Practical Machine Learning Project
Marijus B
Libraries
library(caret)## Loading required package: lattice## Loading required package: ggplot2library(rattle)## Rattle: A free graphical interface for data science with R.
## Version 5.3.0 Copyright (c) 2006-2018 Togaware Pty Ltd.
## Type 'rattle()' to shake, rattle, and roll your data.library(rpart)
library(rpart.plot)
library(randomForest)## randomForest 4.6-14## Type rfNews() to see new features/changes/bug fixes.##
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library(kernlab)##
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## alphalibrary(ggplot2)
library(MASS)
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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.
Project
The main goal of the project is predict the manner in which exercises were performed by six participants and it is labeled as “classe” in the training data set.
Data for the analysis consists of training and test data sets.
Data will be tested with 4 different models : Classification Tree , Random Forest , Gradient Boosting Method and Linear Discriminant Analysis.
WLE dataset for this project is a courtesy of: Velloso, E.; Bulling, A.; Gellersen, H.; Ugulino, W.; Fuks, H. Qualitative Activity Recognition of Weight Lifting Exercises. Proceedings of 4th International Conference in Cooperation with SIGCHI (Augmented Human ’13) . Stuttgart, Germany: ACM SIGCHI, 2013.
Getting Data
Data is obtained from:
https://d396qusza40orc.cloudfront.net/predmachlearn/pml-training.csv
https://d396qusza40orc.cloudfront.net/predmachlearn/pml-testing.csv
Training Data
trainingData <- read.csv(url("https://d396qusza40orc.cloudfront.net/predmachlearn/pml-training.csv"),header=TRUE)
table(trainingData$classe)##
## A B C D E
## 5580 3797 3422 3216 3607#str(trainingData)
dim(trainingData)## [1] 19622 160#summary(trainingData)Testing Data
testingData <- read.csv(url("https://d396qusza40orc.cloudfront.net/predmachlearn/pml-testing.csv"),header=TRUE)
table(testingData$classe)## < table of extent 0 >#str(testingData)
dim(testingData)## [1] 20 160#summary(testingData)Cleaning Data Sets
Removing variables from the data sets that are close to zero:
NSV <- nearZeroVar(trainingData,saveMetrics=TRUE)
NSV## freqRatio percentUnique zeroVar nzv
## X 1.000000 100.00000000 FALSE FALSE
## user_name 1.100679 0.03057792 FALSE FALSE
## raw_timestamp_part_1 1.000000 4.26562022 FALSE FALSE
## raw_timestamp_part_2 1.000000 85.53154622 FALSE FALSE
## cvtd_timestamp 1.000668 0.10192641 FALSE FALSE
## new_window 47.330049 0.01019264 FALSE TRUE
## num_window 1.000000 4.37264295 FALSE FALSE
## roll_belt 1.101904 6.77810621 FALSE FALSE
## pitch_belt 1.036082 9.37722964 FALSE FALSE
## yaw_belt 1.058480 9.97349913 FALSE FALSE
## total_accel_belt 1.063160 0.14779329 FALSE FALSE
## kurtosis_roll_belt 1921.600000 2.02323922 FALSE TRUE
## kurtosis_picth_belt 600.500000 1.61553358 FALSE TRUE
## kurtosis_yaw_belt 47.330049 