Online knowledge libraries refer to the online data warehouses that systematically organize and categorize the knowledge-based information about different kinds of concepts and entities. In the era of big data, the setup of online knowledge libraries is an extremely challenging and laborious task, in terms of efforts, time and expense required in the completion of knowledge entities. Especially nowadays, a large number of new knowledge entities, like movies, are keeping on being produced and coming out at a continuously accelerating speed, which renders the knowledge library setup and completion problem more difficult to resolve manually. In this paper, we will take the online movie knowledge libraries as an example, and study the "Multiple aligned ISomeric Online Knowledge LIbraries Completion problem" (Miso-Klic) problem across multiple online knowledge libraries. Miso-Klic aims at identifying the missing entities for multiple knowledge libraries synergistically and ranking them for editing based on certain ranking criteria. To solve the problem, a thorough investigation of two isomeric online knowledge libraries, Douban and IMDB, have been carried out in this paper. Based on analyses results, a novel deep online knowledge library completion framework "Integrated Deep alignEd Auto-encoder" (IDEA) is introduced to solve the problem. By projecting the entities from multiple isomeric knowledge libraries to a shared feature space, IDEA solves the Miso-Klic problem via three steps: (1) entity feature space unification via embedding, (2) knowledge library fusion based missing entity identification, and (3) missing entity ranking. Extensive experiments done on the real-world online knowledge library dataset have demonstrated the effectiveness of IDEA in addressing the problem.
Meanwhile, in recent years, some works have been done on aligning social networks @cite_0 @cite_30 @cite_9 . To prune the predicted anchor links in network alignment problems, stable matching is first applied by the PI in @cite_0 , while assuming if a person has multiple accounts in a social network, these accounts can be identified and consolidated as a single account through a preprocessing step @cite_24 . College admission problem @cite_11 and stable marriage problem @cite_18 have been studied for many years and lots of works have been done in the last century. In recent years, some new papers have come out in these areas. @cite_25 propose to analyze the stability of the equilibrium outcomes in the admission games induced by stable matching rules. Meanwhile, in college admission problems, only the small core in nash equilibrium plays an important role, which was analyzed in @cite_29 . Flor ' e @cite_6 propose to study the almost stable matching by truncating the Gale-Shapley algorithm. In this proposal, we will address the problem by extending traditional stable matching to a generalized case to identify the non-anchor users and prune the redundant anchor links connected to them.
@cite_30 @cite_18 @cite_9 @cite_29 @cite_6 @cite_0 @cite_24 @cite_25 @cite_11
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We show that the ratio of matched individuals to blocking pairs grows linearly with the number of propose–accept rounds executed by the Gale–Shapley algorithm for the stable marriage problem. Consequently, the participants can arrive at an almost stable matching even without full information about the problem instance; for each participant, knowing only its local neighbourhood is enough. In distributed-systems parlance, this means that if each person has only a constant number of acceptable partners, an almost stable matching emerges after a constant number of synchronous communication rounds. We apply our results to give a distributed (2+e)-approximation algorithm for maximum-weight matching in bicoloured graphs and a centralised randomised constant-time approximation scheme for estimating the size of a stable matching. We study strategic issues in the Gale-Shapley stable marriage model. In the first part of the paper, we derive the optimal cheating strategy and show that it is not always possible for a woman to recover her women-optimal stable partner from the men-optimal stable matching mechanism when she can only cheat by permuting her preferences. In fact, we show, using simulation, that the chances that a woman can benefit from cheating are slim. In the second part of the paper, we consider a two-sided matching market found in Singapore. We study the matching mechanism used by the Ministry of Education (MOE) in the placement of primary six students in secondary schools, and discuss why the current method has limited success in accommodating the preferences of the students, and the specific needs of the schools (in terms of the “mix” of admitted students). Using insights from the first part of the paper, we show that stable matching mechanisms are more appropriate in this matching market and explain why the strategic behavior of the students need not be a major concern. (Stable Marriage; Strategic Issues; Gale-Shapley Algorithm; Student Posting Exercise) Both rematching proof and strong equilibrium outcomes are stable with respect to the true preferences in the marriage problem. We show that not all rematching proof or strong equilibrium outcomes are stable in the college admissions problem. But we show that both rematching proof and strong equilibrium outcomes in truncations at the match point are all stable in the college admissions problem. Further, all true stable matchings can be achieved in both rematching proof and strong equilibrium in truncations at the match point. We show that any Nash equilibrium in truncations admits one and only one matching, stable or not. Therefore, the core at a Nash equilibrium in truncations must be small. But examples exist such that the set of stable matchings with respect to a Nash equilibrium may contain more than one matching. Nevertheless, each Nash equilibrium can only admit at most one true stable matching. If, indeed, there is a true stable matching at a Nash equilibrium, then the only possible equilibrium outcome will be the true stable matching, no matter how different are players' equilibrium strategies from the true preferences and how many other unstable matchings are there at that Nash equilibrium. Thus, we show that a necessary and sufficient condition for the stable matching rule to be implemented in a subset of Nash equilibria by the direct revelation game induced by a stable mechanism is that every Nash equilibrium profile in that subset admits one and only one true stable matching. An instance of the classical Stable Roommates problem (sr) need not admit a stable matching. This motivates the problem of finding a matching that is “as stable as possible”, i.e. admits the fewest number of blocking pairs. In this paper we prove that, given an sr instance with n agents, in which all preference lists are complete, the problem of finding a matching with the fewest number of blocking pairs is NP-hard and not approximable within @math , for any e>0, unless P=NP. If the preference lists contain ties, we improve this result to n1−e. Also, we show that, given an integer K and an sr instance I in which all preference lists are complete, the problem of deciding whether I admits a matching with exactly K blocking pairs is NP-complete. By contrast, if K is constant, we give a polynomial-time algorithm that finds a matching with at most (or exactly) K blocking pairs, or reports that no such matching exists. Finally, we give upper and lower bounds for the minimum number of blocking pairs over all matchings in terms of some properties of a stable partition, given an sr instance I.