## AbstractThe semi-supervised problem of learning node labels in graphs consists, given a partial graph labeling, in inferring the unknown labels of the unlabeled vertices. Several machine learning algorithms have been proposed for solving this problem, including Hopfield networks and label propagation methods; however, some issues have been only partially con- sidered, e.g. the preservation of the prior knowledge and the unbalance between positive and negative labels. To address these items, we propose a Hopfield-based cost sensitive neural network algorithm (COSNet). The method factorizes the solution of the problem in two parts: 1) the sub-network composed by the labelled vertices is considered, and the network parameters are estimated through a supervised algorithm; 2) the estimated parameters are extended to the subnetwork composed of the unlabeled vertices, and the attractor reached by the dynamics of this subnetwork allows to predict the labeling of the unlabeled vertices. The proposed method embeds in the neural algorithm the ”a priori” knowl- edge coded in the labelled part of the graph, and separates node labels and neuron states, allowing to differentially weight positive and nega- tive node labels. Moreover, COSNet introduces an efficient cost-sensitive strategy which allows to learn the near-optimal parameters of the net- work in order to take into account the unbalance between positive and negative node labels. Finally, the dynamics of the network is restricted to its unlabeled part, preserving the minimization of the overall objective function and significantly reducing the time complexity of the learning algorithm. COSNet has been applied to the genome-wide prediction of gene function in a model organism. The results, compared with those ob- tained by other semi-supervised label propagation algorithms and super- vised machine learning methods, show the effectiveness of the proposed approach.
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