library(ggplot2)
library(dplyr)
library(caret)
library(scales)#pml.training <- read.csv("http://groupware.les.inf.puc-rio.br/static/WLE/WearableComputing_weight_lifting_exercises_biceps_curl_variations.csv", na.strings = c(NA,"","#DIV/0!"))
#pml.training <- read.csv("https://d396qusza40orc.cloudfront.net/predmachlearn/pml-training.csv", na.strings = c(NA,"","#DIV/0!"))
pml.training <- read.csv("pml-training.csv", na.strings = c(NA,"","#DIV/0!"))The data set pml.training is comprised of 19622 observations produced
and released from this source:
http://groupware.les.inf.puc-rio.br/har. We have data on 160 different
variables, some categorical and some numerical.
For data recording they use data from accelerometers on the belt, forearm, arm, and dumbell of 6 participants. Participants were asked to perform one set of 10 repetitions of the Unilateral Dumbbell Biceps Curl in five 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) and throwing the hips to the front (Class E). Class A corresponds to the specified execution of the exercise, while the other 4 classes correspond to common mistakes. The exercises were performed by six male participants aged between 20-28 years, with little weight lifting experience. We made sure that all participants could easily simulate the mistakes in a safe and controlled manner by using a relatively light dumbbell (1.25kg).
pml.training %>%
ggplot(aes(user_name,fill=classe)) +
geom_bar(aes(y=(..count../sum(..count..))))+
scale_y_continuous(labels = percent_format())+
ylab("Percent of exercises") +
xlab("User name partecipant ") +
ggtitle("Percentage of exercises in the sample by classe")
For the Euler angles of each of the four sensors they calculated eight features: mean, variance, standard deviation, max, min, amplitude, kurtosis and skewness, generating in total 96 derived feature sets.
These variables contain numerous missing values (NA) because they concern a single sensor excluding the others. Also 7 variables concerning the name of the participants, the date of execution of the exercises, etc. are not considered in the following analysis as predictors and therefore are excluded. These variables are:
colnames(pml.training)[1:7]## [1] "X" "user_name" "raw_timestamp_part_1"
## [4] "raw_timestamp_part_2" "cvtd_timestamp" "new_window"
## [7] "num_window"
which(colMeans(is.na(pml.training))>0.97)## kurtosis_roll_belt kurtosis_picth_belt kurtosis_yaw_belt
## 12 13 14
## skewness_roll_belt skewness_roll_belt.1 skewness_yaw_belt
## 15 16 17
## max_roll_belt max_picth_belt max_yaw_belt
## 18 19 20
## min_roll_belt min_pitch_belt min_yaw_belt
## 21 22 23
## amplitude_roll_belt amplitude_pitch_belt amplitude_yaw_belt
## 24 25 26
## var_total_accel_belt avg_roll_belt stddev_roll_belt
## 27 28 29
## var_roll_belt avg_pitch_belt stddev_pitch_belt
## 30 31 32
## var_pitch_belt avg_yaw_belt stddev_yaw_belt
## 33 34 35
## var_yaw_belt var_accel_arm avg_roll_arm
## 36 50 51
## stddev_roll_arm var_roll_arm avg_pitch_arm
## 52 53 54
## stddev_pitch_arm var_pitch_arm avg_yaw_arm
## 55 56 57
## stddev_yaw_arm var_yaw_arm kurtosis_roll_arm
## 58 59 69
## kurtosis_picth_arm kurtosis_yaw_arm skewness_roll_arm
## 70 71 72
## skewness_pitch_arm skewness_yaw_arm max_roll_arm
## 73 74 75
## max_picth_arm max_yaw_arm min_roll_arm
## 76 77 78
## min_pitch_arm min_yaw_arm amplitude_roll_arm
## 79 80 81
## amplitude_pitch_arm amplitude_yaw_arm kurtosis_roll_dumbbell
## 82 83 87
## kurtosis_picth_dumbbell kurtosis_yaw_dumbbell skewness_roll_dumbbell
## 88 89 90
## skewness_pitch_dumbbell skewness_yaw_dumbbell max_roll_dumbbell
## 91 92 93
## max_picth_dumbbell max_yaw_dumbbell min_roll_dumbbell
## 94 95 96
## min_pitch_dumbbell min_yaw_dumbbell amplitude_roll_dumbbell
## 97 98 99
## amplitude_pitch_dumbbell amplitude_yaw_dumbbell var_accel_dumbbell
## 100 101 103
## avg_roll_dumbbell stddev_roll_dumbbell var_roll_dumbbell
## 104 105 106
## avg_pitch_dumbbell stddev_pitch_dumbbell var_pitch_dumbbell
## 107 108 109
## avg_yaw_dumbbell stddev_yaw_dumbbell var_yaw_dumbbell
## 110 111 112
## kurtosis_roll_forearm kurtosis_picth_forearm kurtosis_yaw_forearm
## 125 126 