Simple Instance Research Articles

On the Power of Deterministic Mechanisms for Facility Location Games

We consider K -Facility Location games, where n strategic agents report their locations in a metric space and a mechanism maps them to K facilities. The agents seek to minimize their connection cost, namely the distance of their true location to the nearest facility, and may misreport their location. We are interested in deterministic mechanisms that are strategyproof, that is, ensure that no agent can benefit from misreporting her location, do not resort to monetary transfers, and achieve a bounded approximation ratio to the total connection cost of the agents (or to the L p norm of the connection costs, for some p ∈ [1, ∞) or for p = ∞). Our main result is an elegant characterization of deterministic strategyproof mechanisms with a bounded approximation ratio for 2-Facility Location on the line. In particular, we show that for instances with n ≥ 5 agents, any such mechanism either admits a unique dictator or always places the facilities at the leftmost and the rightmost location of the instance. As a corollary, we obtain that the best approximation ratio achievable by deterministic strategyproof mechanisms for the problem of locating 2 facilities on the line to minimize the total connection cost is precisely n -2. Another rather surprising consequence is that the Two-Extremes mechanism of Procaccia and Tennenholtz [2009] is the only deterministic anonymous strategyproof mechanism with a bounded approximation ratio for 2-Facility Location on the line. The proof of the characterization employs several new ideas and technical tools, which provide new insights into the behavior of deterministic strategyproof mechanisms for K -Facility Location games and may be of independent interest. Employing one of these tools, we show that for every K ≥ 3, there do not exist any deterministic anonymous strategyproof mechanisms with a bounded approximation ratio for K -Facility Location on the line, even for simple instances with K +1 agents. Moreover, building on the characterization for the line, we show that there do not exist any deterministic strategyproof mechanisms with a bounded approximation ratio for 2-Facility Location and instances with n ≥ 3 agents located in a star.

A Comparative Evaluation of Curriculum Learning with Filtering and Boosting in Supervised Classification Problems

Not all instances in a data set are equally beneficial for inferring a model of the data, and some instances (such as outliers) can be detrimental. Several machine learning techniques treat the instances in a data set differently during training such as curriculum learning, filtering, and boosting. However, it is difficult to determine how beneficial an instance is for inferring a model of the data. In this article, we present an automated method that orders the instances in a data set by complexity based on their likelihood of being misclassified (instance hardness) for supervised classification problems that generates a hardness ordering. The underlying assumption of this method is that instances with a high likelihood of being misclassified represent more complex concepts in a data set. Using a hardness ordering allows a learning algorithm to focus on the most beneficial instances. We integrate a hardness ordering into the learning process using curriculum learning, filtering, and boosting. We find that focusing on the simpler instances during training significantly increases generalization accuracy. Also, the effects of curriculum learning depend on the learning algorithm that is used. In general, filtering and boosting outperform curriculum learning, and filtering has the most significant effect on accuracy. © 2014 Wiley Periodicals, Inc.

Symbolic Configuration for Interactive Container Ship Stowage Planning

Low‐cost containerized shipping requires high‐quality stowage plans. Scalable stowage planning optimization algorithms have been developed recently. All of these algorithms, however, produce monolithic solutions that are hard for stowage coordinators to modify, which is necessary in practice owing to exceptions and operational disruptions. This article introduces an approach for modifying a stowage plan interactively without breaking its constraints. We focus on rearranging the containers in a single‐bay section and show two approaches for providing complete and backtrack‐free decision support using symbolic configuration techniques, one based on binary decision diagrams and one based on DPLL solvers. We show that binary decision diagrams can be used to solve real‐world sized instances of a single bay, and that search‐based solvers can be used to solve simplified instances going beyond a single bay.

