Measuring Heterogeneous Thermal Patterns in Infrared-Based Diagnostic Systems Using Sparse Low-Rank Matrix Approximation: Comparative Study

Complex data analytics via sparse, low-rank matrix approximation

Sparse Principal Component Analysis via Regularized Low Rank Matrix Approximation

Principal component analysis (PCA) is a widely used tool for data analysis and dimension reduction in applications throughout science and engineering. However, the principal components (PCs) can sometimes be difficult to interpret, because they are linear combinations of all the original variables. To facilitate interpretation, sparse PCA produces modified PCs with sparse loadings, i.e. loading...

Local Low-Rank Matrix Approximation

Matrix approximation is a common tool in recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the partially observed matrix is of low-rank. We propose a new matrix approximation model where we assume instead that the matrix is locally of low-rank, leading to a representation of the observed matrix as a weighted sum of low...

Sparse and Low Rank Approximation (11w5036)

Digital computers and their efficiency at processing data play a central role in our modern technology. Today, we use digital hardware in every aspect of our daily lives. Cell phones, digital cameras, MP3 players and DVD players are only a few examples where signals of interest, which are inherently analog, are acquired, converted to digital bit streams, stored in compressed form, and transmitt...

Low Rank Matrix Approximation in Linear Time

Given a matrix M with n rows and d columns, and fixed k and ε, we present an algorithm that in linear time (i.e., O(N)) computes a k-rank matrix B with approximation error ‖M−B‖2F ≤ (1+ ε)μopt(M, k), where N = nd is the input size, and μopt(M, k) is the minimum error of a k-rank approximation to M. This algorithm succeeds with constant probability, and to our knowledge it is the first linear-ti...