0.01019264 FALSE TRUE
## skewness_roll_belt 2135.111111 2.01304658 FALSE TRUE
## skewness_roll_belt.1 600.500000 1.72255631 FALSE TRUE
## skewness_yaw_belt 47.330049 0.01019264 FALSE TRUE
## max_roll_belt 1.000000 0.99378249 FALSE FALSE
## max_picth_belt 1.538462 0.11211905 FALSE FALSE
## max_yaw_belt 640.533333 0.34654979 FALSE TRUE
## min_roll_belt 1.000000 0.93772296 FALSE FALSE
## min_pitch_belt 2.192308 0.08154113 FALSE FALSE
## min_yaw_belt 640.533333 0.34654979 FALSE TRUE
## amplitude_roll_belt 1.290323 0.75425543 FALSE FALSE
## amplitude_pitch_belt 3.042254 0.06625217 FALSE FALSE
## amplitude_yaw_belt 50.041667 0.02038528 FALSE TRUE
## var_total_accel_belt 1.426829 0.33126083 FALSE FALSE
## avg_roll_belt 1.066667 0.97339721 FALSE FALSE
## stddev_roll_belt 1.039216 0.35164611 FALSE FALSE
## var_roll_belt 1.615385 0.48924676 FALSE FALSE
## avg_pitch_belt 1.375000 1.09061258 FALSE FALSE
## stddev_pitch_belt 1.161290 0.21914178 FALSE FALSE
## var_pitch_belt 1.307692 0.32106819 FALSE FALSE
## avg_yaw_belt 1.200000 1.22311691 FALSE FALSE
## stddev_yaw_belt 1.693878 0.29558659 FALSE FALSE
## var_yaw_belt 1.500000 0.73896647 FALSE FALSE
## gyros_belt_x 1.058651 0.71348486 FALSE FALSE
## gyros_belt_y 1.144000 0.35164611 FALSE FALSE
## gyros_belt_z 1.066214 0.86127816 FALSE FALSE
## accel_belt_x 1.055412 0.83579655 FALSE FALSE
## accel_belt_y 1.113725 0.72877383 FALSE FALSE
## accel_belt_z 1.078767 1.52379982 FALSE FALSE
## magnet_belt_x 1.090141 1.66649679 FALSE FALSE
## magnet_belt_y 1.099688 1.51870350 FALSE FALSE
## magnet_belt_z 1.006369 2.32901845 FALSE FALSE
## roll_arm 52.338462 13.52563449 FALSE FALSE
## pitch_arm 87.256410 15.73234125 FALSE FALSE
## yaw_arm 33.029126 14.65701763 FALSE FALSE
## total_accel_arm 1.024526 0.33635715 FALSE FALSE
## var_accel_arm 5.500000 2.01304658 FALSE FALSE
## avg_roll_arm 77.000000 1.68178575 FALSE TRUE
## stddev_roll_arm 77.000000 1.68178575 FALSE TRUE
## var_roll_arm 77.000000 1.68178575 FALSE TRUE
## avg_pitch_arm 77.000000 1.68178575 FALSE TRUE
## stddev_pitch_arm 77.000000 1.68178575 FALSE TRUE
## var_pitch_arm 77.000000 1.68178575 FALSE TRUE
## avg_yaw_arm 77.000000 1.68178575 FALSE TRUE
## stddev_yaw_arm 80.000000 1.66649679 FALSE TRUE
## var_yaw_arm 80.000000 1.66649679 FALSE TRUE
## gyros_arm_x 1.015504 3.27693405 FALSE FALSE
## gyros_arm_y 1.454369 1.91621649 FALSE FALSE
## gyros_arm_z 1.110687 1.26388747 FALSE FALSE
## accel_arm_x 1.017341 3.95984099 FALSE FALSE
## accel_arm_y 1.140187 2.73672409 FALSE FALSE
## accel_arm_z 1.128000 4.03628580 FALSE FALSE
## magnet_arm_x 1.000000 6.82397309 FALSE FALSE
## magnet_arm_y 1.056818 4.44399144 FALSE FALSE
## magnet_arm_z 1.036364 6.44684538 FALSE FALSE
## kurtosis_roll_arm 246.358974 1.68178575 FALSE TRUE
## kurtosis_picth_arm 240.200000 1.67159311 FALSE TRUE
## kurtosis_yaw_arm 1746.909091 2.01304658 FALSE TRUE
## skewness_roll_arm 249.558442 1.68688207 FALSE TRUE
## skewness_pitch_arm 240.200000 