Matrix factorization model using Kacmarz algorithm: Application in sensor localization

Matrix factorization finds applications in a variety of problems arising in signal processing and machine learning including (but not limited to) pattern recognition, recommender systems, wireless sensor network, audio signal processing and image analysis. In this work, we address the problem of reconstructing a low-rank matrix from its partially observed entries; popularly known as the matrix completion problem. Our algorithm is based on the randomized Kacmarz and block Kacmarz methods. Kaczmarz type algorithms have not been used before to solve matrix factorization problems. We have compared our algorithms with state-of-the-art techniques in matrix completion. We observe that our method is better than almost all prior algorithms in terms of reconstruction accuracy even in cases with substantial amount of missing information.