Low-rank matrix approximation has been widely used for data subspace clustering and feature representation in many computer vision and pattern recognition applications. However, in order to enhance the discriminability, most of the matrix approximation based feature extraction algorithms usually generate the cluster labels by certain clustering algorithm (e.g., the kmeans) and then perform the matrix approximation guided by such label information. In addition, the noises and outliers in the dataset with large reconstruction errors will easily dominate the objective function by the conventional ℓ 2 -norm based squared residue minimization. In this paper, we propose a novel clustering and feature extraction algorithm based on an unified low-rank matrix factorization framework, which suggests that the observed data matrix can be approximated by the production of projection matrix and low dimensional representation, among which the low-dimensional representation can be approximated by the cluster indicator and latent feature matrix simultaneously. Furthermore, we have proposed using the ℓ 2,1 -norm and integrating the manifold regularization to further promote the proposed model. A novel Augmented Lagrangian Method (ALM) based procedure is designed to effectively and efficiently seek the optimal solution of the problem. The experimental results in both clustering and feature extraction perspectives demonstrate the superior performance of the proposed method.

In this paper, we propose an approach to ensure the diagnosability of a partially controllable system. Given a model of correct and faulty behaviors of a partially observable discrete event system, equipped with a set of elementary actions that do not intertwine with autonomous events, we search a diagnosability plan, i.e., a sequence of applicable actions that leads the system from an initial belief state (a set of potentially current states) to a diagnosable belief state, in which the system is then left to run freely. This helps in reducing the diagnosis interaction with running systems and can be applied, e.g., on the output of a repair plan, like in power networks. The two successive stages of this approach keep diagnosability planning, including diagnosability tests, in PSpace in comparison to the Exptime test for the more complex active diagnosability used usually in such cases. For this, we propose to construct incrementally the twin plant structure of the given system and to exploit its parts already constructed while testing the candidate plans and constructing its next parts. This helps in pruning the twin plant constructions and many non-diagnosability plan tests. We have created a special benchmark and tested three proposed methods, according to the recycling level of twin plants construction, with one cost function used for plan optimality and an optional heuristics.

In many real-world systems, strategic agents' decisions can be understood as complex - i.e., consisting of multiple sub-decisions - and hence can give rise to an exponential number of pure strategies. Examples include network congestion games, simultaneous auctions, and security games. However, agents' sets of strategies are often structured, allowing them to be represented compactly. There currently exists no general modeling language that captures a wide range of commonly seen strategy structure and utility structure. We propose Resource Graph Games (RGGs), the first general compact representation for games with structured strategy spaces, which is able to represent a wide range of games studied in literature. We leverage recent results about multilinearity, a key property of games that allows us to represent the mixed strategies compactly, and, as a result, to compute various equilibrium concepts efficiently. While not all RGGs are multilinear, we provide a general method of converting RGGs to those that are multilinear, and identify subclasses of RGGs whose converted version allow efficient computation.

We consider Max-min Share (MmS) fair allocations of indivisible chores (items with negative utilities). We show that allocation of chores and classical allocation of goods (items with positive utilities) have some fundamental connections but also differences which prevent a straightforward application of algorithms for goods in the chores setting and vice-versa. We prove that an MmS allocation does not need to exist for chores and computing an MmS allocation - if it exists - is strongly NP-hard. In view of these non-existence and complexity results, we present a polynomial-time 2-approximation algorithm for MmS fairness for chores. We then introduce a new fairness concept called optimal MmS that represents the best possible allocation in terms of MmS that is guaranteed to exist. We use connections to parallel machine scheduling to give (1) a polynomial-time approximation scheme for computing an optimal MmS allocation when the number of agents is fixed and (2) an effective and efficient heuristic with an ex-post worst-case analysis.

Sequential allocation is a simple allocation mechanism in which agents are given pre-specified turns in which they take one item among those that are still available. It has long been known that sequential allocation is not strategyproof. This raises the question of the complexity of computing a preference report that yields a higher utility than the truthful preference. We show that the problem is NP-complete for one manipulating agent with additive utilities and several non-manipulating agents. In doing so, we correct a wrong claim made in a previous paper. We then give two additional results. First, we present a polynomial-time algorithm for optimal manipulation when the manipulator has additive binary utilities. Second, we consider a stronger notion of manipulation whereby the untruthful outcome yields more utility than the truthful outcome for all utilities consistent with the ordinal preferences; for this notion, we show that a manipulation, if any, can be computed in polynomial time.

