🎬 Movie Recommendation System

GitHub Repository: Recommendation-Engine

📘 Project Overview

This project implements a comprehensive Movie Recommendation System using seven different methods, designed to provide movie suggestions either based on a selected movie or through user interaction data. The algorithms used in this project are:

K-Nearest Neighbors (KNN)
Gaussian Mixture Models (GMM)
Content-Based Filtering
Clustering (K-Means)
Support Vector Machines (SVM)
Artificial Neural Networks (ANN)
Bayesian Recommendation Method

Each method is implemented independently and demonstrates a unique approach to personalization and filtering of movie content.

Preprocessing Steps

The preprocessing pipeline of the movie recommendation system involved the following steps:

Step 1: Original Dataset

Original dataset contained $24$ columns and more than $700,!000$ rows.

$$ \text{Original Size} = 700,!000 \text{ rows} \times 24 \text{ columns} $$

Step 2: Null Value Cleaning

Removed all rows or entries with missing/null values.

Let:

$D$ be the original dataset.
$D_{\text{cleaned}}$ be the dataset after cleaning nulls.

Then: $$ D_{\text{cleaned}} = D \setminus { \text{rows with nulls} } $$

Step 3: Sampling

To reduce computational load, kept only the top $5000$ rows.

Let:

$D_{\text{sampled}}$ be the dataset after sampling.

Then: $$ D_{\text{sampled}} = \text{Top } 5000 \text{ rows of } D_{\text{cleaned}} $$

Step 4: Feature Encoding

a) One-Hot Encoding for Categorical Columns

Converted categorical data (e.g., genres, tags) to binary vector format.

For a feature with $n$ categories: $$ x_i \in {c_1, c_2, \dots, c_n} \Rightarrow \text{OneHot}(x_i) = [0, 0, \dots, 1, \dots, 0] $$

Dropped categorical columns with too few entries (low cardinality).

b) TF-IDF for Textual Columns

Applied TF-IDF vectorization to string data (e.g., overview, tagline).

Let:

$tf(t,d)$ = term frequency of term $t$ in document $d$
$idf(t)$ = inverse document frequency of term $t$

Then: $$ \text{TF-IDF}(t,d) = tf(t,d) \cdot \log\left( \frac{N}{df(t)} \right) $$

Where:

$N$ is the total number of documents
$df(t)$ is the number of documents containing term $t$
Dropped textual columns with insufficient data.

Step 5: Final Feature Vector Creation

After all transformations, each movie is represented as a vector of $800$ dimensions:

$$ \vec{v}_{\text{movie}} \in \mathbb{R}^{800} $$

These vectors are then used as input for all recommendation algorithms.

🧠 1. K-Nearest Neighbors (KNN)

Purpose: Recommend movies that are similar to a selected movie using proximity in feature space.

📐 Mathematical Foundation

Given:

A movie query vector $q$
A set of movie vectors $x_1, x_2, ..., x_n$

We compute the Euclidean distance:

$$ d(q, x_i) = \sqrt{\sum_{j=1}^{m}(q_j - x_{ij})^2} $$

We then select the $k$ smallest distances and recommend the corresponding movies.

Alternatively, cosine similarity can be used:

$$ \text{sim}(A, B) = \frac{A \cdot B}{|A| |B|} $$

📈 2. Gaussian Mixture Model (GMM)

Purpose: Probabilistic clustering of movies based on their features and recommending from similar distributions.

📐 Mathematical Foundation

GMM assumes data points are generated from a mixture of several Gaussian distributions:

$$ p(x) = \sum_{k=1}^{K} \pi_k \mathcal{N}(x \mid \mu_k, \Sigma_k) $$

Where:

$\pi_k$ = weight of the $k^{\text{th}}$ component
$\mu_k$ = mean of the $k^{\text{th}}$ component
$\Sigma_k$ = covariance matrix of the $k^{\text{th}}$ component
$\mathcal{N}(x|\mu_k,\Sigma_k)$ = multivariate normal distribution

📚 3. Content-Based Filtering

Purpose: Recommend movies similar to the selected movie based on descriptive features (genre, tags, cast, etc.).

📐 Mathematical Foundation

Content features are typically vectorized using TF-IDF or embeddings. Then similarity is measured using cosine similarity:

$$ \text{sim}(A, B) = \frac{\sum_{i=1}^{n} A_i B_i}{\sqrt{\sum_{i=1}^{n} A_i^2} \cdot \sqrt{\sum_{i=1}^{n} B_i^2}} $$

Recommendations are sorted by similarity score.

Analysis

4. Clustering (K-Means)

Purpose

Group similar movies together based on features. This enables the system to recommend movies from the same cluster, assuming that users might enjoy other items within a group of similar ones.

Mathematical Foundation

K-Means aims to partition n data points into k clusters in which each data point belongs to the cluster with the nearest mean (centroid), minimizing intra-cluster variance.

Working :-

Choose the number of clusters (k)
Randomly initialize k centroids
Assign each point to the nearest cluster centroid
Recalculate cluster centroids as the mean of assigned points
Repeat steps 3-4 until convergence (or until reach max epoch)

Use in Recommendation

After clustering movies:

For a given user’s liked movie, find the cluster it belongs to
Recommend other movies from the same cluster

This helps in:

Discovering niche patterns in data
Making content-based or collaborative recommendations more effective

5. Support Vector Machine (SVM)

Purpose: Classify user-preferred genres or features to recommend movies falling within the same classification boundaries.

