This paper explores a new measure of similarity between point sets in arbitrary metric spaces. The measure is based on the spatial overlap of the “shapes” and “densities” of these point sets. It is applicable in any domain where point sets are a natural representation for data. Specifically, we show examples of its use in natural language processing, object recognition in images and point set classification. We provide a geometric interpretation of this measure and show that it is well-motivated, intuitive, parameter-free, and straightforward to use. We further demonstrate that it is computationally tractable and applicable to both supervised and unsupervised learning problems.

The research on low-complexity nonmonotonic description logics recently identified a fragment of EL with bottom, supporting defeasible inheritance with overriding, where reasoning can be carried out in polynomial time. We contribute to that framework by supporting more axiom schemata and all the concept constructors of EL++ without increasing asymptotic complexity. Moreover, we show that all the syntactic restrictions we adopt are necessary by proving several coNP-hardness results.

Building on a general theory of action by Reiter and his colleagues, Bacchus et al. give an account for formalizing degrees of belief and noisy actions in the situation calculus. Unfortunately, there is no clear solution to the projection problem for the formalism. And, while the model has epistemic features, it is not obvious what the agent's knowledge base should look like. Also, reasoning about uncertainty essentially resorts to second-order logic. In recent work, Gabaldon and Lakemeyer remedy these shortcomings somewhat, but here too the utility seems to be restricted to queries (with action operators) about the initial theory. In this paper, we propose a fresh amalgamation of a modal fragment of the situation calculus and uncertainty, where the idea will be to update the initial knowledge base, containing both ordinary and (certain kinds of) probabilistic beliefs, when noisy actions are performed. We show that the new semantics has the right properties, and study a special case where updating probabilistic beliefs is computable. Our ideas are closely related to the Lin and Reiter notion of progression.

The most critical challenge for the recommendation system is to achieve the high prediction quality on the large scale sparse data contributed by the users. In this paper, we present a novel approach to the social recommendation problem, which takes the advantage of the graph Laplacian regularization to capture the underlying social relationship among the users. Differently from the previous approaches, that are based on the conventional gradient descent optimization, we formulate the presented graph Laplacian regularized social recommendation problem into a low-rank semidefinite program, which is able to be efficiently solved by the quasi-Newton algorithm. We have conducted the empirical evaluation on a large scale dataset of high sparsity, the promising experimental results show that our method is very effective and efficient for the social recommendation task.

In real-world recommender systems, some users are easily influenced by new products and whereas others are unwilling to change their minds. So the preference varying speeds for users are different. Based on this observation, we propose a dynamic nonlinear matrix factorization model for collaborative filtering, aimed to improve the rating prediction performance as well as track the preference varying speeds for different users. We assume that user-preference changes smoothly over time, and the preference varying speeds for users are different. These two assumptions are incorporated into the proposed model as prior knowledge on user feature vectors, which can be learned efficiently by MAP estimation. The experimental results show that our method not only achieves state-of-the-art performance in the rating prediction task, but also provides an effective way to track user-preference varying speed.

The problem of influence maximization, i.e., mining top-k influential nodes from a social network such that the spread of influence in the network is maximized, is NP-hard. Most of the existing algorithms for the prob- lem are based on greedy algorithm. Although greedy algorithm can achieve a good approximation, it is computational expensive. In this paper, we propose a totally different approach based on Simulated Annealing(SA) for the influence maximization problem. This is the first SA based algorithm for the problem. Additionally, we propose two heuristic methods to accelerate the con- vergence process of SA, and a new method of comput- ing influence to speed up the proposed algorithm. Experimental results on four real networks show that the proposed algorithms run faster than the state-of-the-art greedy algorithm by 2-3 orders of magnitude while being able to improve the accuracy of greedy algorithm.

We present three new ideas for grid-based path-planning algorithms that improve the search speed and quality of the paths found. First, we introduce a new type of database, the Local Distance Database (LDDB), that contains distances between boundary points of a local neighborhood. Second, an LDDB based algorithm is introduced, called Block A*, that calculates the optimal path between start and goal locations given the local distances stored in the LDDB. Third, our experimental results for any-angle path planning in a wide variety of test domains, including real game maps, show that Block A* is faster than both A* and the previously best grid-based any-angle search algorithm, Theta*.

Freuder and Elfe (1996) introduced Neighborhood Inverse Consistency (NIC) as a strong local consistency property for binary CSPs. While enforcing NIC can significantly filter the variables domains, the proposed algorithm is too costly to be used on dense graphs or for lookahead during search. In this paper, we introduce and characterize Relational Neighborhood Inverse Consistency (RNIC) as a local consistency property that operates on the dual graph of a non-binary CSP. We describe and characterize a practical algorithm for enforcing it. We argue that defining RNIC on the dual graph unveils unsuspected opportunities to reduce the computational cost of our algorithm and increase its filtering effectiveness. We show how to achieve those effects by modifying the topology of the dual graph, yielding new variations the RNIC property. We also introduce an adaptive strategy to automatically select the appropriate property to enforce given the connectivity of the dual graph. We integrate the resulting techniques as full lookahead strategies in a backtrack search procedure for solving CSPs, and demonstrate the effectiveness of our approach for solving known difficult benchmark problems.

Anytime variants of Dijkstra's and A* shortest path algorithms quickly produce a suboptimal solution and then improve it over time. For example, ARA* introduces a weighting value "epsilon" to rapidly find an initial suboptimal path and then reduces "epsilon" to improve path quality over time. In ARA*, "epsilon" is based on a linear trajectory with ad-hoc parameters chosen by each user. We propose a new Anytime A* algorithm, Anytime Nonparametric A* (ANA*), that does not require ad-hoc parameters, and adaptively reduces varepsilon to expand the most promising node per iteration, adapting the greediness of the search as path quality improves. We prove that each node expanded by ANA* provides an upper bound on the suboptimality of the current-best solution. We evaluate the performance of ANA* with experiments in the domains of robot motion planning, gridworld planning, and multiple sequence alignment. The results suggest that ANA* is as efficient as ARA* and in most cases: (1) ANA* finds an initial solution faster, (2) ANA* spends less time between solution improvements, (3) ANA* decreases the suboptimality bound of the current-best solution more gradually, and (4) ANA* finds the optimal solution faster. ANA* is freely available from Maxim Likhachev's Search-based Planning Library (SBPL).

Researchers from interval analysis and constraint (logic) programming communities have studied intervals for their ability to manage infinite solution sets of numerical constraint systems. In particular, inner regions represent subsets of the search space in which all points are solutions. Our main contribution is the use of recent and new inner region extraction algorithms in the upper bounding phase of constrained global optimization. Convexification is a major key for efficiently lower bounding the objective function. We have adapted the convex interval taylorization proposed by Lin and Stadherr for producing a reliable outer and inner polyhedral approximation of the solution set and  a linearization of the objective function. Other original ingredients are part of our optimizer, including an efficient interval constraint propagation algorithm exploiting monotonicity of functions. We end up with a new framework for reliable continuous constrained global optimization. Our interval B&B is implemented in the interval-based explorer Ibex and extends this free C++ library. Our strategy outperforms the best reliable global optimizers.