Here we will talk about the simplified explanation of Principal Component Analysis, Which will be helpful to answers the basic confusions that data science aspirants go through while reading and those who are already doing well in PCA will recall the basics. The explanation is good for those also who don’t have a strong mathematical background.
What Is Principal Component Analysis?
PCA is a method to shorten or reducing the vastness of large data, it diminishes the outsized dataset into smaller chunks with loosing on much information as on large sets. As we will understand that working with large data creates a lot of chaos, with PCA in Data Science small datasets can be made and important information can be saved. Reducing the number of variables from data will obviously cost little accuracy too, but the simplification is given little more preference there. The reason behind this practice is smaller datasets are easier to deal with, explore and visualize and make analyzing data much faster for machine learning algorithms without extraneous variables to process.
So to sum up, the idea of PCA is simple — reduces the number of variables of a data set, while preserving as much information as possible.
Before getting to the explanation, this post delivers reasonable clarifications of what PCA is doing in each step and simplifies the mathematical concepts behind it, like standardization, covariance, eigenvectors, and eigenvalues without focusing on how to compute them.
Standardization- The aim of this step is to regulate the range of unceasing initial variables so that each one of them contributes equally to the process of analysis. While dealing with large data there are a lot of initial variances in variables, it’s very important to level the dominant ranges to get the results and basically to achieve the initial structure (For example, a variable that ranges between 0 and 100 will dominate over a variable that ranges between 0 and 1). So, transforming the data to comparable scales can prevent this problem.
Covariance Matrix computation- To understand the relation between the variables this step is all about it. Because sometimes variables are highly correlated and they contain dismissed information. So, in order to identify these correlations, we compute the covariance matrix.
Eigenvectors and eigenvalues - Eigenvectors and eigenvalues are the concepts of linear algebra that we need to calculate from the covariance matrix in order to determine the principal components of the data. By ranking your eigenvectors in order of their eigenvalues, highest to lowest, you get the principal components in order of significance.
Feature Vector- Now let’s come down to the step where we decide which components to keep and which to discard which are of lesser importance (of low eigenvalues) while conducting Principal Component Analysis. So, the feature vector is simply a matrix that has as columns the eigenvectors of the modules that we decide to keep. This makes it the first step towards dimensionality reduction because if we choose to keep only X eigenvectors (components) out of n, the final data set will have only X dimensions.
Final Step- In this step, which is the last one, the aim is to use the feature vector formed using the eigenvectors of the covariance matrix, to re-orient the data from the original axes to the ones represented by the principal components (hence the name Principal Components Analysis).
Here we have discussed an overview of vital algorithm/ feature that is being taught in Data Science. Through knowledge can be just achieved by practicing and taking up different tasks, more the complexity more PCA becomes interesting.