EEL 6825: Pattern Recognition and Intelligent Systems - 4 Weeks Course Prep

This is a strategic approach to prepare for EEL 6825: Pattern Recognition and Intelligent Systems, a course that intersects statistics, machine learning, signal processing, and AI.

This plan is heavy on math and modeling, with applications in robotics, vision, speech, and bioinformatics.

🗓️ Study Plan Overview

• Week 1 (July 20–27): Introductory Foundations
• Week 2–3 (July 28–Aug 10): Intermediate Core
• Week 4–5 (Aug 11–Aug 24): Advanced Prep for Course Readiness

🔰 WEEK 1: FOUNDATIONS — “Stat-Driven Pattern Recognition Basics”

🎯 GOAL: Build strong grounding in the math behind pattern recognition.

🔢 1. Statistics & Probability Refresher

Key Topics:

• Bayes’ Theorem
• Conditional & joint probability
• PDFs, PMFs
• Expectation, variance, covariance

Practice:

• Solve Bayes classification problems on paper
• Simulate with Python: sample from numpy.random, calculate distributions

# Basic class probability simulation
import numpy as np

# Assume class priors
priors = [0.3, 0.7]
samples = np.random.choice([0, 1], size=1000, p=priors)

print("Class 0:", np.sum(samples == 0))
print("Class 1:", np.sum(samples == 1))

📚 2. Linear Algebra Refresher

Key Topics:

• Vectors, dot products, matrix multiplication
• Eigenvectors/eigenvalues
• Orthogonality, projection

Practice:

• Use numpy or SymPy to find eigenvalues, singular values
• Visualize 2D vector projections

✍️ 3. Basic Pattern Recognition Concepts

Key Topics:

• What is a pattern?
• Types of classifiers:
  • Supervised vs unsupervised
  • Nearest neighbor, Bayes classifier (generative)

Read:

• Duda, Hart & Stork, Pattern Classification, Ch. 1–2 (classic)
• Or Bishop’s Pattern Recognition and Machine Learning, Ch. 1–2

🪜 WEEK 2–3: INTERMEDIATE — “Classic Models and Decision Theory”

📌 1. Bayesian Decision Theory

Key Topics:

• Loss function, risk minimization
• Classifiers under known distributions
• MAP (Maximum A Posteriori) and ML (Maximum Likelihood) rules

Practice:

• Derive classifiers given Gaussian class distributions
• Apply MAP rule to a toy dataset

📌 2. Parametric vs Nonparametric Models

Key Topics:

• Parametric: Assume distribution (e.g., Gaussian)
• Nonparametric: k-NN, Parzen windows

Practice:

• Build a 2D Gaussian classifier in Python
• Compare with a k-NN model using scikit-learn

📌 3. Dimensionality Reduction

Key Topics:

• PCA (Principal Component Analysis)
• LDA (Linear Discriminant Analysis)

Practice:

• Use sklearn.decomposition.PCA to reduce to 2D and visualize

📌 4. Feature Extraction

Key Topics:

• Manual vs learned features
• Understand: Why good features matter more than the model

🚀 WEEK 4–5: ADVANCED PREP — “Toward Intelligent Systems”

🤖 1. Intro to Learning Algorithms

Key Topics:

• Logistic Regression
• Perceptron Algorithm
• Support Vector Machines (SVMs)

Practice:

• Implement Perceptron or Logistic Regression from scratch
• Use sklearn.svm.SVC on linearly separable data

🧠 2. Neural Networks as Pattern Recognizers

Key Topics:

• Single-layer vs multi-layer perceptrons
• Activation functions
• Training with gradient descent

Practice:

• Use PyTorch or TensorFlow to build a small NN on MNIST

🧠 3. Unsupervised Learning

Key Topics:

• k-means clustering
• Gaussian Mixture Models (GMMs)
• Expectation Maximization (EM)

Practice:

• Compare k-means vs GMM on same dataset

🧠 4. Evaluation Metrics

Key Topics:

• Confusion matrix, ROC curve, F1-score
• Cross-validation

Practice:

• Evaluate models using sklearn.metrics