Many real-world networks have a rich collection of objects. The semantics of these objects allows us to capture different classes of proximities, thus enabling an important task of semantic proximity search. As the core of semantic proximity search, we have to measure the proximity on a heterogeneous graph, whose nodes are various types of objects. Most of the existing methods rely on engineering features about the graph structure between two nodes to measure their proximity. With recent development on graph embedding, we see a good chance to avoid feature engineering for semantic proximity search. There is very little work on using graph embedding for semantic proximity search. We also observe that graph embedding methods typically focus on embedding nodes, which is an "indirect'' approach to learn the proximity. Thus, we introduce a new concept of proximity embedding, which directly embeds the network structure between two possibly distant nodes. We also design our proximity embedding, so as to flexibly support both symmetric and asymmetric proximities. Based on the proximity embedding, we can easily estimate the proximity score between two nodes and enable search on the graph. We evaluate our proximity embedding method on three real-world public data sets, and show it outperforms the state-of-the-art baselines.

In many real tasks there are human knowledge expressed in logic formulae as well as data samples described by raw features (e.g., pixels, strings). It is popular to apply SRL or PILPtechniques to exploit human knowledge through learning of symbolic data, or statistical learning techniques to learn from the raw data samples; however, it is often desired to directly exploit these logic formulae on raw data processing, like human beings utilizing knowledge to guide perception. In this paper, we propose an approach, LASIN, which combines Logical Abduction and Statistical Induction. The LASIN approach generates candidate hypotheses based on the abduction of first-order formulae, and then, the hypotheses are exploited as constraints for statistical induction. We apply theLASIN approach to the learning of representation of written primitives, where a primitive is a basic component in human writing. Our results show that the discovered primitives are reasonable for human perception, and these primitives, if used in learning tasks such as classification and domain adaptation, lead to better performances than simply applying feature learning based on raw data only.

Security problems can be modeled as two-player partially observable stochastic games with one-sided partial observability and infinite horizon (one-sided POSGs). We seek for optimal strategies of player 1 that correspond to robust strategies against the worst-case opponent (player 2) that is assumed to have a perfect information about the game. We present a novel algorithm for approximately solving one-sided POSGs based on the heuristic search value iteration (HSVI) for POMDPs. Our results include (1) theoretical properties of one-sided POSGs and their value functions, (2) guarantees showing the convergence of our algorithm to optimal strategies, and (3) practical demonstration of applicability and scalability of our algorithm on three different domains: pursuit-evasion, patrolling, and search games.

We study the problem of computing an Extensive-Form Perfect Equilibrium (EFPE) in 2-player games. This equilibrium concept refines the Nash equilibrium requiring resilience with respect to a specific vanishing perturbation, representing  mistakes of the players at each decision node. The scientific challenge is intrinsic to the EFPE definition: it requires a perturbation over the agent form, but the agent form is computationally inefficient due to the presence of highly nonlinear constraints. We show that the sequence form can be exploited in a non-trivial way and that, for general-sum games, finding an EFPE is equivalent to solving a suitably perturbed linear complementarity problem. We prove that Lemke's algorithm can be applied, showing that computing an EFPE is PPAD-complete. In the notable case of zero-sum games, the problem is in FP and can be solved by linear programming. Our algorithms also allow one to find a Nash equilibrium when players cannot perfectly control their moves, being subject to a given execution uncertainty, as is the case in most realistic physical settings.

When faced with complex choices, users refine their own preference criteria as they explore the catalogue of options. In this paper we propose an approach to preference elicitation suited for this scenario. We extend Coactive Learning, which iteratively collects manipulative feedback, to optionally query example critiques. User critiques are integrated into the learning model by dynamically extending the feature space. Our formulation natively supports constructive learning tasks, where the option catalogue is generated on-the-fly. We present an upper bound on the average regret suffered bythe learner. Our empirical analysis highlights the promise of our approach.