PCA, LDA & Perceptron : ONE-SHOT GATE DA | Concept to Combat Session 6 🔥

Welcome to Session 6 of the Concept to Combat series! This is your ultimate one-stop resource for mastering some of the most high-weight and frequently tested topics in the GATE DA Machine Learning syllabus: PCA, LDA & Perceptron. What you'll learn: In this session, we will do a recap of the concepts and then go in deep dive for extensive practice of GATE-level problems. We don’t just stop at the theory; we ensure you can apply every formula and geometric intuition to solve complex questions under pressure. 📘 Click the link below to download all session PDFs: drive.google.com/drive/folders/1f7sZIS4-icsxaHEB1i… Join our Communities for Notes: Telegram: t.me/ManojGateDA Discord: discord.com/invite/AwZqYz9wvK ML Module Schedule: Jan 20 – Feb 1. Subscribe to TAAI- Manoj Kumar to join the combat live! Jump to Topics: [00:00] – Start: Overview of Session 6 covering PCA, LDA, and Perceptron. [02:05] – Series Status: Review of previous sessions and current progress. [03:56] – Dimensionality Reduction: Why it's needed (training time, overfitting, visualization). [07:32] – Curse of Dimensionality: How high dimensions affect distance metrics and data sparsity. [11:45] – Feature Extraction vs. Selection: PCA as a feature extraction technique using linear combinations. [13:14] – Core Concept: Variance as Information; finding directions of maximum variability. [15:50] – Vector Projection: Mathematical foundation using linear algebra. [22:56] – Covariance Matrix: Deriving the relationship between the covariance matrix and PCA. [31:01] – Eigenvalues & Eigenvectors: Identifying principal components through eigenvalue decomposition. [38:12] – Reconstruction Error: Viewing PCA as a way to minimize information loss. [43:17] – Practice Problems: Solving numerical problems on design matrices, eigenvalues, and variance captured [01:02:15] – Singular Value Decomposition (SVD): Relation between singular values and PCA [GATE DA 2024 content]. [01:05:03] – GATE DA 2025 Analysis: Deep dive into a specific 2nd-mark question on PCA. [01:11:02] – PCA Weakness: Why PCA fails for classification by ignoring labels. [01:15:07] – LDA Core Concept: Maximizing between-class separation while minimizing within-class variance. [01:20:02] – Scatter Matrices: Defining "Within-class" ($S_W$) and "Between-class" ($S_B$) scatter matrices. [01:28:15] – Optimization: Solving the generalized eigenvalue problem for LDA. [01:32:46] – Numerical Walkthrough: Step-by-step example of calculating means and projection directions. [01:36:52] – Multi-Class LDA: Handling more than two classes and the $(C-1)$ rank constraint. [01:43:29] – GATE Question: Analysis of LDA results and Fisher's Criterion. [01:47:12] – The Biological Neuron: Pre-activation and activation functions. [01:49:27] – Perceptron Mechanism: Weights, biases, and thresholding (Step Function). [01:52:07] – Linear Separability: What Perceptrons can (AND, OR) and cannot (XOR) learn. [02:01:15] – Perceptron Training Rule: Step-by-step weight update logic ([02:09:26] – Convergence: Conditions for convergence and the margin-based error bound ($R/\gamma$)^2. [02:10:56] – Multi-Layer Perceptron (MLP): Introduction to hidden layers and universal approximation. [02:18:38] – Practice & GATE Questions: Analyzing perceptron updates and decision boundary shifts [GATE DA 2025 question at 02:30:13]. [02:33:31] – Conclusion: Summary of the high-weightage topics and prep for the final Neural Networks session. #GATEDA #MachineLearning #LinearRegression #TAAI #ConceptToCombat GATE DA 2026 GATE Data Science AI GATE 2026 preparation GATE DA free course GATE DA practice questions GATE DA MCQ MSQ NAT GATE DA strategy GATE DA toppers preparation GATE DA machine learning Linear algebra for GATE DA Probability for GATE DA GATE DA exam tips GATE DA concepts and questions GATE DA next level preparation TAAI GATE Tomorrow's Architect of AI GATE DA rank oriented GATE DA 2026 full syllabus GATE DA beyond concepts To check out the course- www.taai.live/ Join our complete course to boost your GATE DA preparation. 🔹About the complete course: ✅ Complete syllabus coverage for GATE DA. ✅ Concept-focused lectures + regular doubt sessions. ✅ Subject-specific doubt channels. ✅ Expert guidance from our faculty (Manoj Sir, AIR-13 and Sahitya Sir). This course is for anyone who wishes to crack GATE DA, whether you're an absolute beginner or a pro. Join our community: 📌 Website: www.taai.live/ 📌 Telegram: t.me/Manoj_Gate_DSAI 📌 Discord: discord.gg/Yj7pSxMT 📌LinkedIn: www.linkedin.com/company/taai-gate-da-placements/?… 🔔 Subscribe to our channel and hit the bell icon to get more u