Efficient Algorithms for Attributed Graph Alignment with Vanishing Edge Correlation

Graph alignment refers to the task of finding the vertex correspondence between two positively correlated graphs. Extensive study has been done on polynomial-time algorithms for the graph alignment problem under the Erd\H{o}s--R\'enyi graph pair model, where the two graphs are Erd\H{o}s--R\'enyi graphs with edge probability $q_\mathrm{u}$, correlated under certain vertex correspondence. To achieve exact recovery of the vertex correspondence, all existing algorithms at least require the edge correlation coefficient $\rho_\mathrm{u}$ between the two graphs to satisfy $\rho_\mathrm{u} > \sqrt{\alpha}$, where $\alpha \approx 0.338$ is Otter's tree-counting constant. Moreover, it is conjectured in [1] that no polynomial-time algorithm can achieve exact recovery under weak edge correlation $\rho_\mathrm{u}<\sqrt{\alpha}$. In this paper, we show that with a vanishing amount of additional attribute information, exact recovery is polynomial-time feasible under vanishing edge correlation $\rho_\mathrm{u} \ge n^{-\Theta(1)}$. We identify a local tree structure, which incorporates one layer of user information and one layer of attribute information, and apply the subgraph counting technique to such structures. A polynomial-time algorithm is proposed that recovers the vertex correspondence for all but a vanishing fraction of vertices. We then further refine the algorithm output to achieve exact recovery. The motivation for considering additional attribute information comes from the widely available side information in real-world applications, such as the user's birthplace and educational background on LinkedIn and Twitter social networks

Two Novel Learning-Based Criteria and Methods Based on Multiple Classifiers for Rejecting Poor Handwritten Digits

In pattern recognition, the reliability and the recognition accuracy of a classification system are of same importance, because even a small percentage of errors could cause a huge loss in real-life handwritten numeral recognition systems, like cheque-reading at financial institutions. Aiming at improving the reliability of recognition systems, this thesis presents two novel learning-based rejection criteria for single classifiers including SVM-based measurement (SVMM) and Area Under the Curve measurement (AUCM). Voting based combination methods of multiple classifier system (MCS) are also proposed for rejecting poor handwritten digits. Different rejection criteria (FRM, FTRM and SVMM) are individually combined with MCSs as weight parameters in voting. This method is then evaluated on three renowned databases including MNIST, CENPARMI and USPS. Experimental results indicate that these combinations improve the rejection performances consistently. To further improve the performance of the MCS based rejection method, specialist information has been integrated into the combination process by introducing a new confidence weight parameter. The best result on MNIST is obtained by the simpler one of the two proposed methods of deriving this parameter, which reaches 100% reliability with a rejection rate of only 4.09%, the best value in this field