1.67159311 FALSE TRUE
## skewness_yaw_arm 1746.909091 2.01304658 FALSE TRUE
## max_roll_arm 25.666667 1.47793293 FALSE TRUE
## max_picth_arm 12.833333 1.34033228 FALSE FALSE
## max_yaw_arm 1.227273 0.25991234 FALSE FALSE
## min_roll_arm 19.250000 1.41677709 FALSE TRUE
## min_pitch_arm 19.250000 1.47793293 FALSE TRUE
## min_yaw_arm 1.000000 0.19366018 FALSE FALSE
## amplitude_roll_arm 25.666667 1.55947406 FALSE TRUE
## amplitude_pitch_arm 20.000000 1.49831821 FALSE TRUE
## amplitude_yaw_arm 1.037037 0.25991234 FALSE FALSE
## roll_dumbbell 1.022388 84.20650290 FALSE FALSE
## pitch_dumbbell 2.277372 81.74498012 FALSE FALSE
## yaw_dumbbell 1.132231 83.48282540 FALSE FALSE
## kurtosis_roll_dumbbell 3843.200000 2.02833554 FALSE TRUE
## kurtosis_picth_dumbbell 9608.000000 2.04362450 FALSE TRUE
## kurtosis_yaw_dumbbell 47.330049 0.01019264 FALSE TRUE
## skewness_roll_dumbbell 4804.000000 2.04362450 FALSE TRUE
## skewness_pitch_dumbbell 9608.000000 2.04872082 FALSE TRUE
## skewness_yaw_dumbbell 47.330049 0.01019264 FALSE TRUE
## max_roll_dumbbell 1.000000 1.72255631 FALSE FALSE
## max_picth_dumbbell 1.333333 1.72765263 FALSE FALSE
## max_yaw_dumbbell 960.800000 0.37203139 FALSE TRUE
## min_roll_dumbbell 1.000000 1.69197839 FALSE FALSE
## min_pitch_dumbbell 1.666667 1.81429008 FALSE FALSE
## min_yaw_dumbbell 960.800000 0.37203139 FALSE TRUE
## amplitude_roll_dumbbell 8.000000 1.97227602 FALSE FALSE
## amplitude_pitch_dumbbell 8.000000 1.95189073 FALSE FALSE
## amplitude_yaw_dumbbell 47.920200 0.01528896 FALSE TRUE
## total_accel_dumbbell 1.072634 0.21914178 FALSE FALSE
## var_accel_dumbbell 6.000000 1.95698706 FALSE FALSE
## avg_roll_dumbbell 1.000000 2.02323922 FALSE FALSE
## stddev_roll_dumbbell 16.000000 1.99266130 FALSE FALSE
## var_roll_dumbbell 16.000000 1.99266130 FALSE FALSE
## avg_pitch_dumbbell 1.000000 2.02323922 FALSE FALSE
## stddev_pitch_dumbbell 16.000000 1.99266130 FALSE FALSE
## var_pitch_dumbbell 16.000000 1.99266130 FALSE FALSE
## avg_yaw_dumbbell 1.000000 2.02323922 FALSE FALSE
## stddev_yaw_dumbbell 16.000000 1.99266130 FALSE FALSE
## var_yaw_dumbbell 16.000000 1.99266130 FALSE FALSE
## gyros_dumbbell_x 1.003268 1.22821323 FALSE FALSE
## gyros_dumbbell_y 1.264957 1.41677709 FALSE FALSE
## gyros_dumbbell_z 1.060100 1.04984201 FALSE FALSE
## accel_dumbbell_x 1.018018 2.16593619 FALSE FALSE
## accel_dumbbell_y 1.053061 2.37488533 FALSE FALSE
## accel_dumbbell_z 1.133333 2.08949139 FALSE FALSE
## magnet_dumbbell_x 1.098266 5.74864948 FALSE FALSE
## magnet_dumbbell_y 1.197740 4.30129447 FALSE FALSE
## magnet_dumbbell_z 1.020833 3.44511263 FALSE FALSE
## roll_forearm 11.589286 11.08959331 FALSE FALSE
## pitch_forearm 65.983051 14.85577413 FALSE FALSE
## yaw_forearm 15.322835 10.14677403 FALSE FALSE
## kurtosis_roll_forearm 228.761905 1.64101519 FALSE TRUE
## kurtosis_picth_forearm 226.070588 1.64611151 FALSE TRUE
## kurtosis_yaw_forearm 47.330049 0.01019264 FALSE TRUE
## skewness_roll_forearm 