Neighborhood Structure Assisted Non-negative Matrix Factorization and Its Application in Unsupervised Point-wise Anomaly Detection
Neighborhood Structure Assisted Non-negative Matrix Factorization and Its Application in Unsupervised Point-wise Anomaly Detection
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发表时间：
2021
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通讯作者：
Imtiaz Ahmed;Xia Ben Hu;Mithun P. Acharya;Yu Ding
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作者：
Imtiaz Ahmed;Xia Ben Hu;Mithun P. Acharya;Yu Ding
降维被认为是确保异常检测等无监督学习竞争性能的重要一步。非负矩阵分解（NMF）是实现这一目标的广泛使用的方法。但 NMF 没有提供包含邻域结构信息的规定，因此，在存在非线性流形结构的情况下可能无法提供令人满意的性能。为了解决这个缺点，我们建议考虑 NMF 框架内的邻域结构相似性信息，并通过最小生成树对数据进行建模来实现这一点。我们将所得方法标记为邻域结构辅助 NMF。我们进一步开发离线和在线算法来实现所提出的方法。使用 20 个基准数据集以及从水电站提取的工业数据集进行的实证比较证明了邻域结构辅助 NMF 的优越性。仔细研究所提出的 NMF 方法的公式和属性，并将其与几种 NMF 变体进行比较，我们发现基于 MST 的邻域结构的包含在增强异常检测性能方面发挥着关键作用
Dimensionality reduction is considered as an important step for ensuring competitive performance in unsupervised learning such as anomaly detection. Non-negative matrix factorization (NMF) is a widely used method to accomplish this goal. But NMF do not have the provision to include the neighborhood structure information and, as a result, may fail to provide satisfactory performance in presence of nonlinear manifold structure. To address this shortcoming, we propose to consider the neighborhood structural similarity information within the NMF framework and do so by modeling the data through a minimum spanning tree. We label the resulting method as the neighborhood structure-assisted NMF. We further develop both offline and online algorithms for implementing the proposed method. Empirical comparisons using twenty benchmark data sets as well as an industrial data set extracted from a hydropower plant demonstrate the superiority of the neighborhood structure-assisted NMF. Looking closer into the formulation and properties of the proposed NMF method and comparing it with several NMF variants reveal that inclusion of the MST-based neighborhood structure plays a key role in attaining the enhanced performance in anomaly detection