Scatter Plot Matrix

In a dataset, for k set of variables/columns (X₁, X₂, ....X_k), the scatter plot matrix plot all the pairwise scatter between different variables in the form of a matrix.  

Scatter plot matrix answer the following questions:

• Are there any pair-wise relationships between different variables? And if there are relationships, what is the nature of these relationships?
• Are there any outliers in the dataset?
• Is there any clustering by groups present in the dataset on the basis of a particular variable?

For k variables in the dataset, the scatter plot matrix contains k rows and k columns. Each row and column represents as a single scatter plot. Each individual plot (i, j) can be defined as:

• Vertical Axis: Variable X_j
• Horizontal Axis: Variable X_i

Below are some important factors we consider when plotting the Scatter plot matrix:

• The plot lies on the diagonal is just a 45 line because we are plotting here X_i vs X_i. However, we can plot the histogram for the X_i in the diagonals or just leave it blank.
• Since X_i vs X_j is equivalent to X_j vs X_i with the axes reversed, we can also omit the plots below the diagonal.
• It can be more helpful if we overlay some line plot on the scattered points in the plots to give more understanding of the plot.
• The idea of the pair-wise plot can also be extended to different other plots such as quantile-quantile plots or bihistogram.

Implementation

• For this implementation, we will be using the Titanic dataset. This dataset can be downloaded from Kaggle. Before plotting the scatter matrix, we will be performing some preprocessing operations on the dataframe to obtain it into the desired form.

PassengerId Survived Pclass Name Sex Age SibSp Parch Ticket Fare Cabin Embarked
0 892 0 3 Kelly, Mr. James male 34.5 0 0 330911 7.8292 NaN Q
1 893 1 3 Wilkes, Mrs. James (Ellen Needs) female 47.0 1 0 363272 7.0000 NaN S
2 894 0 2 Myles, Mr. Thomas Francis male 62.0 0 0 240276 9.6875 NaN Q
3 895 0 3 Wirz, Mr. Albert male 27.0 0 0 315154 8.6625 NaN S
4 896 1 3 Hirvonen, Mrs. Alexander (Helga E Lindqvist) female 22.0 1 1 3101298 12.2875 NaN S

PassengerId int64
Survived int64
Pclass int64
Sex object
Age float64
SibSp int64
Parch int64
Fare float64
Embarked object
dtype: object

Survived Pclass Sex Age SibSp Parch Fare Embarked
0 0 3 1 34.5 0 0 7.8292 1
1 1 3 0 47.0 1 0 7.0000 2
2 0 2 1 62.0 0 0 9.6875 1
3 0 3 1 27.0 0 0 8.6625 2
4 1 3 0 22.0 1 1 12.2875 2

References:

• NIST handbook