Classification is a classic problem in data analytics and has been approached from many different angles, including machine learning. Traditionally, machine learning methods classify samples based solely on their features. This paradigm is evolving . Recent developments on Graph Convolutional Networks have shown that explicitly using information not directly present in the features to represent a type of relationship between samplescan improve the classification performance by a significant margin. However, graphs are not often immediately present in data sets, thus limiting the applicability of Graph Convolutional Networks. In this paper, we explore if graphs extracted from the features themselves can aid classification performance. First, we show that constructing optimal geometric graphs directly from data features can aid classification tasks on both synthetic and real-world data sets from different domains. Second, we introduce two metrics to characterize optimal graphs: i) by measuring the alignment between the subspaces spanned by the features convolved with the graph and the ground truth ; and ii) ratio of class separationin the output activations of Graph Convolutional Networks: this shows that the optimal graph maximally separates classes. Finally, we find that sparsifying the optimal graph can potentially improve classification performance .
Traditional classification tasks learn to assign samples to given classes based solely on sample features. This paradigm is evolving to include other sources of information, such as known relations between samples. Here we show that, even if additional relational information is not available in the data set, one can improve classification by constructing geometric graphs from the features themselves, and using them within a Graph Convolutional Network. The improvement in classification accuracy is maximized by graphs that capture sample similarity with relatively low edge density. We show that such feature-derived graphs increase the alignment of the data to the ground truth while improving class separation. We also demonstrate that the graphs can be made more efficient using spectral sparsification, which reduces the number of edges while still improving classification performance. We illustrate our findings using synthetic and real-world data sets from various scientific domains .
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Classification is a classic problem in data analytics and has been approached from many different angles, including machine learning. Traditionally, machine learning methods classify samples
Traditional classification tasks learn to assign samples to given classes
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their
sample
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. Recent developments on Graph Convolutional Networks have shown that explicitly using information not directly present in the features to represent a type of relationship between samplescan improve the classification performance by a significant margin. However, graphs are not often immediately present in data sets, thus limiting the applicability of Graph Convolutional Networks. In this paper, we explore if graphs extracted from the features themselves can aid classification performance. First, we show that constructing optimal geometric graphs directly from data features can aid classification tasks on both synthetic and
to include other sources of information, such as known relations between samples. Here we show that, even if additional relational information is not available in the data set, one can improve classification by constructing geometric graphs from the features themselves, and using them within a Graph Convolutional Network. The improvement in classification accuracy is maximized by graphs that capture sample similarity with relatively low edge density. We show that such feature-derived graphs increase the alignment of the data to the ground truth while improving class separation. We also demonstrate that the graphs can be made more efficient using spectral sparsification, which reduces the number of edges while still improving classification performance. We illustrate our findings using synthetic and
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data sets from different domains. Second, we introduce two metrics to characterize optimal graphs: i) by measuring the alignment between the subspaces spanned by the features convolved with the graph and the ground truth ; and ii) ratio of class separationin the output activations of Graph Convolutional Networks: this shows that the optimal graph maximally separates classes. Finally, we find that sparsifying the optimal graph can potentially improve classification performance
data sets from various scientific domains