low rank approximation
Single Pass PCA of Matrix Products
Shanshan Wu, Srinadh Bhojanapalli, Sujay Sanghavi, Alexandros G. Dimakis
Neural Information Processing Systems http://nips.cc/
Sublinear Time Low-Rank Approximation of Distance Matrices
Such distance matrices are commonly computed in software packages and have applications to learning image manifolds, handwriting recognition, and multi-dimensional unfolding, among other things. In an attempt to reduce their description size, we study low rank approximation of such matrices. Our main result is to show that for any underlying distance metric $d$, it is possible to achieve an additive error low rank approximation in sublinear time. We note that it is provably impossible to achieve such a guarantee in sublinear time for arbitrary matrices $\AA$, and our proof exploits special properties of distance matrices. We develop a recursive algorithm based on additive projection-cost preserving sampling.
Hardness of Low Rank Approximation of Entrywise Transformed Matrix Products
Some related lower bounds include the work of Backurs et al. [2017] that solving kernel Support V ector Machines (SVM), ridge regression, or Principal Component Analysis (PCA) problems to high accuracy or approximating kernel density estimates up to a constant factor for kernels with
Sketching Algorithms for Sparse Dictionary Learning: PTAS and Turnstile Streaming
Classically, sketching has been applied to design low-memory algorithms in the streaming setting, when the input is presented to the algorithm as a sequence of updates.
Towards a Zero-One Law for Column Subset Selection
Zhao Song, David Woodruff, Peilin Zhong
Indeed, this is a central question of recent workstudyinggeneralized lowrankmodels.
Regularized Weighted Low Rank Approximation
Frank Ban, David Woodruff, Richard Zhang
Neural Information Processing Systems http://nips.cc/