Principal Component Analysis- Data Science
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.
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