Face-Recognition-using-Principal-Component-Analysis

This repository contains a .ipynb file which contains the code for facial recognitation of PCA

Objective:

We have created a basic facial recognition system using a technique called principal component analysis (PCA) by projecting the face images on the feature space (face space) which best represents the variations among distinct faces. The face space is defined as the “Eigenfaces", which are the eigenvectors of the set of faces.

The goal of implementing this system is to recognize a person's face by comparing it to a pre-existing database of faces, and identifying the closest match.

Link to paper on Eigenfaces: https://sites.cs.ucsb.edu/~mturk/Papers/mturk-CVPR91.pdf

About the dataset:

The AT&T face dataset contains a set of grayscale face images with dimensions 92x112. There is a folder in this repo named AT&T from which we have loaded our dataset. The images are organised in 40 directories (one for each subject), which have names of the form sX, where X indicates the subject number (between 1 and 40). In each of these directories, there are ten different images of that subject, which have names of the form Y.pgm, where Y is the image number for that subject (between 1 and 10). These 10 images per person are taken at different times, varying the lighting, facial expressions (open / closed eyes, smiling / not smiling) and facial details (glasses / no glasses). All the images were taken against a dark homogeneous background with the subjects in an upright, frontal position (with tolerance for some side movement). Link: https://git-disl.github.io/GTDLBench/datasets/att_face_dataset/

Tasks Performed

1. Loading dataset and divide the date into training and test sets.
2. Implement the PCA algorithm from scratch.
3. Implement image reconstruction using the eigen projections and visualise differences for different number of components.
4. Visualise the mean(Eigen face) generated.
5. Given training set, obtain accuracy by attempting a face regonition module and obtaining the accuracy for different number of principal components.

Steps for Implementation of PCA Algorithm

1. Standardize the data: PCA is sensitive to the scale of the input data, so it is important to standardize the data to have zero mean and unit variance.

2. Compute the covariance matrix: Calculate the covariance matrix of the standardized data. This matrix shows how the different features of the data are related to each other.

3. Compute the eigenvectors and eigenvalues of the covariance matrix: The eigenvectors are the principal components, and the eigenvalues indicate the amount of variance explained by each principal component.

4. Select the principal components: Sort the eigenvectors by their corresponding eigenvalues in descending order, and select the top k eigenvectors to form the new lower-dimensional space. This new space will have k dimensions, where k is less than the original number of dimensions.

Steps for Implementation of Image Reconstruction from Eigenfaces

1. Load the image: Load the image that you want to reconstruct.

2. Vectorize the image: Convert the grayscale image into a 1D vector.

3. Standardize the data

4. Compute the eigenvectors and eigenvalues: Compute the eigenvectors and eigenvalues of the covariance matrix of the standardized vector.

5. Select the principal components: Choose the top k eigenvectors that explain the most variance in the data. This will be the lower-dimensional representation of the image.

6. Project the image onto the lower-dimensional space: Project the standardized vector onto the selected eigenvectors to obtain the lower-dimensional representation.

7. Reconstruct the image: Multiply the lower-dimensional representation by the selected eigenvectors and add the mean of the standardized vector to obtain the reconstructed image.

Advantages of using PCA in general and limitations of PCA in context of face recognitation.

Answer:

Advantages:

• Reduces the number of variables: PCA can help reduce the number of variables in a dataset while retaining the most important information. This can help simplify analysis and improve model performance.

• Increases interpretability: PCA transforms variables into a new set of variables that are uncorrelated and have a clear interpretation. This can help improve the interpretability of the data and make it easier to understand.

• Improves visualization: PCA can be used to visualize high-dimensional data in a lower-dimensional space, making it easier to see patterns and relationships.

Limitations:

• Assumes linear relationships: PCA assumes that the relationships between variables are linear. If there are non-linear relationships, PCA may not be appropriate.

• Can be sensitive to outliers: PCA can be sensitive to outliers, which can have a significant impact on the results. Requires data scaling: PCA requires that variables be scaled to have the same variance, which can be problematic if variables have very different scales.

In the context of face recognition, PCA has some additional limitations:

• Limited ability to capture facial variations: PCA is not always able to capture the full range of facial variations, such as changes in lighting or expression, which can limit its effectiveness in face recognition applications.

• Limited accuracy: While PCA can be effective for face recognition in some situations, it is not always accurate enough for use in high-security applications where identification must be highly reliable.

• Limited ability to handle large datasets: PCA can be computationally expensive and may not be suitable for very large datasets.