Parallel MMF: a Multiresolution Approach to Matrix Computation

Multiresolution Matrix Compression

Multiresolution Matrix Factorization (MMF) is a recently introduced method for finding multiscale structure and defining wavelets on graphs and matrices. MMF can also be used for matrix compression (sketching). However, the original MMF algorithm of (Kondor et al., 2014) scales with n or worse (where n is the number of rows/columns in the matrix to be factorized) making it infeasible for large ...

Fast Finite Element Method Using Multi-Step Mesh Process

This paper introduces a new method for accelerating current sluggish FEM and improving memory demand in FEM problems with high node resolution or bulky structures. Like most of the numerical methods, FEM results to a matrix equation which normally has huge dimension. Breaking the main matrix equation into several smaller size matrices, the solving procedure can be accelerated. For implementing ...

A Projected Alternating Least square Approach for Computation of Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) is a common method in data mining that have been used in different applications as a dimension reduction, classification or clustering method. Methods in alternating least square (ALS) approach usually used to solve this non-convex minimization problem.  At each step of ALS algorithms two convex least square problems should be solved, which causes high com...

The theory of matrix-valued multiresolution analysis frames

A Multiresolution Algorithm for Feature Tracking in Image Sequences

In this paper we describe a real-time oriented algorithm for tracking a feature in a sequence of images. The algorithm is based on the search of the feature in an area around the position of the feature in the previous frame of the sequence. In order to obtain a fast response, the process is performed by massively parallel computation, with a multiresolution approach.