231.518072 1.64611151 FALSE TRUE
## skewness_pitch_forearm 226.070588 1.62572623 FALSE TRUE
## skewness_yaw_forearm 47.330049 0.01019264 FALSE TRUE
## max_roll_forearm 27.666667 1.38110284 FALSE TRUE
## max_picth_forearm 2.964286 0.78992967 FALSE FALSE
## max_yaw_forearm 228.761905 0.22933442 FALSE TRUE
## min_roll_forearm 27.666667 1.37091020 FALSE TRUE
## min_pitch_forearm 2.862069 0.87147080 FALSE FALSE
## min_yaw_forearm 228.761905 0.22933442 FALSE TRUE
## amplitude_roll_forearm 20.750000 1.49322189 FALSE TRUE
## amplitude_pitch_forearm 3.269231 0.93262664 FALSE FALSE
## amplitude_yaw_forearm 59.677019 0.01528896 FALSE TRUE
## total_accel_forearm 1.128928 0.35674243 FALSE FALSE
## var_accel_forearm 3.500000 2.03343186 FALSE FALSE
## avg_roll_forearm 27.666667 1.64101519 FALSE TRUE
## stddev_roll_forearm 87.000000 1.63082255 FALSE TRUE
## var_roll_forearm 87.000000 1.63082255 FALSE TRUE
## avg_pitch_forearm 83.000000 1.65120783 FALSE TRUE
## stddev_pitch_forearm 41.500000 1.64611151 FALSE TRUE
## var_pitch_forearm 83.000000 1.65120783 FALSE TRUE
## avg_yaw_forearm 83.000000 1.65120783 FALSE TRUE
## stddev_yaw_forearm 85.000000 1.64101519 FALSE TRUE
## var_yaw_forearm 85.000000 1.64101519 FALSE TRUE
## gyros_forearm_x 1.059273 1.51870350 FALSE FALSE
## gyros_forearm_y 1.036554 3.77637346 FALSE FALSE
## gyros_forearm_z 1.122917 1.56457038 FALSE FALSE
## accel_forearm_x 1.126437 4.04647844 FALSE FALSE
## accel_forearm_y 1.059406 5.11160942 FALSE FALSE
## accel_forearm_z 1.006250 2.95586586 FALSE FALSE
## magnet_forearm_x 1.012346 7.76679238 FALSE FALSE
## magnet_forearm_y 1.246914 9.54031189 FALSE FALSE
## magnet_forearm_z 1.000000 8.57710733 FALSE FALSE
## classe 1.469581 0.02548160 FALSE FALSEnsv <- nearZeroVar(trainingData)
nsv## [1] 6 12 13 14 15 16 17 20 23 26 51 52 53 54 55 56 57 58 59
## [20] 69 70 71 72 73 74 75 78 79 81 82 87 88 89 90 91 92 95 98
## [39] 101 125 126 127 128 129 130 131 133 134 136 137 139 142 143 144 145 146 147
## [58] 148 149 150training <- trainingData[, -nsv]
testing <- testingData[, -nsv]
dim(training)## [1] 19622 100dim(testing)## [1] 20 100Removing missing values, NAs from data sets:
indColToRemove <- which(colSums(is.na(trainingData) |trainingData=="")>0.8*dim(trainingData)[1])
training <- trainingData[,-indColToRemove]
str(training)## 'data.frame': 19622 obs. of 60 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 ...
## $ 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 ...dim(training)## [1] 19622 60indColToRemove <- which(colSums(is.na(testingData) |testingData=="")>0.8*dim(testingData)[1])
testing <- testingData[,-indColToRemove]
str(testing)## 'data.frame': 20 obs. of 60 variables:
## $ X : int 1 2 3 4 5 6 7 8 9 10 ...
## $ user_name : Factor w/ 6 levels "adelmo","carlitos",..: 6 5 5 1 4 5 5 5 2 3 ...
## $ raw_timestamp_part_1: int 1323095002 1322673067 1322673075 1322832789 1322489635 1322673149 1322673128 1322673076 1323084240 1322837822 ...