Pairwise-similarity-based instance reduction for efficient instance selection in multiple-instance learning

Unlike the traditional supervised learning, multiple-instance learning (MIL) deals with learning from bags of instances rather than individual instances. Over the last couple of years, some researchers have attempted to solve the MIL problem from the perspective of instance selection. The basic idea is selecting some instance prototypes from the training bags and then converting MIL to single-instance learning using these prototypes. However, a bag is composed of one or more instances, which often leads to high computational complexity for instance selection. In this paper, we propose a simple and general instance reduction method to speed up the instance selection process for various instance selection-based MIL (ISMIL) algorithms. We call it pairwise-similarity-based instance reduction for multiple-instance learning (MIPSIR), which is based on the pairwise similarity between instances in a bag. Instead of the original training bag, we use a pair of instances with the highest or lowest similarity value depending on the bag label within this bag for instance selection. We have applied our method to four effective ISMIL algorithms. The evaluation on three benchmark datasets demonstrates that the MIPSIR method can significantly improve the efficiency of an ISMIL algorithm while maintaining or even improving its generalization capability.

Modeling and Simulation of Space Situation Awareness System Based on Parallel Control Theory

The basic components and complex property of SSA (space situational awareness) system is introduced. It is elaborated that the reason and method of researching SSA system based on parallel control theory. Specific idea and steps of modeling and simulation are proposed through ACP method of parallel control theory, and a simple simulated instance was used as a prototype of achieving artificial system of SSA.

Hierarchical Method of Urban Building Extraction Inspired by Human Perception

In a high-resolution satellite image, buildings can be considered as clustered objects belonging to the same category. Human perception of such objects consists of an initial identification of simple instances followed by recognition of more complicated ones by deduction. Inspired by this observation, a hierarchical building extraction framework is proposed to simulate the process, which includes three major components. First, a total variation-based segmentation algorithm is presented to decompose the given image into object-level elements. Then, a shape analysis is applied to extract some common and easily identified rectangular buildings. Finally, the detection of buildings with complex structures is formulated as a deduction problem based on preceding extracted information in terms of maximum a posteriori (MAP) estimation and a Bayesian based approach is proposed to deal with it. The experimental results demonstrate that the proposed framework is capable of efficiently identified urban buildings from high-resolution satellite images.

GENERAL FORMULATION FOR A MANUFACTURING OF DEFECTIVE SETUP WITH DIFFERENT ADJUSTMENT METHODS

Consider the problem of adjusting a machine that starts production after a defective setup operation. This setup adjustment problem was first studied by Grubbs (1954, 1983). A general formulation for setup adjustment problems is presented in this paper. The formulation unifies some well-known process adjustment schemes, including Grubbs’ harmonic and extended rules, adjustment methods based on stochastic approximation and recursive least squares, and a recent method on adaptive EWMA feedback controllers. The proposed formulation is Bayesian and based on a Kalman Filter. The formulation allows to show the equivalence of the setup process adjustment problem with a simple instance of what in the control engineering literature is called a Linear Quadratic Gaussian (LQG) controller. As an important byproduct, the LQG model allows to solve more complicated setup adjustment problems with readily available techniques. Extensions to cases when there are quadratic adjustment costs and when the problem is multivariate are discussed. The multivariate setup adjustment solution is illustrated with a multihead filling machine example.

Combining example selection with instance selection to speed up multiple-instance learning

Recently, several instance selection-based methods have been presented to solve the multiple-instance learning (MIL) problem. The basic idea is converting MIL into standard supervised learning by selecting some representative instance prototypes from the training set. However, training examples are not single instances but bags composed of one or more instances in MIL, so the computational complexity is often very high. Previous methods consider this issue only from the perspective of instance selection not from that of example selection. In this paper, we try to address this issue via combining example selection with instance selection. Three general example selection methods are derived by adapting three immune-inspired algorithms to MIL. Additionally, we propose a simple instance selection method for MIL based on the probability that an instance is positive given a set of negative instances. Our example selection methods are combined with the new MIL method and other previous instance selection-based ones as a preprocessing step. The theoretical analysis and empirical results show that our MIL method is competitive to the state-of-the-art and the proposed example selection methods could significantly speed up various instance selection-based MIL methods with slightly weakening their performance or even strengthening it.

