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Many studies have been conducted on seeking the efficient solution for subgraph similarity search over certain (deterministic) graphs due to its wide application in many fields, including bioinformatics, social network analysis, and Resource Description Framework (RDF) data management. All these works assume that the underlying data are certain. However, in reality, graphs are often noisy and uncertain due to various factors, such as errors in data extraction, inconsistencies in data integration, and privacy preserving purposes. Therefore, in this paper, we study subgraph similarity search on large probabilistic graph databases. Different from previous works assuming that edges in an uncertain graph are independent of each other, we study the uncertain graphs where edges' occurrences are correlated. We formally prove that subgraph similarity search over probabilistic graphs is #P-complete, thus, we employ a filter-and-verify framework to speed up the search. In the filtering phase, we develop tight lower and upper bounds of subgraph similarity probability based on a probabilistic matrix index, PMI. PMI is composed of discriminative subgraph features associated with tight lower and upper bounds of subgraph isomorphism probability. Based on PMI, we can sort out a large number of probabilistic graphs and maximize the pruning capability. During the verification phase, we develop an efficient sampling algorithm to validate the remaining candidates. The efficiency of our proposed solutions has been verified through extensive experiments.

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Predicting patients' risk of developing certain diseases is an important research topic in healthcare. Accurately identifying and ranking the similarity among patients based on their historical records is a key step in personalized healthcare. The electric health records (EHRs), which are irregularly sampled and have varied patient visit lengths, cannot be directly used to measure patient similarity due to the lack of an appropriate representation. Moreover, there needs an effective approach to measure patient similarity on EHRs. In this paper, we propose two novel deep similarity learning frameworks which simultaneously learn patient representations and measure pairwise similarity. We use a convolutional neural network (CNN) to capture local important information in EHRs and then feed the learned representation into triplet loss or softmax cross entropy loss. After training, we can obtain pairwise distances and similarity scores. Utilizing the similarity information, we then perform disease predictions and patient clustering. Experimental results show that CNN can better represent the longitudinal EHR sequences, and our proposed frameworks outperform state-of-the-art distance metric learning methods.