## $ raw_timestamp_part_2: int 868349 778725 342967 560311 814776 510661 766645 54671 916313 384285 ...
## $ cvtd_timestamp : Factor w/ 11 levels "02/12/2011 13:33",..: 5 10 10 1 6 11 11 10 3 2 ...
## $ new_window : Factor w/ 1 level "no": 1 1 1 1 1 1 1 1 1 1 ...
## $ num_window : int 74 431 439 194 235 504 485 440 323 664 ...
## $ roll_belt : num 123 1.02 0.87 125 1.35 -5.92 1.2 0.43 0.93 114 ...
## $ pitch_belt : num 27 4.87 1.82 -41.6 3.33 1.59 4.44 4.15 6.72 22.4 ...
## $ yaw_belt : num -4.75 -88.9 -88.5 162 -88.6 -87.7 -87.3 -88.5 -93.7 -13.1 ...
## $ total_accel_belt : int 20 4 5 17 3 4 4 4 4 18 ...
## $ gyros_belt_x : num -0.5 -0.06 0.05 0.11 0.03 0.1 -0.06 -0.18 0.1 0.14 ...
## $ gyros_belt_y : num -0.02 -0.02 0.02 0.11 0.02 0.05 0 -0.02 0 0.11 ...
## $ gyros_belt_z : num -0.46 -0.07 0.03 -0.16 0 -0.13 0 -0.03 -0.02 -0.16 ...
## $ accel_belt_x : int -38 -13 1 46 -8 -11 -14 -10 -15 -25 ...
## $ accel_belt_y : int 69 11 -1 45 4 -16 2 -2 1 63 ...
## $ accel_belt_z : int -179 39 49 -156 27 38 35 42 32 -158 ...
## $ magnet_belt_x : int -13 43 29 169 33 31 50 39 -6 10 ...
## $ magnet_belt_y : int 581 636 631 608 566 638 622 635 600 601 ...
## $ magnet_belt_z : int -382 -309 -312 -304 -418 -291 -315 -305 -302 -330 ...
## $ roll_arm : num 40.7 0 0 -109 76.1 0 0 0 -137 -82.4 ...
## $ pitch_arm : num -27.8 0 0 55 2.76 0 0 0 11.2 -63.8 ...
## $ yaw_arm : num 178 0 0 -142 102 0 0 0 -167 -75.3 ...
## $ total_accel_arm : int 10 38 44 25 29 14 15 22 34 32 ...
## $ gyros_arm_x : num -1.65 -1.17 2.1 0.22 -1.96 0.02 2.36 -3.71 0.03 0.26 ...
## $ gyros_arm_y : num 0.48 0.85 -1.36 -0.51 0.79 0.05 -1.01 1.85 -0.02 -0.5 ...
## $ gyros_arm_z : num -0.18 -0.43 1.13 0.92 -0.54 -0.07 0.89 -0.69 -0.02 0.79 ...
## $ accel_arm_x : int 16 -290 -341 -238 -197 -26 99 -98 -287 -301 ...
## $ accel_arm_y : int 38 215 245 -57 200 130 79 175 111 -42 ...
## $ accel_arm_z : int 93 -90 -87 6 -30 -19 -67 -78 -122 -80 ...
## $ magnet_arm_x : int -326 -325 -264 -173 -170 396 702 535 -367 -420 ...
## $ magnet_arm_y : int 385 447 474 257 275 176 15 215 335 294 ...
## $ magnet_arm_z : int 481 434 413 633 617 516 217 385 520 493 ...
## $ roll_dumbbell : num -17.7 54.5 57.1 43.1 -101.4 ...
## $ pitch_dumbbell : num 25 -53.7 -51.4 -30 -53.4 ...
## $ yaw_dumbbell : num 126.2 -75.5 -75.2 -103.3 -14.2 ...
## $ total_accel_dumbbell: int 9 31 29 18 4 29 29 29 3 2 ...
## $ gyros_dumbbell_x : num 0.64 0.34 0.39 0.1 0.29 -0.59 0.34 0.37 0.03 0.42 ...
## $ gyros_dumbbell_y : num 0.06 0.05 0.14 -0.02 -0.47 0.8 0.16 0.14 -0.21 0.51 ...
