Due to their effectiveness in capturing similarities between different entities, graphical models are widely used to represent datasets that reside on irregular and complex manifolds. Graph signal processing offers support to handle such complex datasets. In this paper, we propose a novel graph filter design method for semi-supervised data classification. The proposed design uses multiple graph shift matrices, one for each feature, and is shown to provide improved performance when the feature qualities are uneven. We introduce three methods to optimize for the graph filter coefficients and the graph combining coefficients. The first method uses the alternating minimization approach. In the second method, we optimize our objective function by convex relaxation that provides a performance benchmark. The third method adopts a genetic algorithm, which is computationally efficient and better at controlling overfitting. In our simulation experiments, we use both synthetic and real datasets with informative and non-informative features. Monte Carlo simulations demonstrate the effectiveness of multiple graph shift operators in the graph filters. Significant improvements in comparison to conventional graph filters are shown, in terms of average error rate and confidence scores. Furthermore, we perform cross validation to show how our approach can control overfitting and improve generalization performance.

中文翻译：

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具有多个移位矩阵的基于图的分类

由于它们在捕获不同实体之间的相似性方面的有效性，图形模型被广泛用于表示驻留在不规则和复杂流形上的数据集。图形信号处理提供了处理此类复杂数据集的支持。在本文中，我们提出了一种用于半监督数据分类的新型图滤波器设计方法。所提出的设计使用多个图形移位矩阵，每个特征一个，并且显示在特征质量不均匀时提供改进的性能。我们介绍了三种优化图滤波器系数和图组合系数的方法。第一种方法使用交替最小化方法。在第二种方法中，我们通过提供性能基准的凸松弛来优化我们的目标函数。第三种方法采用遗传算法，这在计算上是有效的，并且在控制过度拟合方面更好。在我们的模拟实验中，我们使用具有信息性和非信息性特征的合成数据集和真实数据集。蒙特卡罗模拟证明了图形过滤器中多个图形移位算子的有效性。在平均错误率和置信度得分方面，显示了与传统图形过滤器相比的显着改进。此外，我们执行交叉验证以展示我们的方法如何控制过度拟合并提高泛化性能。蒙特卡罗模拟证明了图形过滤器中多个图形移位算子的有效性。在平均错误率和置信度得分方面，显示了与传统图形过滤器相比的显着改进。此外，我们执行交叉验证以展示我们的方法如何控制过度拟合并提高泛化性能。蒙特卡罗模拟证明了图形过滤器中多个图形移位算子的有效性。在平均错误率和置信度得分方面，显示了与传统图形过滤器相比的显着改进。此外，我们执行交叉验证以展示我们的方法如何控制过度拟合并提高泛化性能。