127
## skewness_roll_forearm skewness_pitch_forearm skewness_yaw_forearm
## 128 129 130
## max_roll_forearm max_picth_forearm max_yaw_forearm
## 131 132 133
## min_roll_forearm min_pitch_forearm min_yaw_forearm
## 134 135 136
## amplitude_roll_forearm amplitude_pitch_forearm amplitude_yaw_forearm
## 137 138 139
## var_accel_forearm avg_roll_forearm stddev_roll_forearm
## 141 142 143
## var_roll_forearm avg_pitch_forearm stddev_pitch_forearm
## 144 145 146
## var_pitch_forearm avg_yaw_forearm stddev_yaw_forearm
## 147 148 149
## var_yaw_forearm
## 150
pml.training <- subset(pml.training, select = -c(1:7,which(colMeans(is.na(pml.training))>0.97)))Is it possible to predict to which type of class A, B, C, D, E (predicted variable) a weight lifting exercise will belong, using as predictors some of the 52 remaining variables of the data set?
So we’re trying to predict whether weight lifting exercises are of classe A,B,C,D or E. So one thing that we can do right off is use createDataPartition, to separate the data set into training and test sets. If I do this i want a split based on the classe. And I want to create a data set that’s 70%, is allocated to the training set, and 30% is allocated to the testing set.
inTrain <- createDataPartition(y=pml.training$classe, p=0.7,list = FALSE)
training <- pml.training[inTrain,]
testing <- pml.training[-inTrain,]
dim(training); dim(testing)## [1] 13737 53
## [1] 5885 53
I fit a model using the train command from the caret package with algorithm Random Forest . I use the tilde and the dot to say use the other 52 variables in this data frame, in order to predict the variable classe .
Of the 52 predictors we choose the most important, using varImp(), a generic function for calculating variable importance for objects produced by train. The 52 variables are sorted by importance:
get_vars_importance <-function()
{
df <- features$importance
df <- cbind(df,dimnames(features$importance)[1])
names(df)[2]<-"vars"
df <-df %>%
arrange(desc(Overall)) %>%
select(vars,Overall)
return(df)
}
set.seed(1234)
modelFit <- train(classe ~ ., data = training, method="rf", ntree =10)
predictions <- predict(modelFit, newdata = testing)
conf <-confusionMatrix(predictions,testing$classe)
features <- varImp(modelFit)
print(conf$overall[1])## Accuracy
## 0.9857264
df <- get_vars_importance()
df## vars Overall
## 1 roll_belt 100.0000000
## 2 yaw_belt 45.1246821
## 3 roll_forearm 44.3001807
## 4 pitch_belt 41.6992881
## 5 pitch_forearm 40.8997775
## 6 magnet_dumbbell_z 40.3357167
## 7 magnet_dumbbell_y 36.8917573
## 8 accel_forearm_x 22.3237044
## 9 roll_dumbbell 20.3716840
## 10 magnet_belt_z 19.2190295
## 11 accel_dumbbell_y 17.0099801
## 12 magnet_forearm_z 15.7725951
## 13 total_accel_dumbbell 13.3866906
## 14 magnet_dumbbell_x 12.6190913
## 15 accel_dumbbell_z 12.3676513
## 16 magnet_arm_x 10.2622518
## 17 gyros_dumbbell_y 10.0827456
## 18 gyros_belt_z 9.3530427
## 19 roll_arm 9.3277094
## 20 yaw_dumbbell 9.1811635
## 21 magnet_forearm_y 8.0002449
## 22 accel_dumbbell_x 7.8201442
## 23 magnet_belt_x 7.7069185
## 24 magnet_forearm_x 7.5530359
## 25 accel_belt_z 7.5015415
## 26 yaw_forearm 7.2901091
## 27 magnet_arm_y 6.8595394
## 28 yaw_arm 6.6594656
## 29 magnet_belt_y 6.6204262
## 30 accel_forearm_z 6.2495198
## 31 magnet_arm_z 5.3162436
## 32 accel_arm_x 4.8503973
## 33 pitch_arm 4.2329677
## 34 pitch_dumbbell 4.0451321
## 35 gyros_arm_y 3.6832645
## 36 accel_arm_y 3.1315192
## 37 gyros_forearm_z 2.9867542
## 38 gyros_arm_x 2.6934299
## 39 gyros_dumbbell_x 2.5540445
## 40 accel_forearm_y 2.5086419
## 41 gyros_forearm_y 2.4483686
## 42 accel_belt_y 2.1942326
## 43 accel_arm_z 2.0073691
## 44 accel_belt_x 1.8410914
## 45 gyros_belt_x 1.8061482
## 46 gyros_belt_y 1.7653476
## 47 total_accel_forearm 1.3354570
## 48 total_accel_belt 1.1088184
## 49 gyros_dumbbell_z 0.6085910
## 50 gyros_forearm_x 0.3671664
## 51 gyros_arm_z 0.1921715
## 52 total_accel_arm 0.0000000
The following for loop selects the first 7 variables by importance, fit model with Random Forest algorithm and calculates Accuracy of Confusion Matrix, so as to select the model with the greater Accuracy.