A Closed-Form, Consistent and Robust Solution to Uncalibrated Photometric Stereo Via Local Diffuse Reflectance Maxima

Images of an object under different illumination are known to provide strong cues about the object surface. A mathematical formalization of how to recover the normal map of such a surface leads to the so-called uncalibrated photometric stereo problem. In the simplest instance, this problem can be reduced to the task of identifying only three parameters: the so-called generalized bas-relief (GBR) ambiguity. The challenge is to find additional general assumptions about the object, that identify these parameters uniquely. Current approaches are not consistent, i.e., they provide different solutions when run multiple times on the same data. To address this limitation, we propose exploiting local diffuse reflectance (LDR) maxima, i.e., points in the scene where the normal vector is parallel to the illumination direction (see Fig. 1). We demonstrate several noteworthy properties of these maxima: a closed-form solution, computational efficiency and GBR consistency. An LDR maximum yields a simple closed-form solution corresponding to a semi-circle in the GBR parameters space (see Fig. 2); because as few as two diffuse maxima in different images identify a unique solution, the identification of the GBR parameters can be achieved very efficiently; finally, the algorithm is consistent as it always returns the same solution given the same data. Our algorithm is also remarkably robust: It can obtain an accurate estimate of the GBR parameters even with extremely high levels of outliers in the detected maxima (up to 80 % of the observations). The method is validated on real data and achieves state-of-the-art results.

Restricted Normal Cones and the Method of Alternating Projections: Applications

The method of alternating projections (MAP) is a common method for solving feasibility problems. While employed traditionally to subspaces or to convex sets, little was known about the behavior of the MAP in the nonconvex case until 2009, when Lewis, Luke, and Malick derived local linear convergence results provided that a condition involving normal cones holds and at least one of the sets is superregular (a property less restrictive than convexity). However, their results failed to capture very simple classical convex instances such as two lines in a three-dimensional space. In this paper, we extend and develop the Lewis-Luke-Malick framework so that not only any two linear subspaces but also any two closed convex sets whose relative interiors meet are covered. We also allow for sets that are more structured such as unions of convex sets. The key tool required is the restricted normal cone, which is a generalization of the classical Mordukhovich normal cone. Numerous examples are provided to illustrate the theory.

Establishing non-Abelian topological order in Gutzwiller-projected Chern insulators via entanglement entropy and modularS-matrix

We use entanglement entropy signatures to establish non-Abelian topological order in projected Chern-insulator wavefunctions. The simplest instance is obtained by Gutzwiller projecting a filled band with Chern number C=2, whose wavefunction may also be viewed as the square of the Slater determinant of a band insulator. We demonstrate that this wavefunction is captured by the $SU(2)_2$ Chern Simons theory coupled to fermions. This is established most persuasively by calculating the modular S-matrix from the candidate ground state wavefunctions, following a recent entanglement entropy based approach. This directly demonstrates the peculiar non-Abelian braiding statistics of Majorana fermion quasiparticles in this state. We also provide microscopic evidence for the field theoretic generalization, that the Nth power of a Chern number C Slater determinant realizes the topological order of the $SU(N)_C$ Chern Simons theory coupled to fermions, by studying the $SU(2)_3$ (Read-Rezayi type state) and the $SU(3)_2$ wavefunctions. An advantage of our projected Chern insulator wavefunctions is the relative ease with which physical properties, such as entanglement entropy and modular S-matrix can be numerically calculated using Monte Carlo techniques.

A dynamical composition law for boundary conditions

We analyze the quantum dynamics of a non-relativistic particle moving in a bounded domain of physical space, when the boundary conditions are rapidly changed. In general, this yields new boundary conditions, via a dynamical composition law that is a very simple instance of the superposition of different topologies. In all cases, unitarity is preserved and the quick change of boundary conditions does not introduce any decoherence in the system. Among the emerging boundary conditions, the Dirichlet case (vanishing wavefunction at the boundary) plays the role of an attractor. Possible experimental implementations with superconducting quantum interference devices are explored and analyzed.

