Learning Multiresolution Matrix Factorization and its Wavelet Networks on Graphs

• URL: http://arxiv.org/abs/2111.01940v1
• Date: Tue, 2 Nov 2021 23:14:17 GMT
• Title: Learning Multiresolution Matrix Factorization and its Wavelet Networks on Graphs
• Authors: Truong Son Hy and Risi Kondor
• Abstract summary: Multiresolution Matrix Factorization (MMF) is unusual amongst fast matrix factorization algorithms. We propose a learnable version of MMF that carfully optimize the factorization with a combination of reinforcement learning and Stiefel manifold optimization. We show that the resulting wavelet basis far outperforms prior MMF algorithms and provides the first version of this type of factorization that can be robustly deployed on standard learning tasks.
• Score: 11.256959274636724
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Multiresolution Matrix Factorization (MMF) is unusual amongst fast matrix factorization algorithms in that it does not make a low rank assumption. This makes MMF especially well suited to modeling certain types of graphs with complex multiscale or hierarchical strucutre. While MMF promises to yields a useful wavelet basis, finding the factorization itself is hard, and existing greedy methods tend to be brittle. In this paper we propose a learnable version of MMF that carfully optimizes the factorization with a combination of reinforcement learning and Stiefel manifold optimization through backpropagating errors. We show that the resulting wavelet basis far outperforms prior MMF algorithms and provides the first version of this type of factorization that can be robustly deployed on standard learning tasks.

Related papers

• Learning to Solve Multiresolution Matrix Factorization by Manifold Optimization and Evolutionary Metaheuristics [6.4671761956203655]
  We propose a learnable'' version of Multiresolution Matrix Factorization (MMF) We show that the resulting wavelet basis far outperforms prior MMF algorithms. We construct the wavelet neural networks (WNNs) learning graphs on the spectral domain with the wavelet basis produced by our MMF learning algorithm.
  arXiv  Detail & Related papers  (2024-06-01T15:38:57Z)
• Exponentially Convergent Algorithms for Supervised Matrix Factorization [2.1485350418225244]
  Supervised factorization (SMF) is a machine learning method that converges extraction and classification tasks. Our paper provides a novel framework that 'lifts' SMF as a low-rank estimation problem in a combined factor space estimation.
  arXiv  Detail & Related papers  (2023-11-18T23:24:02Z)
• Quadratic Matrix Factorization with Applications to Manifold Learning [1.6795461001108094]
  We propose a quadratic matrix factorization (QMF) framework to learn the curved manifold on which the dataset lies. Algorithmically, we propose an alternating minimization algorithm to optimize QMF and establish its theoretical convergence properties. Experiments on a synthetic manifold learning dataset and two real datasets, including the MNIST handwritten dataset and a cryogenic electron microscopy dataset, demonstrate the superiority of the proposed method over its competitors.
  arXiv  Detail & Related papers  (2023-01-30T15:09:00Z)
• Unitary Approximate Message Passing for Matrix Factorization [90.84906091118084]
  We consider matrix factorization (MF) with certain constraints, which finds wide applications in various areas. We develop a Bayesian approach to MF with an efficient message passing implementation, called UAMPMF. We show that UAMPMF significantly outperforms state-of-the-art algorithms in terms of recovery accuracy, robustness and computational complexity.
  arXiv  Detail & Related papers  (2022-07-31T12:09:32Z)
• FastSTMF: Efficient tropical matrix factorization algorithm for sparse data [0.0]
  Matrix factorization, one of the most popular methods in machine learning, has recently benefited from introducing non-linearity in prediction tasks using tropical semiring. In our work, we propose a new method FastSTMF based on Sparse Tropical Matrix Factorization (STMF) We evaluate FastSTMF on synthetic and real gene expression data from the TCGA database, and the results show that FastSTMF outperforms STMF in both accuracy and running time.
  arXiv  Detail & Related papers  (2022-05-13T13:13:06Z)
• Permutation Invariant Policy Optimization for Mean-Field Multi-Agent Reinforcement Learning: A Principled Approach [128.62787284435007]
  We propose the mean-field proximal policy optimization (MF-PPO) algorithm, at the core of which is a permutation-invariant actor-critic neural architecture. We prove that MF-PPO attains the globally optimal policy at a sublinear rate of convergence. In particular, we show that the inductive bias introduced by the permutation-invariant neural architecture enables MF-PPO to outperform existing competitors.
  arXiv  Detail & Related papers  (2021-05-18T04:35:41Z)
• Self-supervised Symmetric Nonnegative Matrix Factorization [82.59905231819685]
  Symmetric nonnegative factor matrix (SNMF) has demonstrated to be a powerful method for data clustering. Inspired by ensemble clustering that aims to seek better clustering results, we propose self-supervised SNMF (S$3$NMF) We take advantage of the sensitivity to code characteristic of SNMF, without relying on any additional information.
  arXiv  Detail & Related papers  (2021-03-02T12:47:40Z)
• Positive Semidefinite Matrix Factorization: A Connection with Phase Retrieval and Affine Rank Minimization [71.57324258813674]
  We show that PSDMF algorithms can be designed based on phase retrieval (PR) and affine rank minimization (ARM) algorithms. Motivated by this idea, we introduce a new family of PSDMF algorithms based on iterative hard thresholding (IHT)
  arXiv  Detail & Related papers  (2020-07-24T06:10:19Z)
• Towards Minimax Optimal Reinforcement Learning in Factored Markov Decision Processes [53.72166325215299]
  We study minimax optimal reinforcement learning in episodic factored Markov decision processes (FMDPs) First one achieves minimax optimal regret guarantees for a rich class of factored structures. Second one enjoys better computational complexity with a slightly worse regret.
  arXiv  Detail & Related papers  (2020-06-24T00:50:17Z)
• Augmentation of the Reconstruction Performance of Fuzzy C-Means with an Optimized Fuzzification Factor Vector [99.19847674810079]
  Fuzzy C-Means (FCM) is one of the most frequently used methods to construct information granules. In this paper, we augment the FCM-based degranulation mechanism by introducing a vector of fuzzification factors. Experiments completed for both synthetic and publicly available datasets show that the proposed approach outperforms the generic data reconstruction approach.
  arXiv  Detail & Related papers  (2020-04-13T04:17:30Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.