min_pitch_forearm min_yaw_forearm amplitude_roll_forearm
## 1 NA NA NA
## 2 NA NA NA
## 3 NA NA NA
## 4 NA NA NA
## 5 NA NA NA
## 6 NA NA NA
## amplitude_pitch_forearm amplitude_yaw_forearm total_accel_forearm
## 1 NA 36
## 2 NA 36
## 3 NA 36
## 4 NA 36
## 5 NA 36
## 6 NA 36
## var_accel_forearm avg_roll_forearm stddev_roll_forearm var_roll_forearm
## 1 NA NA NA NA
## 2 NA NA NA NA
## 3 NA NA NA NA
## 4 NA NA NA NA
## 5 NA NA NA NA
## 6 NA NA NA NA
## avg_pitch_forearm stddev_pitch_forearm var_pitch_forearm avg_yaw_forearm
## 1 NA NA NA NA
## 2 NA NA NA NA
## 3 NA NA NA NA
## 4 NA NA NA NA
## 5 NA NA NA NA
## 6 NA NA NA NA
## stddev_yaw_forearm var_yaw_forearm gyros_forearm_x gyros_forearm_y
## 1 NA NA 0.03 0.00
## 2 NA NA 0.02 0.00
## 3 NA NA 0.03 -0.02
## 4 NA NA 0.02 -0.02
## 5 NA NA 0.02 0.00
## 6 NA NA 0.02 -0.02
## gyros_forearm_z accel_forearm_x accel_forearm_y accel_forearm_z
## 1 -0.02 192 203 -215
## 2 -0.02 192 203 -216
## 3 0.00 196 204 -213
## 4 0.00 189 206 -214
## 5 -0.02 189 206 -214
## 6 -0.03 193 203 -215
## magnet_forearm_x magnet_forearm_y magnet_forearm_z classe
## 1 -17 654 476 A
## 2 -18 661 473 A
## 3 -18 658 469 A
## 4 -16 658 469 A
## 5 -17 655 473 A
## 6 -9 660 478 AThe predicted variable, or way in which the dumbbell exercise was performed, is “classe”. There are 160 variables and 19622 observations.
# subdivide training data set into training and test set
set.seed(242)
inTrainingSet <- createDataPartition(trainingData$classe, p=0.7, list=FALSE)
trainingSet <- trainingData[inTrainingSet,]
testingSet <- trainingData[-inTrainingSet,]Features that will not add any substantial information to the prediction model should be removed. These include ID variables, variables with mostly NA values, and variables with near-zero variance.
From the summary, the first five columns of the dataset can easily be interpreted as ID variables. These are removed from the training, testing and validation sets:
trainingSet <- trainingSet[, -(1:5)]
testingSet <- testingSet[, -(1:5)]
validationSet <- validationSet[, -(1:5)]Next, variables with “NA” values for at least 90% of observations are removed from the training, testing and validation sets, with the percentage of “NA” values based on the training set:
mostlyNAvals <- sapply(trainingSet, function(x) mean(is.na(x))) > 0.90
trainingSet <- trainingSet[, mostlyNAvals==FALSE]
testingSet <- testingSet[, mostlyNAvals==FALSE]
validationSet <- validationSet[, mostlyNAvals==FALSE]Finally, near-zero variance variables are removed from the training, testing and validation sets, based on the variables’ variances in the training set:
nearZeroVar <- nearZeroVar(trainingSet)
trainingSet <- trainingSet[, -nearZeroVar]
testingSet <- testingSet[, -nearZeroVar]
validationSet <- validationSet[, -nearZeroVar]dim(trainingSet)## [1] 13737 54The total number of variables has been reduced from 160 to 54.
Exploratory Data Analysis
To qualitatively determine if the number of features should be further reduced, the correlation values between all predictor variable pairs are plotted using the training set:
correlations <- cor(trainingSet[, -length(names(trainingSet))])
par(xpd=TRUE)
corrplot(correlations, method="color", type="lower", tl.cex=0.6, tl.col=rgb(0, 0, 0), order = "FPC", mar = c(2, 2, 2, 2))
Although most predictor variable pairs have a low correlation, there are some variable pairs that appear to be nearly perfectly correlated or anticorrelated. Applying Principal Component Analysis (PCA) would further reduce the number of features. However, the interpretability of the prediction model would also be greatly reduced by creating features out of combinations of individual predictor variables. Ideally, the resulting prediction model could be used to also provide user specific feedback regarding why an exercise was performed incorrectly. Therefore, PCA will not be applied here.
Prediction Model Building and Model Selection
Three prediction models are built from the training set, using 5-fold cross-validation, and then applied to the testing set to determine the expected out-of-sample error. The model with the highest accuracy, i.e. lowest out-of-sample error, is selected and used to predict the activity type from the validation dataset. For this project, only accuracy will be considered in model selection, although with more information about how the model would be implemented, other factors such as scalability and interpretability could be just as important to take into account.