Sherali--Adams Relaxations and Indistinguishability in Counting Logics

Two graphs with adjacency matrices $\mathbf{A}$ and $\mathbf{B}$ are isomorphic if there exists a permutation matrix $\mathbf{P}$ for which the identity $\mathbf{P}^{\mathrm{T}} \mathbf{A} \mathbf{P} = \mathbf{B}$ holds. Multiplying through by $\mathbf{P}$ and relaxing the permutation matrix to a doubly stochastic matrix leads to the linear programming relaxation known as fractional isomorphism. We show that the levels of the Sherali--Adams (SA) hierarchy of linear programming relaxations applied to fractional isomorphism interleave in power with the levels of a well-known color-refinement heuristic for graph isomorphism called the Weisfeiler--Lehman algorithm, or, equivalently, with the levels of indistinguishability in a logic with counting quantifiers and a bounded number of variables. This tight connection has quite striking consequences. For example, it follows immediately from a deep result of Grohe in the context of logics with counting quantifiers that a fixed number of levels of SA suffice to determine isomorphism of planar and minor-free graphs. We also offer applications in both finite model theory and polyhedral combinatorics. First, we show that certain properties of graphs, such as that of having a flow circulation of a prescribed value, are definable in the infinitary logic with counting with a bounded number of variables. Second, we exploit a lower bound construction due to Cai, Fürer, and Immerman in the context of counting logics to give simple explicit instances that show that the SA relaxations of the vertex-cover and cut polytopes do not reach their integer hulls for up to $\Omega(n)$ levels, where $n$ is the number of vertices in the graph.

Higher Lie algebra actions on Lie algebroids

We consider a simple instance of action up to homotopy. More precisely, we consider strict actions of DGLAs in degrees −1 and 0 on degree 1 NQ-manifolds. In a more conventional language this means: strict actions of Lie algebra crossed modules on Lie algebroids.When the action is strict, we show that it integrates to group actions in the categories of Lie algebroids and Lie groupoids (i.e. actions of LA-groups and 2-groups). We perform the integration in the framework of Mackenzie’s doubles.

Bounded Model Checking for Probabilistic Computation Tree Logic

In order to overcome the state explosion problem in model checking the probabilistic computation tree logic,a bounded model checking technique is proposed.First,the bounded semantics of the probabilistic computation tree logic is presented,and then its correctness is proved.Second,by a simple instance the criterion of the traditional termination,based on the length of path,is shown to fail.Based on the termination criterion used in the Newton iteration in numerical computing,a new criterion is given.Third,the bounded model checking procedure of the probabilistic computation tree logic is transformed into linear equations.Finally,three benchmarks are used to present the advantages of the bounded model checking.

Popularity at minimum cost

We consider an extension of the popular matching problem in this paper. The input to the popular matching problem is a bipartite graph \(G = (\mathcal{A}\cup\mathcal{B},E)\), where \(\mathcal{A}\) is a set of people, \(\mathcal{B}\) is a set of items, and each person \(a \in\mathcal{A}\) ranks a subset of items in order of preference, with ties allowed. The popular matching problem seeks to compute a matching M ∗ between people and items such that there is no matching M where more people are happier with M than with M ∗. Such a matching M ∗ is called a popular matching. However, there are simple instances where no popular matching exists.Here we consider the following natural extension to the above problem: associated with each item \(b \in\mathcal{B}\) is a non-negative price cost(b), that is, for any item b, new copies of b can be added to the input graph by paying an amount of cost(b) per copy. When G does not admit a popular matching, the problem is to “augment” G at minimum cost such that the new graph admits a popular matching. We show that this problem is NP-hard; in fact, it is NP-hard to approximate it within a factor of \(\sqrt{n_{1}}/2\), where n 1 is the number of people. This problem has a simple polynomial time algorithm when each person has a preference list of length at most 2. However, if we consider the problem of constructing a graph at minimum cost that admits a popular matching that matches all people, then even with preference lists of length 2, the problem becomes NP-hard. On the other hand, when the number of copies of each item is fixed, we show that the problem of computing a minimum cost popular matching or deciding that no popular matching exists can be solved in O(mn 1) time, where m is the number of edges.