## $ gyros_dumbbell_z : num -0.61 -0.71 -0.34 0.05 -0.46 1.1 -0.23 -0.39 -0.21 -0.03 ...
## $ accel_dumbbell_x : int 21 -153 -141 -51 -18 -138 -145 -140 0 -7 ...
## $ accel_dumbbell_y : int -15 155 155 72 -30 166 150 159 25 -20 ...
## $ accel_dumbbell_z : int 81 -205 -196 -148 -5 -186 -190 -191 9 7 ...
## $ magnet_dumbbell_x : int 523 -502 -506 -576 -424 -543 -484 -515 -519 -531 ...
## $ magnet_dumbbell_y : int -528 388 349 238 252 262 354 350 348 321 ...
## $ magnet_dumbbell_z : int -56 -36 41 53 312 96 97 53 -32 -164 ...
## $ roll_forearm : num 141 109 131 0 -176 150 155 -161 15.5 13.2 ...
## $ pitch_forearm : num 49.3 -17.6 -32.6 0 -2.16 1.46 34.5 43.6 -63.5 19.4 ...
## $ yaw_forearm : num 156 106 93 0 -47.9 89.7 152 -89.5 -139 -105 ...
## $ total_accel_forearm : int 33 39 34 43 24 43 32 47 36 24 ...
## $ gyros_forearm_x : num 0.74 1.12 0.18 1.38 -0.75 -0.88 -0.53 0.63 0.03 0.02 ...
## $ gyros_forearm_y : num -3.34 -2.78 -0.79 0.69 3.1 4.26 1.8 -0.74 0.02 0.13 ...
## $ gyros_forearm_z : num -0.59 -0.18 0.28 1.8 0.8 1.35 0.75 0.49 -0.02 -0.07 ...
## $ accel_forearm_x : int -110 212 154 -92 131 230 -192 -151 195 -212 ...
## $ accel_forearm_y : int 267 297 271 406 -93 322 170 -331 204 98 ...
## $ accel_forearm_z : int -149 -118 -129 -39 172 -144 -175 -282 -217 -7 ...
## $ magnet_forearm_x : int -714 -237 -51 -233 375 -300 -678 -109 0 -403 ...
## $ magnet_forearm_y : int 419 791 698 783 -787 800 284 -619 652 723 ...
## $ magnet_forearm_z : int 617 873 783 521 91 884 585 -32 469 512 ...
## $ problem_id : int 1 2 3 4 5 6 7 8 9 10 ...dim(testing)## [1] 20 60Removing variables from data sets with no significance:
training <- training[,-c(1:7)]
testing <- testing[,-c(1:7)]dim(training)## [1] 19622 53dim(testing)## [1] 20 53After removing variables that has no significant role in modeling and NAs split training data set (partition) into 75% and 25% as Training and Testing data sets respectivelly:
set.seed(1234)
inTrain <- createDataPartition(y=training$classe,p=0.75, list=FALSE)
Training <- training[inTrain,]
Testing <- training[-inTrain,]New dimensions of data sets:
dim(Training)## [1] 14718 53dim(Testing)## [1] 4904 53Correlation matrix of columns to map correleted predictors:
Corr_Matrix <- cor(Training[, -53])
corrplot(Corr_Matrix, order = "FPC", method = "color",
tl.cex = 0.6, tl.col = rgb(0, 0, 0))
Testing Models
This data analysis will test four models: Classification Tree , Random Forest, Gradient Boosting Method, Linear Discriminant Analysis.
