# Activity perfomance from body sensor data

## Introduction

For the “Practical Machine Learning” course at Coursera, the class was given a dataset from a Human Activity Recognition (HAR) study1 that tries to assess the quality of an activity (defined as “… the adherence of the execution of an activity to its specification …”), namely a weight lifting exercise, using data from sensors attached to the individuals and their equipment.

In contrast to other HAR studies, this one2 does not attempt to distinguish what activity is being done, but rather to assess how well is the activity being performed.

Figure 1: Location of body sensors3

The aforementioned study used sensors that “… provide three-axes acceleration, gyroscope and magnetometer data …”, with a Bluetooth module that allowed experimental data capture. These sensors were attached (see Figure 1), to “… six male participants aged between 20-28 years …” who performed one set of ten repetitions of the Unilateral Dumbbell Biceps Curl with a 1.25kg (light) dumbbell, in five different manners (one correct and four incorrect):

• 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)

## Getting and cleaning the data

There were two datasets in CSV format, one to be used for training, and another one for testing. The training dataset contained 19622 rows and 160 columns, including the classe variable which classified the entry according to the how well the exercise was performed (vide supra). The testing dataset has only 20 rows and 160 columns, and instead of the classe variable there is an problem_id column to be used as an identifier for the prediction results. The latter set, was to be used for a different part of the assignment dealing with specific class prediction.

Table 1: First 7 columns of the training dataset

Variable Type
X integer
user_name character
raw_timestamp_part_1 integer
raw_timestamp_part_2 integer
cvtd_timestamp character
new_window character
num_window integer

The first seven columns of the training dataset (X, user_name, raw_timestamp_part_1, raw_timestamp_part_2, cvtd_timestamp, new_window, num_window) are not related to the sensor measurements, but rather to the identity of the person, and the time stamps and capture windows for the sensor data (see Table 1). Because I am trying to produce a predictive model that only relies on the quantitative sensor measurements, I decided to remove these columns. In a similar fashion, the first seven columns of the testing dataset were also removed. This operation left me with a total of 153 columns in each data frames.

Thus, the data frame has, for each of the four sensors (positioned at the arm, forearm, belt, and dumbbell respectively), 38 different measurements (see Table 2 in Appendix 1). The problem then is to select from these 152 variables the ones relevant to predict a good exercise execution.

The automatic column type assignment of the read.csv() R function was not always correct, in particular because several of the numeric columns contained text data coming from sensor reading errors (e.g. “#DIV/0!”). So, I forced all of the sensor readings to be numeric, and set the classe column as a factor.

As a result of the type assignment some columns contained only NA values, so these were removed from the dataset. Also, by using the nearZeroVar() function of the caret package, I eliminated columns that were considered uninformative (zero or near zero variance predictors).

Table 3: Number of columns by percentage of missing values

Percentage of missing values Number of columns
0 53
98 65

After that last operation, the training data frame had only 118 variables including the classification column. Of these variables, I checked to see how many of them contained too many missing data values. Initially I set the threshold to 80%, but soon found out that there were two cases: columns without any missing data, and columns that had about 98% missing data (see Table 3). Trying to impute values in the latter cases could be done, but is unlikely that it will give anything reasonable or useful as a predictor, thus, those 65 columns were also removed.

In the end we will use 52 measurements of the x, y, and z axis components of the acceleration, gyroscope, and magnetometer sensors, as well as the overall acceleration, pitch, roll and yaw (see Table 4 in Appendix 2), to predict whether the exercise was done correctly.

## Generating and validating a Random Forest predictive model

Because the provided testing dataset could not be used to validate the predictive model, I decided to split the “training” dataset into one to be used to perform the random forest model training (75% of the data), and another to validate it (25% of the data). The training will also assess the quality of the model using an “out of bag” (OOB) error estimate using cross-validation.

The model training used the standard random forest (rf) algorithm4 method available in the caret package, with the default parameters and doing a 10-fold cross validation. I used the classe variable as the dependent and 52 sensor variables as predictors. This model gave an OOB error of 0.6%, which indicates a possible good classifier.

With the reserved validation set, I calculated the confusion matrix (Table 5), and other relevant statistics using the confusionMatrix() function of the caret package. The confusion matrix shows that the model does a reasonable good job at predicting the exercise quality.

