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##The goal of this machine learning exercise is to predict the manner in which the participants did the exercise–that is, to #predict the “classe” variable found in the training set. The prediction model will then be used to predict twenty different #test cases, ##as provided in the testing dataset.

##Begin by loading the required libraries and reading in the training and testing datasets, assigning missing values to entries #that are currently ##'NA' or blank.

library(corrplot) library(caret)

wm <- read.csv("pml-training.csv", header = TRUE, na.strings = c("NA", "")) wm_test <- read.csv("pml-testing.csv", header = TRUE, na.strings = c("NA", ""))

##Columns in the orignal training and testing datasets that are mostly filled with missing values are then removed. To do this, #count the number of missing values in each column of the full training dataset. We use those sums to create a logical variable #for each column of the dataset. ##The logical variable's value is 'TRUE' if a column has no missing values (i.e. if the colSums = 0). If there are missing #values in the column, the logical variable's value corresponding to that column will be 'FALSE'.

##Applying the logical variable to the columns of the training and testing datasets will only keep those columns that are ##complete. (Note: This is a way of applying the 'complete.cases' function to the columns of a dataset.)

##Our updated training dataset now has fewer variables to review in our analysis. Further, our final testing dataset has ##consistent columns in it. This will allow the fitted model to be applied to the testing dataset.

csums <- colSums(is.na(wm)) csums_log <- (csums == 0) training_fewer_cols <- wm[, (colSums(is.na(wm)) == 0)] wm_test <- wm_test[, (colSums(is.na(wm)) == 0)]

##Create another logical vector in order to delete additional unnecessary columns from the pared-down training and testing ##datasets. Column names in the dataset containing the entries shown in the 'grepl' function will have a value of 'TRUE' ##in the logical vector. Since these are the columns we want to remove, we apply the negation of the logical vector against ##the columns of our dataset.

del_cols_log <- grepl("X|user_name|timestamp|new_window", colnames(training_fewer_cols)) training_fewer_cols <- training_fewer_cols[, !del_cols_log] wm_test_final <- wm_test[, !del_cols_log]

##We now split the updated training dataset into a training dataset and a validation dataset. #This validation dataset will allow us to perform cross validation when developing our model.

inTrain = createDataPartition(y = training_fewer_cols$classe, p = 0.7, list = FALSE) small_train = training_fewer_cols[inTrain, ] small_valid = training_fewer_cols[-inTrain, ]

#At this point, our dataset contains 54 variables, with the last column containing the 'classe' variable we are trying to #predict. We begin by looking at the correlations between the variables in our dataset. #We may want to remove highly correlated predictors from our analysis and replace them with weighted combinations of predictors. This may allow a more #complete capture of the information available.

corMat <- cor(small_train[, -54]) corrplot(corMat, order = "FPC", method = "color", type = "lower", tl.cex = 0.8, tl.col = rgb(0, 0, 0))

![CorreplotGrid]([url=http://postimg.org/image/ukpfds1nb/][img=http://s15.postimg.org/ukpfds1nb/Correlation_Grid.jpg][/url])

#The CorrelationGrid shows the correlation between pairs of the predictors in our dataset. From a high-level perspective darker #blue #and darker red squares indicate high positive and high negative correlations, respectively. Based on this observation, #we choose to implement a principal components analysis to produce a set of linearly uncorrelated variables #to use as our predictors.

Principal Components Analysis and Machine Learning

#We pre-process our data using a principal component analysis, leaving out the last column ('classe'). After pre-processing, #we use the 'predict' function to apply the pre-processing to both the training and validation subsets of the original larger #'training' dataset.

preProc <- preProcess(small_train[, -54], method = "pca", thresh = 0.99) trainPC <- predict(preProc, small_train[, -54]) valid_testPC <- predict(preProc, small_valid[, -54])

#Next, we train a model using a random forest approach on the smaller training dataset. We chose to specify the use of a #cross validation method when applying the random forest routine in the 'trainControl()' parameter. Without specifying this, #the default method (bootstrapping) would have been used. The bootstrapping method seemed to take a lot longer to complete, #while essentially producing the same level of 'accuracy'.

modelFit <- train(small_train$classe ~ ., method = "rf", data = trainPC, trControl = trainControl(method = "cv", number = 4), importance = TRUE)

#We now review the relative importance of the resulting principal components of the trained model, 'modelFit'.

varImpPlot(modelFit$finalModel, sort = TRUE, type = 1, pch = 19, col = 1, cex = 1, main = "Importance of the Individual Principal Components")

#As you look from the top to the bottom on the y-axis, this plot shows each of the principal components in order from most #important to least important. The degree of importance is shown on the x-axis–increasing from left to right. #Therefore, points high and to the right on this graph correspond to those principal components that are especially valuable #in terms of being able to classify the observed training data.

Cross Validation Testing and Out-of-Sample Error Estimate

#Call the 'predict' function again so that our trained model can be applied to our cross validation test dataset. #We can then view the resulting table in the 'confusionMatrix' function's output to see how well the model #predicted/classified the values in the validation test set (i.e. the 'reference' values)

pred_valid_rf <- predict(modelFit, valid_testPC) confus <- confusionMatrix(small_valid$classe, pred_valid_rf) confus$table

#The estimated out-of-sample error is 1.000 minus the model's accuracy, the later of which is provided in the output #of the confusionmatrix, or more directly via the 'postresample' function.

accur <- postResample(small_valid$classe, pred_valid_rf) model_accuracy <- accur1 model_accuracy

out_of_sample_error <- 1 - model_accuracy out_of_sample_error

#The estimated accuracy of the model is 98.4% and the estimated out-of-sample error based on our fitted model applied to #the cross validation dataset is 1.6%.

Predicted Results

#Finally, we apply the pre-processing to the original testing dataset, after removing the extraneous column labeled #'problem_id' (column 54). We then run our model against the testing dataset and display the predicted results.

testPC <- predict(preProc, wm_test_final[, -54]) pred_final <- predict(modelFit, testPC) pred_final