juniorPCA

What is Principal Component Analysis (PCA), and why is it used in machine learning?

Updated Feb 20, 2026

Short answer

Principal Component Analysis (PCA) is a dimensionality reduction technique that transforms a dataset into a new set of features called principal components, which capture the maximum possible variance in the data. It is used in machine learning to reduce the number of features, remove redundancy, speed up training, improve visualization, and sometimes reduce noise. The new features are combinations of the original features and are ordered by how much information (variance) they preserve.

Deep explanation

PCA is an unsupervised learning algorithm that finds the most important directions of variation in a dataset. It does not use target labels; instead, it only looks at the relationships among input features.

Imagine a dataset with many features:

  • Height
  • Weight
  • Arm length
  • Leg length
  • Body mass

Many of these features may be correlated. For example, height and leg length may contain overlapping information. PCA creates new axes that combine these original features into fewer dimensions while preserving as much information as possible.

The main idea is:

Find a new coordinate system where the first few directions explain most of the variation in the data.

These new directions are called principal components.

How PCA works

The typical PCA process is:

  1. Standardize the data

Features often have different scales. For example, age might range from 0–100 while income might range from 0–100,000. PCA is sensitive to scale, so features are usually normalized first.

Common standardization:

TEXT
x_scaled = (x - mean) / standard_deviation
   ```


2. **Compute the covariance matrix**


   The covariance matrix shows how features vary together.


   * High positive covariance: features increase together.
   * Negative covariance: one feature increases while another decreases.
   * Low covariance: features are less related.


3. **Find eigenvectors and eigenvalues**


   PCA calculates:


   * **Eigenvectors**: directions of the new feature space.
   * **Eigenvalues**: how much variance each direction captures.


   Each eigenvector becomes a principal component.


4. **Sort components by explained variance**


   The first principal component captures the most variance.


   Example:


   ```text
   Principal Component 1: 65% of variance
   Principal Component 2: 20% of variance
   Principal Component 3: 8% of variance
   Principal Component 4: 4% of variance
   ```


   If the first two components capture 85% of the information, we may keep only those two.


5. **Project data onto the new components**


   The original features are transformed into principal component values.


   For example:


   ```text
   Original features:
   [height, weight, age, income, education]


   After PCA:
   [PC1, PC2]
   ```


   The dataset has fewer dimensions while retaining most important patterns.
### Why PCA is used in machine learning
#### 1. Reducing dimensionality


High-dimensional datasets can contain thousands or millions of features. Many features may be redundant or contain little useful information.


PCA reduces the number of variables while keeping important patterns.


Benefits:


* Faster model training
* Lower memory usage
* Less computational complexity
* Easier visualization
#### 2. Removing correlated features


Many machine learning algorithms perform better when input features are less correlated.


PCA creates new features that are mathematically uncorrelated with each other.
#### 3. Improving visualization


Humans can easily visualize only two or three dimensions. PCA can reduce high-dimensional data into two dimensions.


For example:


* Customer behavior data with 100 features
* PCA reduces it to 2 components
* A scatter plot reveals customer groups
#### 4. Reducing noise


Features with very low variance often contain noise. By keeping only the most important components, PCA can remove some random variation.
### PCA trade-offs


PCA is useful, but it has limitations.


**Loss of interpretability**


The new features are combinations of original features.


For example:

text PC1 = 0.4 × height + 0.5 × weight - 0.1 × age + ...

TypeScript
It may be difficult to explain what PC1 actually represents.


**Information loss**


Reducing dimensions always removes some information. The goal is to remove less important information while preserving useful patterns.


**Not always helpful**


Some models, especially tree-based models like random forests, can handle many features without needing PCA.
### PCA vs feature selection


These approaches are different:


| PCA                            | Feature Selection             |
| ------------------------------ | ----------------------------- |
| Creates new features           | Keeps original features       |
| Features are combinations      | Features remain interpretable |
| Reduces correlated information | Removes unnecessary features  |
| Can lose explainability        | Easier to explain             |


Example:


Feature selection might keep:

text Age, Income, Education

TypeScript
PCA might create:

text PC1, PC2, PC3 ```

where each component combines all original features.

Real-world example

A company has customer data with 50 behavioral features:

  • Number of purchases
  • Average purchase value
  • Website visits
  • Time spent browsing
  • Product categories viewed
  • Email interactions
  • Many others

The company wants to visualize customer segments and train a clustering model. Using all 50 dimensions makes visualization impossible and increases computation.

They apply PCA:

Python
from sklearn.preprocessing import StandardScaler
from sklearn.decomposition import PCA


# Example customer feature matrix
X = customer_data


# Standardize features
X_scaled = StandardScaler().fit_transform(X)


# Reduce 50 features to 2 components
pca = PCA(n_components=2)


X_reduced = pca.fit_transform(X_scaled)


print(X_reduced.shape)
print(pca.explained_variance_ratio_)

Output might look like:

TEXT
(10000, 2)


[0.52, 0.21]

The two principal components explain 73% of the original variation. The company can now plot customers in two dimensions and identify groups with similar behavior.

Common mistakes

  • * Using PCA without standardizing features when variables have very different scales.
  • * Assuming PCA selects the best original features instead of creating new combinations of features.
  • * Keeping too many or too few components without checking explained variance.
  • * Using PCA when interpretability of individual features is critical.
  • * Applying PCA to training and test data separately instead of fitting PCA only on training data and transforming both.
  • * Assuming PCA always improves model accuracy
  • it may help, hurt, or have little effect depending on the dataset and algorithm.
  • * Forgetting that PCA is an unsupervised method and does not consider the target variable.

Follow-up questions

  • Why is feature scaling important before applying PCA?
  • How do you decide how many principal components to keep?
  • Is PCA a supervised or unsupervised learning algorithm?
  • What is the difference between PCA and Linear Discriminant Analysis (LDA)?
  • Can PCA improve machine learning model performance?

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