Robust Non-Linear Matrix Factorization for Dictionary Learning, Denoising, and Clustering
Robust Non-Linear Matrix Factorization for Dictionary Learning, Denoising, and Clustering
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DOI：
10.1109/tsp.2021.3062988
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发表时间：
2020-05
影响因子：
5.4
通讯作者：
Jicong Fan;Chengrun Yang;Madeleine Udell
中科院分区：
文献类型：
--
作者：
Jicong Fan;Chengrun Yang;Madeleine Udell
低维非线性结构在计算机视觉和机器学习的数据集中大量存在。最近提出了核化矩阵分解技术，通过观察足够大的特征空间中的矩阵图像是低秩的，来学习这些非线性结构，用于去噪、分类、字典学习和缺失数据插补。然而，这些非线性方法在存在稀疏噪声或异常值的情况下会失败。在这项工作中，我们提出了一种新的鲁棒非线性分解方法，称为鲁棒非线性矩阵分解（RNLMF）。 RNLMF通过分解核化特征空间来构造数据空间的字典；然后，噪声矩阵可以分解为稀疏噪声矩阵和位于低维非线性流形中的干净数据矩阵的总和。 RNLMF 对于稀疏噪声和异常值具有鲁棒性，并且可以扩展到具有数千行和列的矩阵。根据经验，RNLMF 在去噪和聚类方面比基线方法取得了显着的改进。
Low dimensional nonlinear structure abounds in datasets across computer vision and machine learning. Kernelized matrix factorization techniques have recently been proposed to learn these nonlinear structures for denoising, classification, dictionary learning, and missing data imputation, by observing that the image of the matrix in a sufficiently large feature space is low-rank. However, these nonlinear methods fail in the presence of sparse noise or outliers. In this work, we propose a new robust nonlinear factorization method called Robust Non-Linear Matrix Factorization (RNLMF). RNLMF constructs a dictionary for the data space by factoring a kernelized feature space; a noisy matrix can then be decomposed as the sum of a sparse noise matrix and a clean data matrix that lies in a low dimensional nonlinear manifold. RNLMF is robust to sparse noise and outliers and scales to matrices with thousands of rows and columns. Empirically, RNLMF achieves noticeable improvements over baseline methods in denoising and clustering.