📐 Mathematical Foundation

SVM aims to find a hyperplane:

$$ \min_{\mathbf{w}, b} \frac{1}{2} |\mathbf{w}|^2 \quad \text{subject to } y_i(\mathbf{w} \cdot \mathbf{x}_i + b) \geq 1 $$

Where:

$\mathbf{w}$ = weight vector
$b$ = bias
$\mathbf{x}_i$ = feature vector of movie
$y_i$ = user label (+1 for like, -1 for dislike)

With kernels:

$$ K(x_i, x_j) = \phi(x_i) \cdot \phi(x_j) $$

🤖 6. Artificial Neural Network (ANN)

Purpose: Learn from user interactions (ratings, clicks, etc.) to recommend personalized content.

📐 Mathematical Foundation

A basic feedforward ANN:

Layer Transformations:

$$ Z^{(1)} = W^{(1)}X + b^{(1)} $$ $$ A^{(1)} = \text{ReLU}(Z^{(1)}) $$ $$ Z^{(2)} = W^{(2)}A^{(1)} + b^{(2)} $$ $$ \hat{Y} = \text{softmax}(Z^{(2)}) $$

Loss Function (Cross-Entropy):

$$ \mathcal{L} = -\sum_{i=1}^{n} y_i \log(\hat{y}_i) $$

Backpropagation Update:

$$ W = W - \alpha \cdot \frac{\partial \mathcal{L}}{\partial W} $$

Where:

$\alpha$ is the learning rate
$\hat{y}_i$ is predicted probability

📊 7. Bayesian Recommendation Method

Purpose: Probabilistically recommend movies based on prior user behavior and item features.

📐 Mathematical Foundation

Using Bayes’ Theorem:

$$ P(\text{Movie} | \text{User}) = \frac{P(\text{User} | \text{Movie}) \cdot P(\text{Movie})}{P(\text{User})} $$

Let:

$M$ be a movie
$U$ be user preferences

Then:

$$ P(M | U) \propto P(U | M) \cdot P(M) $$

With Naive Bayes:

$$ P(M | U) \propto P(M) \prod_{i=1}^{n} P(F_i | M) $$

Where $F_i$ are user’s observed features (genre preferences, past ratings, etc.)

Analysis

📦 Dataset and Feature Engineering (Preprocessing)

We utilized the following for preprocessing and feature engineering:

Movie Metadata: genres, tags, cast, director
User Interaction Data: ratings, watch history, favorites
Textual Features:
- Cleaned and lowercased text
- Removed stopwords and punctuations
- Tokenized, then used TF-IDF vectorization
Numerical Features:
- Normalization using min-max scaling
- PCA for dimensionality reduction
Categorical Features:
- One-hot encoding for genres, directors, and cast

🔍 Model Comparison

Method	Type	User Input Based	Model Type	Strengths	Weaknesses
KNN	Unsupervised	No	Memory-based	Simple, no training	Inefficient at scale
GMM	Unsupervised	No	Probabilistic	Soft clustering	Sensitive to parameters
Content-Based	Unsupervised	No	Metadata-based	No cold-start issue for users	Limited diversity
K-Means Clustering	Unsupervised	No	Hard clustering	Fast and scalable	Assumes spherical clusters
SVM	Supervised	No	Classification	Works with high-dimensional data	Needs labeled data
ANN	Supervised	Yes	Deep learning	Captures nonlinear relationships	Needs large dataset
Bayesian	Probabilistic	No	Probabilistic	Works well with sparse data	Assumes independence of features

🚀 Future Work

Implement hybrid recommender systems combining collaborative + content-based filtering
Use Transformer-based architectures for sequence-aware recommendations
Incorporate temporal dynamics and trends in user behavior
Deploy on cloud with scalable APIs and dashboards

🧩 Dependencies

Python
NumPy, Pandas
Scikit-learn
TensorFlow / PyTorch
Matplotlib / Seaborn

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🎬 Movie Recommendation System

📘 Project Overview

Preprocessing Steps

Step 1: Original Dataset

Step 2: Null Value Cleaning

Step 3: Sampling

Step 4: Feature Encoding

a) One-Hot Encoding for Categorical Columns

b) TF-IDF for Textual Columns

Step 5: Final Feature Vector Creation

🧠 1. K-Nearest Neighbors (KNN)

📐 Mathematical Foundation

📈 2. Gaussian Mixture Model (GMM)

📐 Mathematical Foundation

📚 3. Content-Based Filtering

📐 Mathematical Foundation

Analysis

4. Clustering (K-Means)

Purpose

Mathematical Foundation

Working :-

Use in Recommendation

5. Support Vector Machine (SVM)

📐 Mathematical Foundation

🤖 6. Artificial Neural Network (ANN)

📐 Mathematical Foundation

📊 7. Bayesian Recommendation Method

📐 Mathematical Foundation

Analysis

📦 Dataset and Feature Engineering (Preprocessing)

🔍 Model Comparison

🚀 Future Work

🧩 Dependencies