Hierarchical clustering is typically implemented as a greedy heuristic algorithm with no explicit objective function. In this work we formalize hierarchical clustering as an integer linear programming (ILP) problem with a natural objective function and the dendrogram properties enforced as linear constraints.  Though exact solvers exists for ILP we show that a simple randomized algorithm and a linear programming (LP) relaxation can be used to provide approximate solutions faster.  Formalizing hierarchical clustering also has the benefit that relaxing the constraints can produce novel problem variations such as overlapping clusterings.  Our experiments show that our formulation is capable of outperforming standard agglomerative clustering algorithms in a variety of settings, including traditional hierarchical clustering as well as learning overlapping clusterings.

The role of kernels is central to machine learning. Motivated by the importance of power-law distributions in statistical modeling, in this paper, we propose the notion of power-law kernels to investigate power-laws in learning problem. We propose two power-law kernels by generalizing Gaussian and Laplacian kernels. This generalization is based on distributions, arising out of maximization of a generalized information measure known as nonextensive entropy that is very well studied in statistical mechanics. We prove that the proposed kernels are positive definite, and provide some insights regarding the corresponding Reproducing Kernel Hilbert Space (RKHS). We also study practical significance of both kernels in classification and regression, and present some simulation results.

Over the course of the last decade, infrared (IR) and particularly thermal IR imaging based face recognition has emerged as a promising complement to conventional, visible spectrum based approaches which continue to struggle when applied in the real world. While inherently insensitive to visible spectrum illumination changes, IR images introduce specific challenges of their own, most notably sensitivity to factors which affect facial heat emission patterns, e.g. emotional state, ambient temperature, and alcohol intake. In addition, facial expression and pose changes are more difficult to correct in IR images because they are less rich in high frequency detail which is an important cue for fitting any deformable model. In this paper we describe a novel method which addresses these major challenges. Specifically, to normalize for pose and facial expression changes we generate a synthetic frontal image of a face in a canonical, neutral facial expression from an image of the face in an arbitrary pose and facial expression. This is achieved by piecewise affine warping which follows active appearance model (AAM) fitting. This is the first publication which explores the use of an AAM on thermal IR images; we propose a pre-processing step which enhances detail in thermal images, making AAM convergence faster and more accurate. To overcome the problem of thermal IR image sensitivity to the exact pattern of facial temperature emissions we describe a representation based on reliable anatomical features. In contrast to previous approaches, our representation is not binary; rather, our method accounts for the reliability of the extracted features. This makes the proposed representation much more robust both to pose and scale changes. The effectiveness of the proposed approach is demonstrated on the largest public database of thermal IR images of faces on which it achieved 100% identification rate, significantly outperforming previously described methods.

We introduce a general declarative framework for incorporating domain-specific heuristics into ASP solving. We accomplish this by extending the first-order modeling language of ASP by a distinguished heuristic predicate. The resulting heuristic information is processed as an equitable part of the logic program and subsequently exploited by the solver when it comes to non-deterministically assigning a truth value to an atom. We implemented our approach as a dedicated heuristic in the ASP solver clasp and show its great prospect by an empirical evaluation.

Strong Nash equilibrium (SNE) is an appealing solution concept when rational agents can form coalitions. A strategy profile is an SNE if no coalition of agents can benefit by deviating. We present the first general-purpose algorithms for SNE finding in games with more than two agents. An SNE must simultaneously be a Nash equilibrium (NE) and the optimal solution of multiple non-convex optimization problems. This makes even the derivation of necessary and sufficient mathematical equilibrium constraints difficult. We show that forcing an SNE to be resilient only to pure-strategy deviations by coalitions, unlike for NEs, is only a necessary condition here. Second, we show that the application of Karush-Kuhn-Tucker conditions leads to another set of necessary conditions that are not sufficient. Third, we show that forcing the Pareto efficiency of an SNE for each coalition with respect to coalition correlated strategies is sufficient but not necessary. We then develop a tree search algorithm for SNE finding. At each node, it calls an oracle to suggest a candidate SNE and then verifies the candidate. We show that our new necessary conditions can be leveraged to make the oracle more powerful. Experiments validate the overall approach and show that the new conditions significantly reduce search tree size compared to using NE conditions alone.