Table 5: Confusion Matrix (Predicted vs Reference) for Random Forest model

A B C D E
A 1395 12 0 0 0
B 0 935 5 0 0
C 0 2 847 3 2
D 0 0 3 800 0
E 0 0 0 1 899

Validating the model results in an accuracy of 0.9943 (95% confidence interval: [0.9918, 0.9962]). The estimated accuracy is well above the “no information rate” statistic of 0.2845. The validation results also in a high kappa statistic of 0.9928, which suggest a very good classifier. Overall, this model compares well with the 0.9803 accuracy that was reported in the original work.

The first 20 model predictors can be seen in Figure 2, and the complete list of predictors (ordered by their mean decrease in accuracy) is in Table 6 (Appendix 3)

Figure 2: Variable Importance for Random Forest model (first 20 variables)

This plot indicates that the measurements of the belt sensor (roll, yaw, and pitch), the forearm (pitch) and the dumbbell (magnetic component), are the most important for distinguishing whether this particular exercise is being done correctly or not. This makes sense as the way the core body moves and the rotation of the forearm, are closely related to a correct execution of the biceps curl, and in the case of the metallic dumbbell the position changes are readily detected by the magnetometer.

## Reproducibility information

The source code for the R Markdown document and other accessory artifacts is available at the github repository: https://github.com/jmcastagnetto/practical_machine_learning-coursera-june2015, and the assignment was originally published at https://jmcastagnetto.github.io/practical_machine_learning-coursera-june2015/ using a layout inspired but Tufte’s handout recommendations.

## R version 3.2.0 (2015-04-16)
## Platform: x86_64-pc-linux-gnu (64-bit)
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## other attached packages:
##  [1] randomForest_4.6-7 doMC_1.3.3         iterators_1.0.7    foreach_1.4.2
##  [5] captioner_2.2.2    knitr_1.8          caret_6.0-47       ggplot2_1.0.0
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##  [4] class_7.3-10        tools_3.2.0         digest_0.6.4
##  [7] lme4_1.1-6          evaluate_0.5.5      gtable_0.1.2
## [10] nlme_3.1-120        mgcv_1.8-6          psych_1.4.5
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## [22] stringr_0.6.2       gtools_3.4.1        sjmisc_1.0.2
## [25] grid_3.2.0          nnet_7.3-9          rmarkdown_0.6.1
## [28] minqa_1.2.3         reshape2_1.4        tidyr_0.2.0
## [31] car_2.0-25          magrittr_1.0.1      codetools_0.2-11
## [34] scales_0.2.4        htmltools_0.2.6     MASS_7.3-33
## [37] splines_3.2.0       assertthat_0.1      tufterhandout_1.2.1
## [40] pbkrtest_0.3-8      colorspace_1.2-6    quantreg_5.05
## [43] munsell_0.4.2       RcppEigen_0.3.2.1.2