for (i in 2:7) {
var_temp <-df$vars[1:i]
f <- paste ( 'classe' ,paste(var_temp, collapse = ' + ' ), sep = ' ~ ')
modelFit <- train(x=training[,as.character(var_temp)], y=training[,c("classe")] , form=f , data = training, method="rf", ntree =10)
predictions <- predict(modelFit, newdata = testing)
conf <-confusionMatrix(predictions,testing$classe)
print(f)
print(conf$overall[1])
df <- get_vars_importance()
}## note: only 1 unique complexity parameters in default grid. Truncating the grid to 1 .
##
## [1] "classe ~ roll_belt + yaw_belt"
## Accuracy
## 0.6966865
## note: only 2 unique complexity parameters in default grid. Truncating the grid to 2 .
##
## [1] "classe ~ roll_belt + yaw_belt + roll_forearm"
## Accuracy
## 0.8669499
## [1] "classe ~ roll_belt + yaw_belt + roll_forearm + pitch_belt"
## Accuracy
## 0.926593
## [1] "classe ~ roll_belt + yaw_belt + roll_forearm + pitch_belt + pitch_forearm"
## Accuracy
## 0.9514019
## [1] "classe ~ roll_belt + yaw_belt + roll_forearm + pitch_belt + pitch_forearm + magnet_dumbbell_z"
## Accuracy
## 0.9717927
## [1] "classe ~ roll_belt + yaw_belt + roll_forearm + pitch_belt + pitch_forearm + magnet_dumbbell_z + magnet_dumbbell_y"
## Accuracy
## 0.97774
The final model is what it has as predictors variables: roll_belt, pitch_forearm, yaw_belt, roll_forearm, magnet_dumbbell_z, magnet_dumbbell_y, pitch_belt , in fact this model has an Accuracy di 0.9765506 with 95% Confidence Interval : (0.9812, 0.9877) .
modelFit <- train(classe ~ roll_belt + pitch_forearm + yaw_belt + roll_forearm + magnet_dumbbell_z + magnet_dumbbell_y + pitch_belt, data = training, method="rf", ntree =100)
predictions <- predict(modelFit, newdata = testing)
confusionMatrix(predictions,testing$classe)## Confusion Matrix and Statistics
##
## Reference
## Prediction A B C D E
## A 1649 4 0 0 0
## B 14 1112 6 1 10
## C 11 18 1010 9 2
## D 0 3 10 954 1
## E 0 2 0 0 1069
##
## Overall Statistics
##
## Accuracy : 0.9845
## 95% CI : (0.981, 0.9875)
## No Information Rate : 0.2845
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.9805
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: A Class: B Class: C Class: D Class: E
## Sensitivity 0.9851 0.9763 0.9844 0.9896 0.9880
## Specificity 0.9991 0.9935 0.9918 0.9972 0.9996
## Pos Pred Value 0.9976 0.9729 0.9619 0.9855 0.9981
## Neg Pred Value 0.9941 0.9943 0.9967 0.9980 0.9973
## Prevalence 0.2845 0.1935 0.1743 0.1638 0.1839
## Detection Rate 0.2802 0.1890 0.1716 0.1621 0.1816
## Detection Prevalence 0.2809 0.1942 0.1784 0.1645 0.1820
## Balanced Accuracy 0.9921 0.9849 0.9881 0.9934 0.9938