Evolutionary game theory combines game theory and dynamical systems and is customarily adopted to describe evolutionary dynamics in multi-agent systems. In particular, it has been proven to be a successful tool to describe multi-agent learning dynamics. To the best of our knowledge, we provide in this paper the first replicator dynamics applicable to the sequence form of an extensive-form game, allowing an exponential reduction of time and space w.r.t. the currently adopted replicator dynamics for normal form. Furthermore, our replicator dynamics is realization equivalent to the standard replicator dynamics for normal form. We prove our results for both discrete-time and continuous-time cases. Finally, we extend standard tools to study the stability of a strategy profile to our replicator dynamics.

Full natural language understanding requires identifying and analyzing the meanings of metaphors, which are ubiquitous in both text and speech. Over the last thirty years, linguistic metaphors have been shown to be based on more general conceptual metaphors, partial semantic mappings between disparate conceptual domains. Though some achievements have been made in identifying linguistic metaphors over the last decade or so, little work has been done to date on automatically identifying conceptual metaphors. This paper describes research on identifying conceptual metaphors based on corpus data. Our method uses as little background knowledge as possible, to ease transfer to new languages and to mini- mize any bias introduced by the knowledge base construction process. The method relies on general heuristics for identifying linguistic metaphors and statistical clustering (guided by Wordnet) to form conceptual metaphor candidates. Human experiments show the system effectively finds meaningful conceptual metaphors.

Over the last two decades, propositional satisfiability (S AT ) has become one of the most successful and widely applied techniques for the solution of NP-complete problems. The aim of this paper is to investigate theoretically how S AT can be utilized for the efficient solution of problems that are harder than NP or co-NP. In particular, we consider the fundamental reasoning problems in propositional disjunctive answer set programming (A SP ), B RAVE R EASONING and S KEPTICA R EASONING , which ask whether a given atom is contained in at least one or in all answer sets, respectively. Both problems are located at the second level of the Polynomial Hierarchy and thus assumed to be harder than NP or co-NP. One cannot transform these two reasoning problems into S AT in polynomial time, unless the Polynomial Hierarchy collapses. We show that certain structural aspects of disjunctive logic programs can be utilized to break through this complexity barrier, using new techniques from Parameterized Complexity. In particular, we exhibit transformations from B RAVE and S KEPTICAL R EASONING to S AT that run in time $ O (2^ k n^ 2 )$ where k is a structural parameter of the instance and n the input size. In other words, the reduction is fixed-parameter tractable for parameter k . As the parameter k we take the size of a smallest backdoor with respect to the class of normal (i.e., disjunction-free) programs. Such a backdoor is a set of atoms that when deleted makes the program normal. In consequence, the combinatorial explosion, which is expected when transforming a problem from the second level of the Polynomial Hierarchy to the first level, can now be confined to the parameter k , while the running time of the reduction is polynomial in the input size n , where the order of the polynomial is independent of k . We show that such a transformation is not possible if we consider backdoors with respect to tightness instead of normality. We think that our approach is applicable to many other hard combinatorial problems that lie beyond NP or co-NP, and thus significantly enlarge the applicability of SAT.

Belief change is an important research topic in AI. It becomes more perplexing in multi-agent settings, since the action of an agent may be partially observable to other agents. In this paper, we present a general approach to reasoning about actions and belief change in multi-agent settings. Our approach is based on a multi-agent extension to the situation calculus, augmented by a plausibility relation over situations and another one over actions, which is used to represent agents' different perspectives on actions. When an action is performed, we update the agents' plausibility order on situations by giving priority to the plausibility order on actions, in line with the AGM approach of giving priority to new information. We show that our notion of belief satisfies KD45 properties. As to the special case of belief change of a single agent, we show that our framework satisfies most of the classical AGM, KM, and DP postulates. We also present properties concerning the change of common knowledge and belief of a group of agents.

We introduce abstract preference frameworks to study general properties common across a variety of preference formalisms. In particular, we study strong equivalence in preference formalisms and their separability. We identify abstract postulates on preference frameworks, satisfied by most of the currently studied preference formalisms, that lead to characterizations of both properties of interest.