Dimensionality Reduction in Big Data with Nonnegative Matrix Factorization
Abstract
Nonnegative matrix factorization (NMF) is a linear powerful technique for dimension reduction. It reduces the dimensions of data making learning algorithms faster and more effective. Although NMF and its applications have been developed for more than a decade, they still have limitations in modeling and performance. In this study, the PI's team designed rich models and fast algorithms for NMF. They found solutions for four different problems: 1. Accelerated parallel and distributed algorithm for NMF with Frobenius norm with L1 L2 regularizations.The algorithm is based on the proposed accelerated anti-lop sided algorithm for nonnegative least squares. It attained fast over bounded guaranteed convergence in the space of passive variables, where convex parameter and Lipschitz constant L are bounded. 2. Fast parallel randomized algorithm NMF with Kullback-Leibler divergence. The proposed algorithm has fast convergence, and utilize the sparse properties of data, model and representation. In addition, the experiments indicate that sparse models and sparse representation are archived for large sparse datasets, which is a significant milestone in this research problem.3. New models of simplicial NMF and simplicial nonnegative matrix tri-factorization with Frobenius norm and fast parallel algorithm. The new models have more concise interpretability via these values of factor matrices. The proposed algorithms based on a combination of alternating direction and Frank-Wolfe's scheme attain linear convergence, low iteration complexity, and easily controlled sparsity. The experiments indicate that the proposed model and algorithm outperform the NMF model and its state-of-the-art algorithms.4. New model of simplicial NMF with Kullback-Leibler divergence and fast parallel algorithm. The proposed algorithm as guaranteed instance inference with sub-linear convergence, and easy sparsi.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 20, 2017
- Accession Number
- AD1043681
Entities
People
- Tu-bao Ho
Organizations
- Japan Advanced Institute of Science and Technology