Face Recognition with PCA (Eigenfaces)

Face recognition system built from scratch using Principal Component Analysis (PCA) — also known as the Eigenfaces method — on the AT&T (ORL) face dataset. No pre-built ML or face recognition libraries are used. The entire PCA pipeline is implemented manually with NumPy.

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Overview

This project demonstrates how linear algebra concepts — covariance matrices, eigenvalues, and eigenvectors — can be applied to solve a real-world computer vision problem. Each face image is compressed from a 10,304-dimensional vector down to k dimensions using the top-k eigenfaces, then recognized via nearest-neighbor search in PCA space.

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Dataset

AT&T Face Database (ORL)

• 40 subjects × 10 grayscale images = 400 images total
• Image size: 112 × 92 pixels → flattened to a 10,304-dim vector
• Split: first 7 images/subject → train (280 images), last 3 → test (120 images)

Place the dataset folder in the same directory as pca.py and rename it ATnT/. Expected structure: ATnT/s1/1.pgm, ATnT/s1/2.pgm, ..., ATnT/s40/10.pgm

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Pipeline

Step	Function	Description
1	load_data()	Read .pgm images, flatten each 112×92 matrix to a 10,304-dim float64 vector, split into train/test
2	compute_pca()	Compute mean face, center data, apply the dual trick (eigen-decompose A·Aᵀ of size 280×280 instead of Aᵀ·A of size 10304×10304), project back to image space, sort by descending eigenvalue
3	extract_features()	Keep top-k eigenfaces; project all training images → weight matrix of shape (280, k)
4	recognize_face()	Normalize test image, project into PCA space, find nearest neighbor by Euclidean distance
5	evaluate_accuracy()	Sweep over multiple k values, compute recognition accuracy, plot and save the Accuracy vs k curve
Bonus	show_eigenfaces()	Visualize the mean face and first 10 eigenfaces

Data flow

400 images → flatten → (280 × 10304) train matrix → PCA → 280 eigenfaces → keep k → (280 × k) weight matrix → 1-NN → predicted label

Results

k (components)	Accuracy
5	~80%
20	~93%
50	~95%+
80–150	~96%+

Best accuracy is typically achieved around k = 80–150. See accuracy_vs_k.png for the full curve.

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Outputs

File	Description
eigenfaces.png	Mean face + first 10 eigenfaces visualized as images
accuracy_vs_k.png	Recognition accuracy plotted against number of components k

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Getting Started

1. Install dependencies

pip install numpy opencv-python matplotlib

2. Prepare the dataset

project/
├── pca.py
└── ATnT/
├── s1/
│   ├── 1.pgm
│   └── ...
├── s2/
└── ...
### 3. Run

```bash
python pca.py

The program will:

1. Load and split the dataset
2. Compute PCA and display eigenfaces (close the popup to continue)
3. Evaluate recognition accuracy for k ∈ {5, 10, 20, 30, 50, 80, 100, 150, 200}
4. Print the best k and accuracy, save both plots

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Requirements

1. numpy
2. opencv-python
3. matplotlib

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Project Structure

project/
├── pca.py                # Main script: PCA + Eigenfaces pipeline
├── requirements.txt      # Dependencies (numpy, opencv-python, matplotlib)
├── README.md             # Project documentation
│
├── ATnT/                 # Dataset folder (40 subjects × 10 images each)
│   ├── s1/
│   │   ├── 1.pgm
│   │   ├── 2.pgm
│   │   └── ...
│   ├── s2/
│   ├── ...
│   └── s40/
│
├── outputs/              # Generated results
│   ├── eigenfaces.png    # Mean face + first 10 eigenfaces
│   └── accuracy_vs_k.png # Accuracy vs number of components k