In this paper, a new unsupervised learning algorithm, namely Nonnegative Discriminative Feature Selection (NDFS), is proposed. To exploit the discriminative information in unsupervised scenarios, we perform spectral clustering to learn the cluster labels of the input samples, during which the feature selection is performed simultaneously. The joint learning of the cluster labels and feature selection matrix enables NDFS to select the most discriminative features. To learn more accurate cluster labels, a nonnegative constraint is explicitly imposed to the class indicators. To reduce the redundant or even noisy features, l 2,1 -norm minimization constraint is added into the objective function, which guarantees the feature selection matrix sparse in rows. Our algorithm exploits the discriminative information and feature correlation simultaneously to select a better feature subset. A simple yet efficient iterative algorithm is designed to optimize the proposed objective function. Experimental results on different real world datasets demonstrate the encouraging performance of our algorithm over the state-of-the-arts.

In many real applications, especially those involving data objects with complicated semantics, it is generally desirable to discover the relation between patterns in the input space and labels corresponding to different semantics in the output space. This task becomes feasible with MIML (Multi-Instance Multi-Label learning), a recently developed learning framework, where each data object is represented by multiple instances and is allowed to be associated with multiple labels simultaneously. In this paper, we propose KISAR , an MIML algorithm that is able to discover what instances trigger what labels. By considering the fact that highly relevant labels usually share some patterns, we develop a convex optimization formulation and provide an alternating optimization solution. Experiments show that KISAR is able to discover reasonable relations between input patterns and output labels, and achieves performances that are highly competitive with many state-of-the-art MIML algorithms.

Current modularity-based community detection methods show decreased performance as relational networks become increasingly noisy. These methods also yield a large number of diverse community structures as solutions, which is problematic for applications that impose constraints on the acceptable solutions or in cases where the user is focused on specific communities of interest. To address both of these problems, we develop a semi-supervised spin-glass model that enables current community detection methods to incorporate background knowledge in the forms of individual labels and pairwise constraints. Unlike current methods, our approach shows robust performance in the presence of noise in the relational network, and the ability to guide the discovery process toward specific community structures. We evaluate our algorithm on several benchmark networks and a new political sentiment network representing cooperative events between nations that was mined from news articles over six years.

The FLP semantics presented by (Faber, Leone, and Pfeifer 2004) has been widely used to define answer sets, called FLP answer sets, for different types of logic programs such as logic programs with aggregates, description logic programs (dl-programs), Hex programs, and logic programs with first-order formulas (general logic programs). However, it was recently observed that the FLP semantics may produce unintuitive answer sets with circular justifications caused by self-supporting loops. In this paper, we address the circular justification problem for general logic programs by enhancing the FLP semantics with a level mapping formalism. In particular, we extend the Gelfond-Lifschitz three step definition of the standard answer set semantics from normal logic programs to general logic programs and define for general logic programs the first FLP semantics that is free of circular justifications. We call this FLP semantics the well-justified FLP semantics. This method naturally extends to general logic programs with additional constraints like aggregates, thus providing a unifying framework for defining the well-justified FLP semantics for various types of logic programs. When this method is applied to normal logic programs with aggregates, the well-justified FLP semantics agrees with the conditional satisfaction based semantics defined by (Son, Pontelli, and Tu 2007); and when applied to dl-programs, the semantics agrees with the strongly well-supported semantics defined by (Shen 2011).

The paper identifies a special case in which the complex problem of synthesis from specifications in temporal-epistemic logic can be reduced to the simpler problem of model checking such specifications. An application is given of strategy synthesis in pursuit-evasion games, where one or more pursuers with incomplete information aim to discover theexistence of an evader. Experimental results are provided to evaluate the feasibility of the approach.

A probabilistic variant of ATL* logic is proposed to work with multi-player games of incomplete information and synchronous perfect recall. The semantics of the logic is settled over probabilistic interpreted system and partially observed probabilistic concurrent game structure. While unexpectedly, the model checking problem is in general undecidable even for single-group fragment, we find a fragment whose complexity is in 2-EXPTIME. The usefulness of this fragment is shown over a land search scenario.

Inferring probabilistic networks from data is a notoriously difficult task. Under various goodness-of-fit measures, finding an optimal network is NP-hard, even if restricted to polytrees of bounded in-degree. Polynomial-time algorithms are known only for rare special cases, perhaps most notably for branchings, that is, polytrees in which the in-degree of every node is at most one. Here, we study the complexity of finding an optimal polytree that can be turned into a branching by deleting some number of arcs or nodes, treated as a parameter. We show that the problem can be solved via a matroid intersection formulation in polynomial time if the number of deleted arcs is bounded by a constant. The order of the polynomial time bound depends on this constant, hence the algorithm does not establish fixed-parameter tractability when parameterized by the number of deleted arcs. We show that a restricted version of the problem allows fixed-parameter tractability and hence scales well with the parameter. We contrast this positive result by showing that if we parameterize by the number of deleted nodes, a somewhat more powerful parameter, the problem is not fixed-parameter tractable, subject to a complexity-theoretic assumption.

Abduction belongs to the most fundamental reasoning methods. It is a method for reverse inference, this means one is interested in explaining observed behavior by finding appropriate causes. We study logic-based abduction, where knowledge is represented by propositional formulas. The computational complexity of this problem is highly intractable in many interesting settings. In this work we therefore present an extensive parameterized complexity analysis of abduction within various fragments of propositional logic together with (combinations of) natural parameters.

In this paper we introduce the notion of mapping-based knowledge base (MKB) to formalize the situation where both the extensional and the intensional level of the ontology are determined by suitable mappings to a set of (relational) data sources. This allows for making the intensional level of the ontology as dynamic as traditionally the extensional level is. To do so, we resort to the meta-modeling capabilities of higher-order Description Logics, which allow us to see concepts and roles as individuals, and vice versa. The challenge in this setting is to design tractable query answering algorithms. Besides the definition of MKBs, our main result is that answering instance queries posed to MKBs expressed in Hi(DL-LiteR) can be done efficiently. In particular, we define a query rewriting technique that produces first-order (SQL) queries to be posed to the data sources.

We propose a novel sequential decision approach to modeling ordinal ratings in collaborative filtering problems. The rating process is assumed to start from the lowest level, evaluates against the latent utility at the corresponding level and moves up until a suitable ordinal level is found. Crucial to this generative process is the underlying utility random variables that govern the generation of ratings and their modelling choices. To this end, we make a novel use of the generalised extreme value distributions, which is found to be particularly suitable for our modeling tasks and at the same time, facilitate our inference and learning procedure. The proposed approach is flexible to incorporate features from both the user and the item. We evaluate the proposed framework on three well-known datasets: MovieLens, Dating Agency and Netflix. In all cases, it is demonstrated that the proposed work is competitive against state-of-the-art collaborative filtering methods.