Understanding Feature extraction using Correlation Matrix and Scatter Plots

Understanding Feature extraction using Correlation Matrix and Scatter Plots

The data out there in the world is very huge and needs to be dealt very consciously for any sensible outcome we’d like to achieve through a novel data science approach.

This article is going to deal with a very fundamental and important concept when dealing with large no. of features in a given dataset.

Any typical machine learning or deep learning model is made to provide a single output from huge amounts of data be it structured or unstructured. These factors may contribute to the required result at various coefficients and degrees. These factors need to be filtered out in a way based on their significance in determining the output and also considering the frequency of these factors.

In supervised learning, we know that there is always an output variable and n input variables. To understand this concept very clearly let’s take an example of a simple linear regression problem and then we can jump to multiple regression.

In a simple linear regression model, we ultimately generate an equation from the model of the form y=mx+c where x is an independent variable and y is a dependent variable. Since there is only one variable y has to depend on the value of x. Although in real-time there might be few other ignored external factors such as air resistance while calculating the average velocity of a bus from A to B. These definitely make an impact on the output but yet has the least significance. In this case, our common sense and experience helped us out in picking the factors hence we picked acceleration given to the bus by the driver and ignored the air resistance. What about the complex situations where we have no idea about the significance of input variables on the output. Can mathematics solve this puzzle?

Yes! Here comes the concept of correlation.

Correlationis a statistical measure that indicates the extent to which two or more variables fluctuate together. In simple terms, it tells us how much does one variable changes for a slight change in another variable. It may take positive, negative and zero values depending on the direction of the change. A high correlation value between a dependent variable and an independent variable indicates that the independent variable is of very high significance in determining the output. In a multiple regression setup where there are many factors to set up, it is imperative to find the correlation between the dependent and all the independent variables to build a viable model with higher accuracy. One must always remember that more number of features does not imply better accuracy. More features may lead to a decline in the accuracy if they contain any irrelevant features creating unrequired noise in our model.

Correlation between 2 variables can be found by various metrics such as Pearson r correlation, Kendall rank correlation, Spearman rank correlation, etc.

Pearson r correlation is the most widely used correlation statistic to measure the degree of the relationship between linearly related variables. The Pearson correlation between any 2 variables x,y can be found using :

n-no. of observations and i-denotes ith observation

Let us consider the dataset 50_Strartups on new startups in New York, California, and Florida. The variables used in the dataset are Profit, R&D spending, Administration Spending, and Marketing Spending. Here Profit is the dependent variable to be predicted.

Let us first apply linear regression for every independent variable separately to visualize the correlation with the independent variable.