Person Recognition with PCA & Cosine Similarity

📌 Introduction

Person recognition is a core task in biometrics and computer vision. This article explores an efficient approach using Principal Component Analysis (PCA) to reduce feature dimensions and Cosine Similarity to compare identity vectors.

🔢 Mathematical Concepts

Principal Component Analysis (PCA) is used to project high-dimensional face images into a lower-dimensional subspace that retains the most variance.

Where:

• X = mean-centered data matrix
• W = eigenvectors (principal components)
• Z = projected data (face embeddings)

Cosine Similarity compares two face vectors A and B:

🧠 Algorithm Steps

1. Preprocess all face images (resize, grayscale, flatten).
2. Apply PCA to reduce dimensionality of image vectors.
3. Store PCA-projected embeddings for known persons.
4. Project a test face image using same PCA transformation.
5. Compare test vector to known embeddings using Cosine Similarity.
6. Return the identity with the highest similarity score.

💻 Python Code

import cv2
import numpy as np
from sklearn.decomposition import PCA
from sklearn.metrics.pairwise import cosine_similarity

# Load face data
X = []  # known face vectors
labels = []

for i in range(1, 6):
    img = cv2.imread(f"person{i}.jpg", cv2.IMREAD_GRAYSCALE)
    img = cv2.resize(img, (100, 100)).flatten()
    X.append(img)
    labels.append(f"Person {i}")

X = np.array(X)

# Apply PCA
pca = PCA(n_components=50)
X_pca = pca.fit_transform(X)

# Test image
test_img = cv2.imread("unknown.jpg", cv2.IMREAD_GRAYSCALE)
test_img = cv2.resize(test_img, (100, 100)).flatten()
test_pca = pca.transform([test_img])

# Compare using cosine similarity
similarities = cosine_similarity(test_pca, X_pca)[0]
best_match = labels[np.argmax(similarities)]

print("Identified as:", best_match)

📊 Applications

• Face-based access control systems
• Biometric authentication in devices
• Attendance systems in schools and offices

✅ Conclusion

PCA reduces computation by projecting faces into a compact vector space, and cosine similarity enables quick and accurate identity matching. This method is lightweight, interpretable, and performs well on small to mid-scale datasets.