ML_MarkDown.Rmd

title: "PracticalML_R"
---
author: "Luis J. Gutierrez"
date: "Wednesday, January 14, 2015"
output: html_document
---

This is an R Markdown document. 

The objective is quantify how well people is doing exercises of Weight
Lifting using dynamic data comming from sensors located in different parts
of the body.  This is extremely useful to avoid physical damages and
injuries. as is mentioned in the abstract of the paper "Qualitative
Activity Recognition of Weight Lifting Exercises" published by Eduardo
Velloso (Lancaster Univ. UK), Andreas Bulling (Max Planck Inst. for
Informatics, Germany), Hans Gellersen (Lancaster Univ., UK), Wallace
Ugulino (PUC University of Rio de Janeiro, Brazil), Hugo Fuks (PUC
University of Rio de Janeiro, Brazil), "In this work we define quality of
execution and investigate three aspects that pertain to qualitative
activity recognition: specifying correct execution, detecting execution
mistakes, providing feedback on the to the user" 

To meet that objective and using the provided data sets, the idea is
identify a number of attributed to predict the exercise quality with an 95%
minimum.

First Step is read de Training data set. 

The data set "ml-training3.csv", is a preprocesses file where all empty columns were deleted, also were deleted all the date/time columns, because I suppose that the day or the time of the day is not relevant to do a well done exercise routine.

```{r}
MData=read.csv("pml-training3.csv",header=TRUE,sep=";",dec=".",na.string="NA");
```

After a couple of tests I realize the column is classified wrongly when data is missing or it is incorrectly entered. That requires identify these columns to correct the errors.  The next sentence identify if the column is not numeric.

```{r}
n<-dim(MData)[2]; for (i in 1:n) { if (!is.numeric(MData[,i])) print(i);}
```
if the result is 49, then is the expected result because the last column is an string ("categorical"). Others column are all numbers. 

After read the data set, the next step is the feature selection. To do that I used two
strategies. First, using the  algorithm to compute the Single Value Decomposition (SVD)
of attribute matrix. When the attribute matrix is standardized, the PCA algorithm for
dimension reduction is equivalent to the eigenvalue problem. Computing the singular
values of the standardized Attribute Matrix, is possible to get the singular values from
the diagonal Matrix of the SVD algorithm. Summing each (normalized) singular values to
reach the 95%, we have found the set of attributes that represent the useful part of the
signal, being the rest of attributes only (mainly) noise.

first step, generate an standardized Matrix from the original data set.

```{r}
MyData=scale(MData[,-49],center=TRUE,scale=TRUE);
```


```{r}
head(MyData)
```
Computing the singular value decomposition algorithm to MyData,
```{r}
s<-svd(MyData)
```

The singular values are in the diagonal matrix s$d, calculating the number of attributes
needed to reach 95%, we get 36 attributes. With this 36 attributes we could get a 
dimensional reduction of the problem, where the 95% of the signal significance is 
captured.

```{r}
sum(s$d[1:36]/sum(s$d))
```

A different approach is to use the covariance matrix for evaluating and selecting the
features with a stronger relationship with each other. The idea is to select a small set of attributes that significantly represent the desired prediction.

Calculating the covariance matrix

```{r}
Cov<-cov(MyData)
```
An ordering the attributes from highest cov. to lower covariance

```{r}
Vc=abs(Cov[,48]/sum(Cov[,48]))
Vco<-order(Vc,decreasing=TRUE)
```
Selecting the first 30 attributes ordered by covariance 
```{r}
MyData<-MData[Vco[1:30]]
head(MyData)
```
To compare results, we train the Random Forest model to predict class with the original set of Data (MData) the results are,
```{r}
library(caret)
#dividing the original data set in Training and Test
InTrain=createDataPartition(y=MData$classe,p=0.75,list=FALSE)
MTrain=MData[InTrain,]
MTest=MData[-InTrain,]
#Training the Random Forest Model
train_control <- trainControl(method="repeatedcv", number=10, repeats=3)
Model<-train(classe~., data=MTrain, trControl=train_control, method="rf")
Pred<-predict(Model,MTest)
```
After 50 minutes, the Model was Trained accuracy of 99%. 

With a reduced set of attributes (the 17 attributes with the highest correlation index), the model is

```{r}
#create a redused set of data for training
MTrainReduced<-MTrain[,Vco[1:17]]
MTrainReduced$classe<-MTrain[,49]
Model<-train(classe~., data=MTrainReduced, trControl=train_control, method="rf")
MTestReduced<-MTest[,Vco[1:17]]
MTestReduced$classe<-MTest[,49]
#Doing the prediction with the trained model
Pred<-predict(Model,MTestReduced)
#And asking for the statistics against the Test set 
confusionMatrix(Pred,MTestReduced$classe)
```
The confusion Matrix statistics shows an accuracy of 98% of the model with the 17 variables with the highest Correlation Index.

Validating with the Test data set available in **https://d396qusza40orc.cloudfront.net/predmachlearn/pml-testing.csv**, and after clean it, I get:
```{r}
#The column selected are
names(Vc[Vco[1:17]])
MValData=read.csv("pml-testing2.csv",header=TRUE,sep=";",dec=".",na.string="NA")
head(MValData)
#making the prediction
predict(Model,MValData)
```
============================================================================= 
**Conclusion**
============================================================================= 

Most of the time necessary for the final prediction was invested in the prepossessing
step, cleaning the data set. The second part of the work was to validate the minimum set
of attributes that can do a good prediction, it is really possible get a good predictor
with a minimum set of variables? . The data selected was the raw data that with presence
in all the cases and after that, select the most significant attributes using a 
correlation matrix and PCA analysis. The most significant attributes gives an accuracy of
98%. The model with 17 attributes was used to predict the 20 submission cases successfully.