Fast Singular Value Decomposition for Large-scale Growing Data

Singular value decomposition (SVD) is a fundamental technique in linear algebra, and it is widely applied in many modern information technologies, for example, high dimensional data visualization, dimension reduction, data mining, latent semantic analysis, etc. However, when the matrix size of the data is huge and continuously growing, the matrix can not be loaded all at once into the computer memory and O(n(3)) computational cost of SVD becomes infeasible. To resolve this problem, we will adapt a fast multidimensional scaling method to obtain a fast SVD method, given that the significant rank of a huge matrix is small. This proposed fast SVD method can be easily implemented via parallel computing. We also propose a fast update method to be applied when the huge data is updated continuously. We will demonstrate that the approximated SVD result is sufficiently accurate, and most importantly it can be derived very efficiently. Using this fast update method, many modern techniques based on SVD which were infeasible will become viable.