Discrete Elastic Inner Vector Spaces with Application to Time Series and Sequence Mining

This paper proposes a framework dedicated to the construction of what we call discrete elastic inner product allowing one to embed sets of non-uniformly sampled multivariate time series or sequences of varying lengths into inner product space structures. This framework is based on a recursive definition that covers the case of multiple embedded time elastic dimensions. We prove that such inner products exist in our general framework and show how a simple instance of this inner product class operates on some prospective applications, while generalizing the Euclidean inner product. Classification experimentations on time series and symbolic sequences datasets demonstrate the benefits that we can expect by embedding time series or sequences into elastic inner spaces rather than into classical Euclidean spaces. These experiments show good accuracy when compared to the euclidean distance or even dynamic programming algorithms while maintaining a linear algorithmic complexity at exploitation stage, although a quadratic indexing phase beforehand is required.

Successions in Words and Compositions

We consider words over the alphabet [k] = {1, 2, . . . , k}, k ≥ 2. For a fixed nonnegative integer p, a p-succession in a word w 1 w 2 . . . w n consists of two consecutive letters of the form (w i , w i + p), i = 1, 2, . . . , n − 1. We analyze words with respect to a given number of contained p-successions. First we find the mean and variance of the number of p-successions. We then determine the distribution of the number of p-successions in words of length n as n (and possibly k) tends to infinity; a simple instance of a phase transition (Gaussian-Poisson-degenerate) is encountered. Finally, we also investigate successions in compositions of integers.

Spin interfaces in the Ashkin–Teller model and SLE

We investigate the scaling properties of the spin interfaces in the Ashkin–Teller model.These interfaces are a very simple instance of lattice curves coexisting with a fluctuatingdegree of freedom, which renders the analytical determination of their exponents verydifficult. One of our main findings is the construction of boundary conditions whichensure that the interface still satisfies the Markov property in this case. Then,using a novel technique based on the transfer matrix, we compute numerically theleft-passage probability, and our results confirm that the spin interface is described by aSchramm–Loewner evolution (SLE) in the scaling limit. Moreover, at a particular pointof the critical line, we describe a mapping of the Ashkin–Teller model onto anintegrable 19-vertex model, which, in turn, relates to an integrable dilute Brauermodel.

Simple instance selection for bankruptcy prediction

Instance selection or outlier detection is an important task during data mining, which focuses on filtering out bad data from a given dataset. However, there is no rigid mathematical definition of what constitutes an outlier and an outlier is not a binary property. Therefore, different volumes of outliers may be detected depending on the setting of the threshold for what constitutes an outlier, e.g., the distance in distance-based outlier detection. In this study, we examine bankruptcy prediction performance achieved after removal of different outlier volumes from four widely used datasets, namely the Australian, German, Japanese, and UC Competition datasets. Specifically, a simple distance-based clustering outlier detection method is used. In addition, four popular classification techniques are compared, artificial neural networks, decision trees, logistic regression, and support vector machines. Experiments are conducted to examine (1) the prediction performance of the bankruptcy prediction models with and without instance selection, (2) the stability of bankruptcy prediction models after the removal of outliers from the testing set, and (3) the characteristics of these four different datasets. The results show that with the German dataset it is much more difficult for the prediction models to provide high rates of accuracy after outlier removal, while it is easier with the UC Competition dataset. Removing 50% of the outliers can lead to optimal performance of these four models. In addition, using the removed outliers to test the prediction accuracy of these models, we find that it is support vector machines (SVM) that provide the highest rate of prediction accuracy and perform with much more stability and good noise tolerance than the other three prediction models. Furthermore, the prediction accuracy of the SVM model followed by instance selection is similar to the one without instance selection (i.e., the SVM baseline). In other words, the difference in performance between the SVM and the SVM baseline is the least of the three models in comparison with their corresponding baselines.