As discussed in the previous segment, PCA is fundamentally a dimensionality reduction technique; it helps in manipulating a data set to one with fewer variables. The following lecture will give you a brief idea of what dimensionality reduction is and how PCA helps in achieving dimensionality reduction.
In simple terms, dimensionality reduction is the exercise of dropping the unnecessary variables, i.e., the ones that add no useful information. Now, this is something that you must have done in the previous modules. In EDA, you dropped columns that had a lot of nulls or duplicate values, and so on. In linear and logistic regression, you dropped columns based on their p-values and VIF scores in the feature elimination step.
Similarly, what PCA does is that it converts the data by creating new features from old ones, where it becomes easier to decide which features to consider and which not to.
Now that you have an idea of the basics of what PCA does, let’s understand its definition in the following lecture.
PCA is a statistical procedure to convert observations of possibly correlated variables to ‘principal components’ such that:
- They are uncorrelated with each other.
- They are linear combinations of the original variables.
- They help in capturing maximum information in the data set.
Now, the aforementioned definition introduces some new terms, such as ‘linear combinations’ and ‘capturing maximum information’, for which you will need some knowledge of linear algebra concepts as well as other building blocks of PCA. In the next session, we will start our journey in the same direction with the introduction of a very basic idea: the vectorial representation of data.
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