Samanvaya Panda supervised by Dr. Srinathan Kannan  received his Master of Science  in Computer Science and Engineering (CSE). Here’s a summary of his research work on PCA on Encrypted Data: Polynomial Approximation of Inverse sqrt() and Using CKKS Scheme to Perform PCA:

Principal component analysis(PCA) is one of the most popular linear dimensionality reduction techniques in machine learning. In this thesis, we present a method for performing PCA on encrypted data using a homomorphic encryption scheme. We used the CKKS homomorphic encryption scheme for our purpose since it is most suitable for machine learning tasks allowing approximate computations on real numbers. In this thesis, we propose a new Homomorphic PCA(HPCA) algorithm that performs PCA. Unlike previously proposed algorithms, our HPCA algorithm is non-interactive in nature. This requires an approximation of the inverse sqrt function. This thesis presents two methods to approximate and securely perform the inverse sqrt function using CKKS homomorphic encryption scheme- Constrained Linear Regression and Pivot-Tangent method. Since the CKKS homomorphic scheme allows only the computation of polynomial functions, we propose a method to approximate the inverse sqrt function polynomially. Ultimately, we implement our approach for the inverse sqrt function. We provide an implementation of our method for the inverse sqrt function. Weusetheinverse sqrt approximations in our HPCA algorithm to make it non-interactive. In the end, we present the experimental results of our proposed HPCA algorithm on a few datasets computing a few principal components. We measure the R2 score on the reconstructed data and use it as an evaluation metric for our HPCA algorithm. 

March 2025