Principal Component Analysis: What Is PCA, How It Works, Examples, Advantages & Disadvantages

Principal Component Analysis (PCA): The fast track to viewing the bigger picture. When the dataset came heavy with pieces like an enormous puzzle, PCA would be the shortcut toward seeing the bigger picture. It doesn’t matter if you’re a student whose data science exploration involves PCA as a must-know or a professional dealing with analytics that reaches complex territory; you know you have to learn.

This guide will tell you what is known as principal component analysis, how it works, when to use it, the advantages and disadvantages, and real-life examples. So this is completely devoid of being buried in complicated math.

Table of Contents

What is Principal Component Analysis?

This is a dimensionality reduction technique that makes it possible to treat large data sets in a simple way, maintaining the underlying important patterns. It changes the original variables into a new set of variables that are uncorrelated called principal components.

The principal components are ordered on the first basis in which the first Principal Component accounts for the maximum possible variance of the dataset, the second Principal Component accounts for the next highest variance, and so on.

Simple analogy:

PNC is like reducing the resolution of a high-resolution photo. Sure, it makes the picture considerably smaller, but to the naked eye, it looks almost the same.

Main purposes of PCA (Principal Component Analysis):

Removal of redundant variables
Accelerate machine learning models
Enable visualization of high dimensions
Spotlight hidden patterns in the data

Importance of Principal Component Analysis

No matter if it’s academic research, predictive modeling, or making decisions for businesses, high-dimensional data will face you one way or another. And here, without PCA:

Longer time to train models
Problems with overfitting
Patterns in raw data emerging with great difficulty
Poor clarity in visualization

By using PCA Principal Component Analysis, you turn complex datasets into neat, informative components that help make decisions faster and more precise.

How Does Principal Component Analysis Work? – Stepwise

Five steps to the principal component analysis without sounding like an introduction to statistics:

Standardize data
All variables are standardized to the same scale.
Calculate the covariance matrix
Measures the way two or more variables vary together.
Eigenvalues and eigenvectors
Lay down direction and the strength of variance.
Sort and select principal components
Keep only components explaining the major variance.
Transform the data
Construct new, reduced dataset using selected components.

Pro Tip: Always check the explained variance ratio to decide how many components to keep.

Principal Component Analysis Example

Imagine you’re looking at 1,000 customers and comparing their different behavioral metrics to include things like how often they buy, how much they spend on average per order, the types of products they usually buy, how much time they spend on the site, etc.

When you do PCA (Principal Component Analysis), you realize that 4 principal components take care of 92% of the variation in the data:

PC1: Overall spending pattern
PC2: Brand loyalty vs. brand switching
PC3: Interest in discounts & promotions
PC4: Seasonal buying behavior

Instead of concentrating on these 15 variables, you can now concentrate on just 4, saving you a lot of time and hassle but also simplifying your models.

Mathematical Intuition Behind PCA

While there is no need to know-or even understand-the math behind Principal Component Analysis, a brief knowledge will help:

The covariance matrix shows the relationships between variables.
The maximum variance is directed by Eigenvectors-the principal components.
Then eigenvalues will tell you how important each principal component is.

Formula for variance explained by a principal component:

Advantages of Principal Component Analysis

Chunkier – Less clutters present in your datasets.
Better Visualization – Reduce dozens of features in 2D/3D space.
Faster Models – Smaller number of variables = less time to compute.
Removes Multicollinearity – Collapses highly correlated variables into one.
Highlights Key Patterns – Focus on the most significant relationships in the database.

Disadvantages of Principal Component Analysis

Harder to interpret – Not direct variables but abstract combinations.
Risk of data loss – If too many components are cut off.
Sensitive to scaling – Results are bad if data are left non-standardized.
Not suited for categorical data – Best applied to continuous variables.

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When to Use Principal Component Analysis

Large datasets, where a lot of features
Highly correlated variables
High-dimensional data visualization for purposes of interpretation
Optimization of training speed of models

When NOT to Use Principal Component Analysis

While dealing with very small datasets
When interpretability of each variable is critical
Primarily categorical data

PCA vs. t-SNE vs. LDA – Which One Should You Use?

Method	Best For	Strength	Weakness
PCA	Large datasets, feature reduction	Fast & interpretable	May lose interpretability of features
t-SNE	Visualizing clusters in high-dim data	Great for visualization	Computationally heavy
LDA	Classification problems	Maximizes class separation	Needs labeled data

Common Mistakes When Using Principal Component Analysis

Not standardizing the dataset before applying PCA
Too few or too many components are retained.
Using PCA without checking the actual need for dimensionality reduction
Misunderstanding principal components as original features.

Best Tools for Applying Principal Component Analysis

Python (Scikitlearn, Numpy, Pandas)
R (prcomp, FactoMineR)
MATLAB
Excel (for small datasets)
Tableau / Power BI for visual analysis

Also Read:

Course on Data Science by PW Skills- Indulging in PCA and beyond

The PW Skills Data Science course is your launchpad into this applied world of principal component analysis. That is,

projects with hands-on experience
experts mentoring
industry-grade instruments
practical case studies

In mastering PCA (Principal Component Analysis) and many other techniques that employers wish to have in their toolbox, you will have everything.

Why Learn PCA

Principal Component Analysis isn’t just academic theory; it is practically an operational way to decompose data, reduce speed and uncover concealed results that cannot be seen in raw data, whether it is a university project or the construction of a business model. PCA has all of these requirements.

Coupled with practice, theory will make you aware of Principal Component Analysis, but it will also teach you when and how it should be used.

Principal Component Analysis FAQs

Can Principal Component Analysis handle missing data?

No; missing values must be managed beforehand to use PCA.

Does PCA work for non-linear relationships?

Standard PCA works best for linear patterns; for non-linear data, try Kernel PCA.

How much variance should my principal components explain?

80-95% is recommended in order to capture most of the informative patterns in the dataset.

Is PCA useful for image compression?

Yes; it is known that PCA is widely used to compress images without compromising quality.