Random Forest model:
set.seed(4567)
trControl <- trainControl(method="cv", number=10)
mod_rf <- train(classe ~ ., data = Training, method = "rf", trControl=trControl, verbose=FALSE, ntree = 200)print(mod_rf)plot(mod_rf,col="red", main="Random Forest Model vs Number of Predictors")
Validating Random Forest model:
pred_rf <- predict(mod_rf, Testing)ConfMatRF <- confusionMatrix(pred_rf, Testing$classe)
ConfMatRF## Confusion Matrix and Statistics
##
## Reference
## Prediction A B C D E
## A 1393 10 0 0 0
## B 1 938 5 0 0
## C 1 1 848 4 0
## D 0 0 2 800 1
## E 0 0 0 0 900
##
## Overall Statistics
##
## Accuracy : 0.9949
## 95% CI : (0.9925, 0.9967)
## No Information Rate : 0.2845
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.9936
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: A Class: B Class: C Class: D Class: E
## Sensitivity 0.9986 0.9884 0.9918 0.9950 0.9989
## Specificity 0.9972 0.9985 0.9985 0.9993 1.0000
## Pos Pred Value 0.9929 0.9936 0.9930 0.9963 1.0000
## Neg Pred Value 0.9994 0.9972 0.9983 0.9990 0.9998
## Prevalence 0.2845 0.1935 0.1743 0.1639 0.1837
## Detection Rate 0.2841 0.1913 0.1729 0.1631 0.1835
## Detection Prevalence 0.2861 0.1925 0.1741 0.1637 0.1835
## Balanced Accuracy 0.9979 0.9934 0.9952 0.9971 0.9994Confusion matrix and model accuracy
ConfMatRF$table## Reference
## Prediction A B C D E
## A 1393 10 0 0 0
## B 1 938 5 0 0
## C 1 1 848 4 0
## D 0 0 2 800 1
## E 0 0 0 0 900Accuracy of the Random Forest model:
ConfMatRF$overall[1]## Accuracy
## 0.9949021Accuracy of the Random Forest model is high, 99.4% which is most likely due to overfitting.
Linear Discriminant Analysis Model
mod_lda <- lda(classe~., data = Training)
plot(mod_lda)
lda.data <- cbind(Training, predict(mod_lda)$x)
ggplot(lda.data, aes(LD1, LD2)) +
geom_point(aes(color = classe))
Validating model:
pred_lda <- predict(mod_lda, Testing)Accuracy of Linear Discriminant Analysis model:
mean(pred_lda$class==Testing$classe)## [1] 0.6969821Accuracy of model is around 70%.
Misclasification rate:
lda.pred = (pred_lda$class)
lda.error = mean(Testing$classe != lda.pred)
lda.error## [1] 0.3030179Gradient Boosting Method
Model_GBM <- train(classe~., data=Training, method="gbm", trControl=trControl, verbose=FALSE)print(Model_GBM)## Stochastic Gradient Boosting
##
## 14718 samples
## 52 predictor
## 5 classes: 'A', 'B', 'C', 'D', 'E'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 13247, 13246, 13245, 13245, 13245, 13247, ...
## Resampling results across tuning parameters:
##
## interaction.depth n.trees Accuracy Kappa
## 1 50 0.7511889 0.6844740
## 1 100 0.8209689 0.7733998
## 1 150 0.8535819 0.8147349
## 2 50 0.8533781 0.8142125
## 2 100 0.9056248 0.8805588
## 2 150 0.9292031 0.9103939
## 3 50 0.8955038 0.8677166
## 3 100 0.9420436 0.9266591
## 3 150 0.9621551 0.9521181
##
## Tuning parameter 'shrinkage' was held constant at a value of 0.1
##
## Tuning parameter 'n.minobsinnode' was held constant at a value of 10
## Accuracy was used to select the optimal model using the largest value.
## The final values used for the model were n.trees = 150, interaction.depth =
## 3, shrinkage = 0.1 and n.minobsinnode = 10.plot(Model_GBM)
Validating the boosting method model:
Model_GBMpred <- predict(Model_GBM,newdata=Testing)
ConfMatGBM <- confusionMatrix(Model_GBMpred, Testing$classe)