Before the models are built, the cross-validation parameters are set:
cvControl <- trainControl(method="cv", number=5, verboseIter=FALSE)Model 1: Support-Vector Machine
The support-vector machine model is built from the training data:
model_SVM <- train(classe ~ ., data=trainingSet, method="svmLinear", trcontrol=cvControl, tuneLength=5, verbose=F)and used to predict activity type from the testing data:
predictions_SVM <- predict(model_SVM, testingSet)with the following results:
results_SVM <- confusionMatrix(predictions_SVM, factor(testingSet$classe))
results_SVM## Confusion Matrix and Statistics
##
## Reference
## Prediction A B C D E
## A 1542 154 76 54 38
## B 47 821 105 38 118
## C 36 66 786 102 75
## D 41 19 25 727 64
## E 8 79 34 43 787
##
## Overall Statistics
##
## Accuracy : 0.7924
## 95% CI : (0.7818, 0.8027)
## No Information Rate : 0.2845
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.7362
##
## Mcnemar's Test P-Value : < 2.2e-16
##
## Statistics by Class:
##
## Class: A Class: B Class: C Class: D Class: E
## Sensitivity 0.9211 0.7208 0.7661 0.7541 0.7274
## Specificity 0.9235 0.9351 0.9426 0.9697 0.9659
## Pos Pred Value 0.8273 0.7272 0.7380 0.8299 0.8275
## Neg Pred Value 0.9672 0.9331 0.9502 0.9527 0.9402
## Prevalence 0.2845 0.1935 0.1743 0.1638 0.1839
## Detection Rate 0.2620 0.1395 0.1336 0.1235 0.1337
## Detection Prevalence 0.3167 0.1918 0.1810 0.1489 0.1616
## Balanced Accuracy 0.9223 0.8280 0.8543 0.8619 0.8466The accuracy of the support-vector machine model is 0.7924 with an out-of-sample error of 0.2076.
Model 2: Decision Tree Model
The decision tree model is built from the training data:
model_DT <- train(classe ~ ., data=trainingSet, method="rpart", trControl=cvControl, tuneLength=5)
fancyRpartPlot(model_DT$finalModel)
and used to predict activity type from the testing data:
predictions_DT <- predict(model_DT, testingSet)with the following results:
results_DT <- confusionMatrix(predictions_DT, factor(testingSet$classe))
results_DT## Confusion Matrix and Statistics
##
## Reference
## Prediction A B C D E
## A 1535 322 198 190 23
## B 27 475 33 9 59
## C 87 308 794 554 278
## D 0 34 1 168 19
## E 25 0 0 43 703
##
## Overall Statistics
##
## Accuracy : 0.6245
## 95% CI : (0.612, 0.6369)
## No Information Rate : 0.2845
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.5188
##
## Mcnemar's Test P-Value : < 2.2e-16
##
## Statistics by Class:
##
## Class: A Class: B Class: C Class: D Class: E
## Sensitivity 0.9170 0.41703 0.7739 0.17427 0.6497
## Specificity 0.8259 0.97303 0.7475 0.98903 0.9858
## Pos Pred Value 0.6768 0.78773 0.3929 0.75676 0.9118
## Neg Pred Value 0.9616 0.87429 0.9400 0.85944 0.9259
## Prevalence 0.2845 0.19354 0.1743 0.16381 0.1839
## Detection Rate 0.2608 0.08071 0.1349 0.02855 0.1195
## Detection Prevalence 0.3854 0.10246 0.3434 0.03772 0.1310
## Balanced Accuracy 0.8714 0.69503 0.7607 0.58165 0.8178The accuracy of the decision tree model is 0.6245 with an out-of-sample error of 0.3755.
Model 3: Random Forest Model
The random forest model is built from the training data:
model_RF <- train(classe ~ ., data=trainingSet, method="rf", trainControl=cvControl, tuneLength=5)and used to predict activity type from the testing data:
predictions_RF <- predict(model_RF, testingSet)with the following results:
results_RF <- confusionMatrix(predictions_RF, factor(testingSet$classe))
results_RF## Confusion Matrix and Statistics
##
## Reference
## Prediction A B C D E
## A 1674 4 0 0 0
## B 0 1135 3 0 0
## C 0 0 1023 4 0
## D 0 0 0 960 3
## E 0 0 0 0 1079
##
## Overall Statistics
##
## Accuracy : 0.9976
## 95% CI : (0.996, 0.9987)
## No Information Rate : 0.2845
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.997
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: A Class: B Class: C Class: D Class: E
## Sensitivity 1.0000 0.9965 0.9971 0.9959 0.9972
## Specificity 0.9991 0.9994 0.9992 0.9994 1.0000
## Pos Pred Value 0.9976 0.9974 0.9961 0.9969 1.0000
## Neg Pred Value 1.0000 0.9992 0.9994 0.9992 0.9994
## Prevalence 0.2845 0.1935 0.1743 0.1638 0.1839
## Detection Rate 0.2845 0.1929 0.1738 0.1631 0.1833
## Detection Prevalence 0.2851 0.1934 0.1745 0.1636 0.1833
## Balanced Accuracy 0.9995 0.9979 0.9981 0.9976 0.9986The accuracy of the random forest model is 0.9976 with an out-of-sample error of 0.0024.
Because the out-of-sample error is substantially lower when applying the random forest model compared to the decision tree and support-vector machine model, the random forest model is chosen to predict the class of activity from the validation data.
Predictions from Validation Data
In the last step, activity type is predicted from the validation set. All data pre-processing has already been applied to the validation set in previous steps.
predictValidation <- predict(model_RF, validationSet)
predictValidation## [1] 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