Dimensionality Reduction and Model Families Short Notes for GATE DA: Concepts, Formulas, Worked Examples & Practice

Dimensionality Reduction and Model Families short notes for GATE DA: 4 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

PCA Cheat Sheet

SUMMARY

Step	Action	Math
1	Standardize	$x \leftarrow \frac{x - μ}{σ}$
2	Covariance	$Σ = \frac{1}{n - 1} X^{T} X$
3	Eigen-decomp	$Σ v = λ v$
4	Sort	$λ_{1} \geq λ_{2} \dots$
5	Select $k$	$\sum_{i = 1}^{k} λ_{i} / \sum λ_{j} \geq Thresh$

Golden Rules

Orthogonality: Angle between distinct PCs is exactly 90°.
Unsupervised: Maximizes variance, ignores class labels.
Scaling: Never run PCA on raw, unscaled data.
Total Variance: Sum of eigenvalues = trace of $Σ$ .

Quick Revision: PCA Core Facts

Nature: Unsupervised, linear dimensionality reduction.
Goal: Maximize projected variance (minimize reconstruction error).
Math Core: Eigenvectors of the data covariance matrix $C$ .
Variance: Eigenvalue $λ_{i}$ equals the variance captured by $P C_{i}$ .
Orthogonality: All PCs are mutually orthogonal (angle is always $9 0^{\circ}$ ).
Limitation: Ignores class labels; not optimal if the goal is purely class separation.

Quick Revision: Model Families Cheat Sheet

Generative Models: Learn joint probability $P (X, Y)$ . Can generate data. Handle missing values well. (e.g., Naive Bayes, GMM).
Discriminative Models: Learn conditional probability $P (Y ∣ X)$ . Focus on decision boundaries. Better accuracy with large data. (e.g., Logistic Regression, SVM).
Dimensionality Reduction: Compresses features to lower dimensions.
- Unsupervised: PCA (maximizes total variance).
- Supervised: LDA (maximizes class separation).

Summary: Model Families and Reduction Techniques

Final Quick-Recall Summary

Model Families

Generative: Models

P (X, Y)

. Learns data distribution. Handles missing data. Examples: Naive Bayes, GMM.

Discriminative: Models

P (Y ∣ X)

. Learns decision boundary. Higher asymptotic accuracy. Examples: Logistic Regression, SVM, Neural Networks.

Dimensionality Reduction

Feature Selection: Keeps a subset of original features (e.g., Lasso).

Feature Extraction: Creates new combined features (e.g., PCA, LDA).

Reduction Algorithms

PCA: Unsupervised. Maximizes total variance.

LDA: Supervised. Maximizes class separability.

t-SNE / Isomap: Non-linear manifold learning. Preserves local/global geometry for complex structures.

More short notes in this unit

chapter

Dimensionality Reduction and Model Families Short Notes for GATE DA: Concepts, Formulas, Worked Examples & Practice

Dimensionality Reduction and Model Families short notes for GATE DA: 4 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice

Free preview ends here

Login to view the complete short notes

Creating an account is free. You get the rest of this chapter, step-by-step solutions, and a study plan built around the topics you are actually weak at.

Why MastersUp

Personalised first. High quality throughout.

Most platforms hand everyone the same content. Here the content moves with your performance, topic by topic.

Built around you, not around a syllabus PDF

Every answer you give moves your topic-level intelligence rate. The next question, the next revision card and tomorrow's plan all change with it.

Revision that hits your weak spots

We only revise topics you have actually attempted and are still below the safe bar on — never the same chapter on repeat.

Questions calibrated to the real exam

Each question carries a measured toughness. You are served a rung above your current level, so practice keeps stretching you.

Notes written for recall, not for volume

Full lesson cards for first study, curated short-note cards for the last mile — with derivations, traps and exam patterns marked.

One place for everything

Notes, chapter practice, previous-year questions, test series and full-length papers — all feeding one picture of your preparation.

Honest progress

No vanity streaks. Progress here means chapters mastered and accuracy that held up on harder questions.

Unlock the whole course

Full notes and short notes, the complete question bank with worked solutions, mock tests, full-length papers, and an adaptive plan that rebuilds itself as you improve.

View all plans Start free