论文标题
用于字典学习，denoing和croptring的强大非线性基质分解
Robust Non-Linear Matrix Factorization for Dictionary Learning, Denoising, and Clustering
论文作者
论文摘要
跨计算机视觉和机器学习的数据集中的低维非线性结构。最近，已经提出了核基质分解技术来学习这些非线性结构，以通过观察到足够大的特征空间中矩阵的图像是低率的，用于降低，分类，词典学习和缺少数据插补。但是，这些非线性方法在存在稀疏噪声或异常值的情况下失败。在这项工作中，我们提出了一种称为鲁棒非线性矩阵分解（RNLMF）的新的鲁棒非线性分解方法。 RNLMF通过考虑内核特征空间来构建数据空间的字典；然后可以将嘈杂的矩阵分解为稀疏噪声矩阵的总和和位于低维非线性歧管的干净数据矩阵。 RNLMF对于稀疏的噪声，离群值和比例很强，到具有数千行和列的矩阵。从经验上讲，RNLMF对基线方法进行了明显的改进，以降级和聚类。
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.