ConfMatGBM$table## Reference
## Prediction A B C D E
## A 1379 36 0 1 0
## B 11 896 34 0 10
## C 4 16 810 26 5
## D 1 1 10 769 13
## E 0 0 1 8 873Accuracy of the model:
ConfMatGBM$overall[1]## Accuracy
## 0.963907Accuracy of the Gradient Boosting Method is high, around 96.4%.
Classification Tree Model
trControl <- trainControl(method="cv", number=10)
Model_ClassTree <- train(classe~., data=Training, method="rpart", trControl=trControl)Model_ClassTree$finalModel## n= 14718
##
## node), split, n, loss, yval, (yprob)
## * denotes terminal node
##
## 1) root 14718 10533 A (0.28 0.19 0.17 0.16 0.18)
## 2) roll_belt< 130.5 13465 9291 A (0.31 0.21 0.19 0.18 0.11)
## 4) pitch_forearm< -34 1189 3 A (1 0.0025 0 0 0) *
## 5) pitch_forearm>=-34 12276 9288 A (0.24 0.23 0.21 0.2 0.12)
## 10) magnet_dumbbell_y< 439.5 10403 7478 A (0.28 0.18 0.24 0.19 0.11)
## 20) roll_forearm< 124.5 6467 3844 A (0.41 0.19 0.18 0.17 0.059) *
## 21) roll_forearm>=124.5 3936 2633 C (0.077 0.18 0.33 0.23 0.18) *
## 11) magnet_dumbbell_y>=439.5 1873 931 B (0.034 0.5 0.038 0.23 0.19) *
## 3) roll_belt>=130.5 1253 11 E (0.0088 0 0 0 0.99) *plot(Model_ClassTree$finalModel, uniform=TRUE,
main="Classification Tree")
text(Model_ClassTree$finalModel, use.n=TRUE, all=TRUE, cex=.7)
print(Model_ClassTree)## CART
##
## 14718 samples
## 52 predictor
## 5 classes: 'A', 'B', 'C', 'D', 'E'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 13245, 13247, 13246, 13247, 13247, 13247, ...
## Resampling results across tuning parameters:
##
## cp Accuracy Kappa
## 0.03569733 0.5040773 0.35163107
## 0.05949555 0.4054068 0.19051168
## 0.11687079 0.3257347 0.06298508
##
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was cp = 0.03569733.fancyRpartPlot(Model_ClassTree$finalModel)
Validating Classification Tree model using Testing data set:
Model_ClassTreePred <- predict(Model_ClassTree,newdata=Testing)plot(Model_ClassTreePred, main="Classification Tree Model Prediction" , col="yellow")
confMatClassTree <- confusionMatrix(Model_ClassTreePred, Testing$classe)
confMatClassTree## Confusion Matrix and Statistics
##
## Reference
## Prediction A B C D E
## A 1274 390 401 386 141
## B 18 344 36 131 127
## C 100 215 418 287 244
## D 0 0 0 0 0
## E 3 0 0 0 389
##
## Overall Statistics
##
## Accuracy : 0.4945
## 95% CI : (0.4804, 0.5086)
## No Information Rate : 0.2845
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.3385
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: A Class: B Class: C Class: D Class: E
## Sensitivity 0.9133 0.36249 0.48889 0.0000 0.43174
## Specificity 0.6244 0.92111 0.79106 1.0000 0.99925
## Pos Pred Value 0.4915 0.52439 0.33070 NaN 0.99235
## Neg Pred Value 0.9477 0.85758 0.87995 0.8361 0.88652
## Prevalence 0.2845 0.19352 0.17435 0.1639 0.18373
## Detection Rate 0.2598 0.07015 0.08524 0.0000 0.07932
## Detection Prevalence 0.5285 0.13377 0.25775 0.0000 0.07993
## Balanced Accuracy 0.7688 0.64180 0.63997 0.5000 0.71550confMatClassTree$table## Reference
## Prediction A B C D E
## A 1274 390 401 386 141
## B 18 344 36 131 127
## C 100 215 418 287 244
## D 0 0 0 0 0
## E 3 0 0 0 389Accuracy of the Classification Tree model:
confMatClassTree$overall[1]## Accuracy
## 0.4944943Accuracy of Classification Tree model is around 50% which is very low so this model will not predict well
Conclusions
The most accurate results were using Random Forests model.
Validating Random Forests model with test dataset:
FinalPred <- predict(mod_rf,newdata=testing)
table(FinalPred)## FinalPred
## A B C D E
## 7 8 1 1 3print(FinalPred)## [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