Machine learning and optimisation are two growing fields of artificial intelligence with an enormous number of computer science applications. The techniques in the former area aim to learn knowledge from data or experience, while the techniques from the latter search for the best option or solution to a given problem. To employ these techniques automatically and effectively aligning with the real aim of artificial intelligence, both sets of techniques are frequently hybridised, interacting with each other and themselves. This study focuses on such interactions aiming at (1) presenting a broad overview of the studies on self and dual interactions between machine learning and optimisation; (2) providing a useful tutorial for researchers and practitioners in both fields in support of collaborative work through investigation of the recent advances and analyses of the advantages and disadvantages of different techniques to tackle the same or similar problems; (3) clarifying the overlapping terminologies having different meanings used in both fields; (4) identifying research gaps and potential research directions.

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Graph convolutional network (GCN) is an emerging neural network approach. It learns new representation of a node by aggregating feature vectors of all neighbors in the aggregation process without considering whether the neighbors or features are useful or not. Recent methods have improved solutions by sampling a fixed size set of neighbors, or assigning different weights to different neighbors in the aggregation process, but features within a feature vector are still treated equally in the aggregation process. In this paper, we introduce a new convolution operation on regular size feature maps constructed from features of a fixed node bandwidth via sampling to get the first-level node representation, which is then passed to a standard GCN to learn the secondlevel node representation. Experiments show that our method outperforms competing methods in semi-supervised node classification tasks. Furthermore, our method opens new doors for exploring new GCN architectures, particularly deeper GCN models.

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