## Introduction

In this assignment for the Johns Hopkins Bloomberg School of Public Health “Practical Machine Learning” course (as presented via Coursera), we are tasked with developing a machine learning algorithm that will allow us to create a model for assessing the quality of a certain category of weight lifting excercise from data gathered from various test subjects.

The data used for the assignment was gathered as part of a Human Activity Recognition (HAR) study1, and was graciously provided for our use by the website http://groupware.les.inf.puc-rio.br/har.

Data was gathered by sensors attached to the test subjects’ torso, arm, and forearm as well as to the dumbell they used during the data capture. The sensors measured three axes each of acceleration, gyroscopic, and magnetometer data.

The test subjects, six young adult males with little prior weight lifting experience, were asked to perform one set of 10 repetitions of the Universal Dumbell Biceps Curl in five manners, one correct (Class A, exactly according to the specification), and four incorrect (Class B, throwing the elbows to the front; Class C, lifting the dumbell only halfway; Class D, lowering the dumbell only halfway; and Class E, throwing the hips forward).

## Data

### Getting the Data

We were provided with links to two CSV files for this assignment, one for training, and one for testing. The CSV files were downloaded and read into R data frames using the readr package.

The training CSV file contained 19622 rows and 160 columns of data. The testing CSV file contained 20 rows and 160 columns of data.

### Cleaning the Data

During inital exploratory analysis of the provided data, I noticed that there were numerous columns in the dataset that were either identification columns, or contained aggregate data from other columns (identified by their names being prefixed with one of min, max, avg, var, stddev, kurtosis, skewness, or amplitude). I removed these columns from the dataset to avoid fitting my model to anything other than sensor data, and to avoid errors caused by missing data in the aggregate columns.

This cleaning resulted in the training dataset being reduced to 53 columns.

The training dataset has a column named classe that contains the class assigned by the study authors to the data in each row of sensor readings. In order to use this column in the training algorithm I converted it to a factor data type column. This column is missing from the test dataset, replaced by a column named problem_id that I left as-is for prediction result identification.

### Splitting into Training and Validation Partitions

In order to perform model validation I partitioned the training dataset into separate training and validation datasets. I arbitrarily chose to split the dataset using a 80% / 20% random allocation of rows from the training dataset to the new training and validation datasets, respectively.

This resulted in there being 15699 rows in the new training dataset, and 3923 rows in the validation dataset.

## Model

### Model Generation

In reading the Coursera Discussion Forums for this course, I learned that models can be very time consuming to calculate, but that running the training on multiple processor cores in parallel can reduce the amount of time taken to process the data. Based on this, I chose to run my training using the doParallel package.

Analysis and model generation were performed using the functions of the caret package. I tried using four different models, namely rf for random forests, gbm for stochastic gradient boosting, knn for k-nearest neighbors, and lda for linear discriminant analysis. Random forests came out with the highest accuracy. In the interest of brevity, I have chosen to only present the results of the random forest model in this report.

In my intial runs using random forest training I used the cross-validation resampling method (cv), but settled on using the out-of-bag resampling method (oob). This change resulted in an approximately 0.45% increase in accuracy.

Following is the final model as reported by caret:


Call:
randomForest(x = x, y = y, mtry = param\$mtry)
Type of random forest: classification
Number of trees: 500
No. of variables tried at each split: 13

OOB estimate of  error rate: 0.46%
Confusion matrix:
A    B    C    D    E class.error
A 4461    3    0    0    0 0.000672043
B   11 3020    7    0    0 0.005924951
C    0   18 2717    3    0 0.007669832
D    0    0   22 2550    1 0.008938982
E    0    0    2    6 2878 0.002772003

The plot of the top 20 model predictors can be seen below:

### Model Validation

I used the validation dataset I split previously from the data to validate the model, calculating the following confusion matrix:

Confusion Matrix and Statistics

Reference
Prediction    A    B    C    D    E
A 1113    1    0    0    0
B    2  756    1    0    0
C    1    2  683    5    0
D    0    0    0  638    1
E    0    0    0    0  720

Overall Statistics

Accuracy : 0.9967
95% CI : (0.9943, 0.9982)
No Information Rate : 0.2845
P-Value [Acc > NIR] : < 2.2e-16

Kappa : 0.9958
Mcnemar's Test P-Value : NA

Statistics by Class:

Class: A Class: B Class: C Class: D Class: E
Sensitivity            0.9973   0.9960   0.9985   0.9922   0.9986
Specificity            0.9996   0.9991   0.9975   0.9997   1.0000
Pos Pred Value         0.9991   0.9960   0.9884   0.9984   1.0000
Neg Pred Value         0.9989   0.9991   0.9997   0.9985   0.9997
Prevalence             0.2845   0.1935   0.1744   0.1639   0.1838
Detection Rate         0.2837   0.1927   0.1741   0.1626   0.1835
Detection Prevalence   0.2840   0.1935   0.1761   0.1629   0.1835
Balanced Accuracy      0.9985   0.9975   0.9980   0.9960   0.9993

As can be seen, this indicates an estimated accuracy of 0.9967, with a 95% confidence interval of 0.9943— 0.9982. This represents an estimated out-of-sample error of 0.3314%.

## Assignment Prediction

I ran a new prediction using my model against the testing data provided for the assignment and submitted the results to Coursera: my predictions scored 20 out of 20 (100%)!

## Appendix

### Environment Information

R version 3.2.2 (2015-08-14)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 8 x64 (build 9200)

locale:

attached base packages:
[1] parallel  stats     graphics  grDevices utils     datasets  methods
[8] base

other attached packages:
[4] caret_6.0-52        ggplot2_1.0.1       lattice_0.20-33
[7] doParallel_1.0.8    iterators_1.0.7     foreach_1.4.2

loaded via a namespace (and not attached):
[1] Rcpp_0.12.1         compiler_3.2.2      formatR_1.2.1
[4] nloptr_1.0.4        plyr_1.8.3          class_7.3-14
[7] tools_3.2.2         digest_0.6.8        lme4_1.1-9
[10] evaluate_0.8        nlme_3.1-122        gtable_0.1.2
[13] mgcv_1.8-7          Matrix_1.2-2        yaml_2.1.13
[16] brglm_0.5-9         SparseM_1.7         proto_0.3-10
[40] stringi_0.5-5       munsell_0.4.2