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首页> 外文期刊>Expert Systems with Application >Feature selection and multi-kernel learning for adaptive graph regularized nonnegative matrix factorization
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Feature selection and multi-kernel learning for adaptive graph regularized nonnegative matrix factorization

机译：自适应图正则化非负矩阵分解的特征选择和多核学习

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摘要

Nonnegative matrix factorization (NMF), a popular part-based representation technique, does not capture the intrinsic local geometric structure of the data space. Graph regularized NMF (GNMF) was recently proposed to avoid this limitation by regularizing NMF with a nearest neighbor graph constructed from the input data set. However, GNMF has two main bottlenecks. First, using the original feature space directly to construct the graph is not necessarily optimal because of the noisy and irrelevant features and nonlinear distributions of data samples. Second, one possible way to handle the nonlinear distribution of data samples is by kernel embedding. However, it is often difficult to choose the most suitable kernel. To solve these bottlenecks, we propose two novel graph-regularized NMF methods, AGNMF_(FS) and AGNMF_(MK), by introducing feature selection and multiple-kernel learning to the graph regularized NMF, respectively. Instead of using a fixed graph as in GNMF, the two proposed methods learn the nearest neighbor graph that is adaptive to the selected features and learned multiple kernels, respectively. For each method, we propose a unified objective function to conduct feature selection/multi-kernel learning, NMF and adaptive graph regularization simultaneously. We further develop two iterative algorithms to solve the two optimization problems. Experimental results on two challenging pattern classification tasks demonstrate that the proposed methods significantly outperform state-of-the-art data representation methods.
机译：非负矩阵分解（NMF）是一种流行的基于零件的表示技术，不能捕获数据空间的固有局部几何结构。最近提出了图正则化NMF（GNMF）来避免此限制，方法是使用从输入数据集构造的最近邻图对NMF进行正则化。但是，GNMF有两个主要瓶颈。首先，由于数据样本的嘈杂和不相关的特征以及非线性分布，直接使用原始特征空间来构造图不一定是最优的。其次，一种处理数据样本非线性分布的可能方法是内核嵌入。但是，通常很难选择最合适的内核。为了解决这些瓶颈，我们通过将特征选择和多核学习分别引入到图形正则化NMF中，提出了两种新颖的图形正则化NMF方法AGNMF_（FS）和AGNMF_（MK）。代替在GNMF中使用固定图，这两种提议的方法分别学习了适应所选特征的最近邻图和学习了多个内核。对于每种方法，我们提出一个统一的目标函数来同时进行特征选择/多核学习，NMF和自适应图正则化。我们进一步开发了两种迭代算法来解决这两个优化问题。在两个具有挑战性的模式分类任务上的实验结果表明，所提出的方法明显优于最新的数据表示方法。

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