solution.Rmd

---
title: "Analysis Report"
output: pdf_document
---
## Description
This report describes the development of a prediction model for Human Activity Recognition data as part of the Coursera Machine Learning course. The data was obtained from http://groupware.les.inf.puc-rio.br/har. This report contains a description of the analysis process and outlines what the expected accuracy of the model is.

## Import and Model
The source data was imported using the standard R tools. Some data clean-up was necessary as follows.

### Division by zero entries
Before hand a number of entries with the mark #DIV/0!" were replaced by NA, as the "#DIV/0!" indicates an error which in R terms means data not available.

### Columns of significance
The training dataset contains 159 possible predictors that characterise the outcome. However, many of these contain a great amount of undefined (or not available) values, which makes them candidates for deletion. In particular, the following columns have over 19000 entries set to NA (or less than 3% of the data in them is meaningful). Conservatively, we can eliminate those from consideration. The remaining columns (or predictors) are as follows:
```{r, echo=TRUE}
rdata <- read.csv("pml-training.csv", header=TRUE, sep=",")
names(rdata[,colSums(is.na(rdata))< 19000])
```

So we are considering 59 predictors out of the 159 original ones.

### Training and Model
We do a 60-40 partition split of the training data into training and testing data. We do this to ensure that we have adequate testing data and avoid overfitting. 
```{r, eval=FALSE}
inTrain <- createDataPartition(y=rdata_clean_m$classe, p=0.60, list=FALSE)
training <- rdata_clean_m[inTrain,]
testing <- rdata_clean_m[-inTrain,]
```
We create a model using random forests. Random forests have been shown to produce powerful prediction models but are computationally intensive. Nonetheless, even with our modest hardware facilities we can derive a promisingly accurate model. We explored other models as well, using a sub-sample of the training data for exploratory purposes but found random forests to perform the best given certain computational time constraints.

The model includes  Principal Componenets Analysis to combine some correlated predictors thereby reducing the number of predictors. The associated train control sets k-fold cross validation (to help with overfitting the data), with k=5. The number of trees to grow is set to 100. Both k and the number of trees were set to lower than default values due to hardware limitations.
```{r, eval=FALSE}
ctrl <-  trainControl(method="repeatedcv", number=5)
modelFit <- train(classe~., data = training, method="rf", ntree=100, trControl=ctrl, preProcess="pca",prox=TRUE)
```

Note that the final model contains `r length(modelFit$finalModel$xNames)` PCA-derived predictors out of the 59 we started with. So via combining correlated predictors, 23 were eliminated.

## Evaluating the model
We test the model against the testing data and note the classification.
```{r, eval=TRUE}
load(file="analysis.RData")
library("caret")
predictions <- predict(modelFit, newdata=testing)
confusionMatrix(predictions, testing$classe)
```
It seems that the model produces what can be described as satisfactory classification. All metrics for statistics per class seem quite high (over 95%) and the model has given a result of 18/20 accurate predictions in the accompanying exercise.

## Results
We derived a satisfactory random forest model for classifying activity according to certain predictors. The model achieved 90% correct classification on the final test data but greater accuracy could possibly have been achieved if we could develop the model further by considering larger forests and bigger k-fold values.