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

Описание: 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.

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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.


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