## Appendices

Table 2: Measurement columns by sensor

arm forearm belt dumbbell
accel_arm_x accel_forearm_x accel_belt_x accel_dumbbell_x
accel_arm_y accel_forearm_y accel_belt_y accel_dumbbell_y
accel_arm_z accel_forearm_z accel_belt_z accel_dumbbell_z
amplitude_pitch_arm amplitude_pitch_forearm amplitude_pitch_belt amplitude_pitch_dumbbell
amplitude_roll_arm amplitude_roll_forearm amplitude_roll_belt amplitude_roll_dumbbell
amplitude_yaw_arm amplitude_yaw_forearm amplitude_yaw_belt amplitude_yaw_dumbbell
avg_pitch_arm avg_pitch_forearm avg_pitch_belt avg_pitch_dumbbell
avg_roll_arm avg_roll_forearm avg_roll_belt avg_roll_dumbbell
avg_yaw_arm avg_yaw_forearm avg_yaw_belt avg_yaw_dumbbell
gyros_arm_x gyros_forearm_x gyros_belt_x gyros_dumbbell_x
gyros_arm_y gyros_forearm_y gyros_belt_y gyros_dumbbell_y
gyros_arm_z gyros_forearm_z gyros_belt_z gyros_dumbbell_z
kurtosis_picth_arm kurtosis_picth_forearm kurtosis_picth_belt kurtosis_picth_dumbbell
kurtosis_roll_arm kurtosis_roll_forearm kurtosis_roll_belt kurtosis_roll_dumbbell
kurtosis_yaw_arm kurtosis_yaw_forearm kurtosis_yaw_belt kurtosis_yaw_dumbbell
magnet_arm_x magnet_forearm_x magnet_belt_x magnet_dumbbell_x
magnet_arm_y magnet_forearm_y magnet_belt_y magnet_dumbbell_y
magnet_arm_z magnet_forearm_z magnet_belt_z magnet_dumbbell_z
max_picth_arm max_picth_forearm max_picth_belt max_picth_dumbbell
max_roll_arm max_roll_forearm max_roll_belt max_roll_dumbbell
max_yaw_arm max_yaw_forearm max_yaw_belt max_yaw_dumbbell
min_pitch_arm min_pitch_forearm min_pitch_belt min_pitch_dumbbell
min_roll_arm min_roll_forearm min_roll_belt min_roll_dumbbell
min_yaw_arm min_yaw_forearm min_yaw_belt min_yaw_dumbbell
pitch_arm pitch_forearm pitch_belt pitch_dumbbell
roll_arm roll_forearm roll_belt roll_dumbbell
skewness_pitch_arm skewness_pitch_forearm skewness_roll_belt skewness_pitch_dumbbell
skewness_roll_arm skewness_roll_forearm skewness_roll_belt.1 skewness_roll_dumbbell
skewness_yaw_arm skewness_yaw_forearm skewness_yaw_belt skewness_yaw_dumbbell
stddev_pitch_arm stddev_pitch_forearm stddev_pitch_belt stddev_pitch_dumbbell
stddev_roll_arm stddev_roll_forearm stddev_roll_belt stddev_roll_dumbbell
stddev_yaw_arm stddev_yaw_forearm stddev_yaw_belt stddev_yaw_dumbbell
total_accel_arm total_accel_forearm total_accel_belt total_accel_dumbbell
var_accel_arm var_accel_forearm var_pitch_belt var_accel_dumbbell
var_pitch_arm var_pitch_forearm var_roll_belt var_pitch_dumbbell
var_roll_arm var_roll_forearm var_total_accel_belt var_roll_dumbbell
var_yaw_arm var_yaw_forearm var_yaw_belt var_yaw_dumbbell
yaw_arm yaw_forearm yaw_belt yaw_dumbbell

Table 4: Remaining measurement columns by sensor

arm forearm belt dumbbell
accel_arm_x accel_forearm_x accel_belt_x accel_dumbbell_x
accel_arm_y accel_forearm_y accel_belt_y accel_dumbbell_y
accel_arm_z accel_forearm_z accel_belt_z accel_dumbbell_z
gyros_arm_x gyros_forearm_x gyros_belt_x gyros_dumbbell_x
gyros_arm_y gyros_forearm_y gyros_belt_y gyros_dumbbell_y
gyros_arm_z gyros_forearm_z gyros_belt_z gyros_dumbbell_z
magnet_arm_x magnet_forearm_x magnet_belt_x magnet_dumbbell_x
magnet_arm_y magnet_forearm_y magnet_belt_y magnet_dumbbell_y
magnet_arm_z magnet_forearm_z magnet_belt_z magnet_dumbbell_z
pitch_arm pitch_forearm pitch_belt pitch_dumbbell
roll_arm roll_forearm roll_belt roll_dumbbell
total_accel_arm total_accel_forearm total_accel_belt total_accel_dumbbell
yaw_arm yaw_forearm yaw_belt yaw_dumbbell

