🎬 Movie Recommendation Engine

📌 Overview

This project is a Movie Recommendation Engine that provides personalized suggestions using six different machine learning algorithms. Each model uses structured movie metadata to learn what the user likes and predict similar content.

👉 Live Demo

---

Workflow

---

1️⃣ Data Preprocessing – Movie Vector Creation

We start by converting raw movie metadata into a fixed 800-dimensional vector representation.

Steps:

• Extract features from: genres, cast, overview, keywords, director
• Use TF-IDF vectorization on text-based columns.
• Reduce dimensionality (e.g., via PCA or Truncated SVD) to form 800-D vectors.

Formula:

• TF-IDF Score:
  TF-IDF(t, d) = TF(t, d) × log(N / DF(t))
  where t = term, d = document, N = total documents, DF(t) = document frequency

➡️ Each movie becomes a numeric vector in ℝ⁸⁰⁰
➡️ These vectors are the basis for all models.

---

2️⃣ K-Nearest Neighbors (KNN)

Finds the most similar movies based on vector distances from liked movies.

Used for:

• Recommending movies close to user's liked history in feature space.

Metrics:

• Cosine Similarity:
  sim(A, B) = (A · B) / (||A|| × ||B||)
• Euclidean Distance:
  dist(A, B) = √Σ (Ai - Bi)²

---

3️⃣ Clustering (K-Means / Hierarchical)

Groups movies into clusters of similar content.

Used for:

• Recommending movies from the same cluster as liked ones.

Core Concept:

• K-Means Objective:
  Minimize total within-cluster variance:
  ∑ᵢ ∑ₓ ∈ Cᵢ ||x - μᵢ||²
  where μᵢ is cluster centroid

• Linkages in Hierarchical Clustering:

  • Single-link: min distance
  • Complete-link: max distance
  • Average-link: average pairwise distance

---

4️⃣ Perceptron (Neural Network)

A shallow neural net that classifies whether a movie will be liked.

Used for:

• Binary classification (like/dislike) from past data.

Model:

• Input → Dense Layer → ReLU → Dense Layer → Sigmoid Output

Core Formula:

• Output:
  y = sigmoid(Wx + b)
  where sigmoid(z) = 1 / (1 + e⁻ᶻ)

• Loss Function: Binary Cross-Entropy
  L = -[y·log(p) + (1-y)·log(1-p)]

---

5️⃣ Bayesian Recommendation (Naïve Bayes)

Classifies based on conditional probabilities assuming feature independence.

Used for:

• Probabilistic prediction of movie preference.

Core Formula:

• Bayes Theorem:
  P(A | B) = (P(B | A) × P(A)) / P(B)

• We predict the class (like/dislike) with the highest posterior.

---

6️⃣ Content-Based Filtering

Recommends movies that are textually or semantically similar to user's liked movies.

Used for:

• Matching metadata (genres, plot, actors) using vector space models.

Similarity:

• Same as cosine similarity:
  sim(A, B) = (A · B) / (||A|| × ||B||)

---

🧠 Summary of Models

Model	Type	Formula / Key Concept
TF-IDF + Vectors	Preprocessing	TF-IDF(t, d) = TF × log(N / DF)
KNN	Similarity-based	Cosine / Euclidean distance
K-Means Clustering	Unsupervised	Minimize ∑
Perceptron	Neural Network	y = sigmoid(Wx + b)
Naïve Bayes	Probabilistic	P(A
Content-Based	Metadata Matching	Cosine similarity on text-based features

---

📊 Dataset

• TMDB or similar movie dataset.
• Features include: Title, Genres, Cast, Overview, Keywords, Ratings, Popularity, etc.

---