Question 1: Glass Identification
Previewing the Glass Dataset:
| RI | Na | Mg | Al | Si | K | Ca | Ba | Fe | Type |
|---|---|---|---|---|---|---|---|---|---|
| 1.52101 | 13.64 | 4.49 | 1.10 | 71.78 | 0.06 | 8.75 | 0 | 0 | 1 |
| 1.51761 | 13.89 | 3.60 | 1.36 | 72.73 | 0.48 | 7.83 | 0 | 0 | 1 |
| 1.51618 | 13.53 | 3.55 | 1.54 | 72.99 | 0.39 | 7.78 | 0 | 0 | 1 |
| 1.51766 | 13.21 | 3.69 | 1.29 | 72.61 | 0.57 | 8.22 | 0 | 0 | 1 |
| 1.51742 | 13.27 | 3.62 | 1.24 | 73.08 | 0.55 | 8.07 | 0 | 0 | 1 |
##
## The dimension of the Glass indentification dataset is [ 214 10 ]
##
## Below is the structure of the Glass identilfication dataset## 'data.frame': 214 obs. of 10 variables:
## $ RI : num 1.52 1.52 1.52 1.52 1.52 ...
## $ Na : num 13.6 13.9 13.5 13.2 13.3 ...
## $ Mg : num 4.49 3.6 3.55 3.69 3.62 3.61 3.6 3.61 3.58 3.6 ...
## $ Al : num 1.1 1.36 1.54 1.29 1.24 1.62 1.14 1.05 1.37 1.36 ...
## $ Si : num 71.8 72.7 73 72.6 73.1 ...
## $ K : num 0.06 0.48 0.39 0.57 0.55 0.64 0.58 0.57 0.56 0.57 ...
## $ Ca : num 8.75 7.83 7.78 8.22 8.07 8.07 8.17 8.24 8.3 8.4 ...
## $ Ba : num 0 0 0 0 0 0 0 0 0 0 ...
## $ Fe : num 0 0 0 0 0 0.26 0 0 0 0.11 ...
## $ Type: Factor w/ 6 levels "1","2","3","5",..: 1 1 1 1 1 1 1 1 1 1 ...Q1a: Using visualizations to explore the predictor variables:
| Type | variable | value |
|---|---|---|
| 1 | RI | 1.52101 |
| 1 | RI | 1.51761 |
| 1 | RI | 1.51618 |
| 1 | RI | 1.51766 |
##
## Density Plot of all the feature variables
##
## Histogram Plot of all the feature variables
## The histogram Plots were plot in order to have a clearer perception of the data##
## Box Plot of all the feature variables per type
The following predictors: Ca, Si, Na, & Ri show some signs of a largely tailed distribution
K and Mg have multiple peaks; this might means a mixture of different distributions.
Very few predictors seem to be correlated: an obvious instance is Ri & Ca. However, must of the predictor
Q1b: Do there appear to be any outliers in the data? Are any predictors skewed?
| skewValue | skewLevel | |
|---|---|---|
| RI | 1.6027151 | Heavily Skewed |
| Na | 0.4478343 | Symmetric |
| Mg | -1.1364523 | Heavily Skewed |
| Al | 0.8946104 | Moderately Skewed |
| Si | -0.7202392 | Moderately Skewed |
| K | 6.4600889 | Heavily Skewed |
| Ca | 2.0184463 | Heavily Skewed |
| Ba | 3.3686800 | Heavily Skewed |
| Fe | 1.7298107 | Heavily Skewed |
Looking at the shape of the box plot, there seem to be posiblity of outliers in the data set; it is unclear whether the extreme point in predicator K is an outlier.
The table above shows the skewness level of each of predictors.
Q1c: Are there any relevant transformations of one or more predictors that might improve the classification model?
Having visually explored the data, it might be helpful to use some transformation techniques in order to deal with the skewness and outliers in the data set. The following transformation could be useful:
Spatial sign transformation to resolve/constraint the outliers/extreme values in the predictors.
Yeo-Johnson transformations for treating the skewness, because they can deal with zero or negative values.
However, Log transformation and Box-Cox transformations cannot be used in this case because must of the predictors contain zero values.
##
## Correlation Plot of the transformed data: Center & Scale Transformation
Spatial Sign transformation has helped to constrain the outliers. Also it has changed the direction of some zero values in the data e.g Fe and B. Thus, correlation between the predictors seem to have improved.
##
## Density Plot of the transformed data: Yeo Johnson Transformation
Apparently, this seems not to have improved the skewness in the data.