### Appendix 3: Random Forest Model - Variable Importance

Table 6: Variable importance per class and overall

Variable A B C D E MeanDecreaseAccuracy MeanDecreaseGini
roll_belt 0.1 0.14 0.18 0.17 0.3 0.17 1538.04
magnet_dumbbell_y 0.13 0.18 0.24 0.25 0.08 0.17 676.76
roll_forearm 0.18 0.14 0.25 0.18 0.09 0.17 651.19
magnet_dumbbell_z 0.17 0.13 0.2 0.15 0.08 0.15 683.12
yaw_belt 0.13 0.12 0.16 0.21 0.07 0.14 856.82
pitch_forearm 0.13 0.07 0.12 0.14 0.07 0.11 917.67
pitch_belt 0.07 0.16 0.14 0.15 0.04 0.11 685.43
accel_dumbbell_y 0.05 0.05 0.13 0.06 0.04 0.06 368.41
magnet_dumbbell_x 0.06 0.06 0.09 0.08 0.03 0.06 270.17
roll_dumbbell 0.03 0.07 0.08 0.07 0.04 0.06 299.67
accel_forearm_x 0.03 0.05 0.05 0.09 0.04 0.05 270.45
magnet_belt_z 0.03 0.07 0.06 0.06 0.04 0.05 246.52
accel_dumbbell_z 0.03 0.05 0.06 0.06 0.05 0.05 232.89
magnet_belt_y 0.02 0.07 0.04 0.05 0.04 0.04 235.13
magnet_forearm_z 0.04 0.03 0.05 0.04 0.02 0.04 230.82
total_accel_dumbbell 0.02 0.03 0.02 0.07 0.03 0.03 240.75
accel_belt_z 0.02 0.03 0.04 0.03 0.02 0.03 218.91
gyros_belt_z 0.02 0.04 0.05 0.02 0.02 0.03 174.78
yaw_dumbbell 0.02 0.04 0.04 0.03 0.02 0.03 142.08
accel_dumbbell_x 0.02 0.03 0.04 0.03 0.01 0.03 109.73
magnet_belt_x 0.01 0.03 0.06 0.02 0.01 0.02 179.06
roll_arm 0.01 0.03 0.03 0.04 0.01 0.02 130.59
accel_forearm_z 0.01 0.02 0.04 0.03 0.02 0.02 134.18
gyros_dumbbell_y 0.03 0.02 0.04 0.02 0.01 0.02 128.5
magnet_arm_x 0.02 0.02 0.02 0.03 0.01 0.02 105.06
yaw_arm 0.03 0.01 0.03 0.02 0.01 0.02 199.59
yaw_forearm 0.01 0.01 0.02 0.05 0.01 0.02 107.99
magnet_forearm_y 0.02 0.01 0.02 0.02 0.01 0.02 119.26
magnet_arm_y 0.01 0.02 0.02 0.03 0.01 0.02 110.55
accel_arm_x 0.01 0.02 0.02 0.03 0.01 0.02 110.08
gyros_belt_x 0.03 0 0.02 0.01 0 0.01 44.61
pitch_dumbbell 0.01 0.03 0.02 0.01 0.01 0.01 85.39
magnet_forearm_x 0.01 0.01 0.01 0.02 0.01 0.01 118.85
pitch_arm 0.01 0.01 0.01 0.01 0.01 0.01 87.83
accel_belt_y 0.01 0.01 0.02 0.02 0 0.01 39.47
magnet_arm_z 0.01 0.01 0.02 0.01 0 0.01 89.67
accel_forearm_y 0.01 0.01 0.02 0.01 0.01 0.01 63.7
gyros_belt_y 0 0.01 0.03 0.01 0 0.01 44.02
gyros_arm_y 0.01 0.01 0.01 0.01 0 0.01 81.3
accel_arm_y 0.01 0.01 0.01 0.01 0 0.01 67.4
accel_belt_x 0.01 0.01 0.01 0.01 0 0.01 36.11
gyros_arm_x 0.01 0.01 0.01 0.01 0 0.01 60.55
gyros_dumbbell_x 0 0.01 0.02 0.01 0 0.01 62.73
total_accel_belt 0.01 0.01 0.01 0.01 0.01 0.01 49.92
accel_arm_z 0.01 0.01 0.01 0.01 0 0.01 53.74
gyros_forearm_y 0 0.01 0.01 0.01 0 0.01 58.59
total_accel_forearm 0.01 0 0.01 0 0 0.01 40.89
total_accel_arm 0 0.01 0.01 0.01 0 0 47.5
gyros_dumbbell_z 0 0 0 0 0 0 40.05
gyros_forearm_z 0 0.01 0 0 0 0 39.34
gyros_forearm_x 0 0 0.01 0.01 0 0 26.71
gyros_arm_z 0 0 0 0 0 0 23.53

1. For more details see “The Weight Lifting Exercises Dataset[return]
2. 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. [return]
3. Image obtained from http://groupware.les.inf.puc-rio.br/har#weight_lifting_exercises [return]
4. randomForest: Breiman and Cutler’s random forests for classification and regression [return]