Maximization Approach Research Articles

The Expectation–Maximization approach for Bayesian quantile regression

This paper deals with Bayesian linear quantile regression models based on a recently developed Expectation–Maximization Variable Selection (EMVS) method. By using additional latent variables, the proposed approach enjoys enormous computational savings compared to commonly used Markov Chain Monte Carlo (MCMC) algorithm. Using location-scale mixture representation of asymmetric Laplace distribution (ALD), we develop a rapid and efficient Expectation–Maximization (EM) algorithm, which is illustrated with several carefully designed simulation examples. We further apply the proposed method to construct financial index tracking portfolios.

Employing Group Decision Support System for the Selection of Internet Information Search Channels for Consumers

A fragmented market and media propagation has emerged as a direct result of the evolution of technology. Media agencies now have a large variety of methods of reaching and engaging with potential customers. The proliferation of media has generated new challenges for marketers and identifying the most effective channel by which to reach online customers can be problematic. Marketers now need to develop an understanding of how consumers conduct their pre-purchase search for information about a given product or service so that they can optimize their promotion efforts. A fuzzy analytical hierarchy process cosine maximization (FAHPCM) approach was employed to assign the relative importance that online consumers give to a range of search factors. Following this, the technique for order of preference by similarity to ideal solution (TOPSIS) was utilized to assess the effectiveness of each respective channel. Finally, sensitivity analysis was conducted to verify the results. The effectiveness of the proposed approach is demonstrated through a numerical example.

Quadratic Program-Based Modularity Maximization for Fuzzy Community Detection in Social Networks

One of the most important elements of social network analysis is community detection, i.e., finding groups of similar people based on their traits. In this paper, we present the fuzzy modularity maximization (FMM) approach for community detection, which finds overlapping—that is, fuzzy—communities (where appropriate) by maximizing a generalized form of Newman's modularity. The first proposed FMM solution uses a tree-based structure to find a globally optimal solution, while the second proposed solution uses alternating optimization to efficiently search for a locally optimal solution. Both of these approaches are based on a proposed algorithm called one-step modularity maximization (OSMM), which computes the optimal cluster memberships for one person in the social network. We prove that OSMM can be formulated as a simplified quadratic knapsack optimization problem, which is $O(n)$ time complexity. We then propose a tree-based algorithm, called FMM/Find Best Leaf Node (FMM/FBLN), which represents sequences of OSMM steps in a tree-based structure. It is proved that FMM/FBLN finds globally optimal solutions for FMM; however, the time complexity of FMM/FBLN is $O(n^d)$ , $d\ge 2$ ; thus, it is impractical for most real-world networks. To combat this inefficiency, we propose five heuristic-based alternating optimization schemes, i.e., FMM/H1–H5, which are all shown to be $O(n^2)$ time complexity. We compare the results of the FMM/H solutions with those of state-of-the-art community detection algorithms, MULTICUT spectral FCM (MSFCM) and GALS, and with those of two fuzzy community detection algorithms called GA and vertex-similarity based gradient-descent method (VSGD) on ten real-world datasets. We conclude that one of the five heuristic algorithms (FMM/H2) is very competitive with GALS and much more effective than MSFCM, GA, and VSGD. Furthermore, all of the FMM/H schemes are at least two orders of magnitude faster than GALS in run time. Finally, FMM/H, unlike GALS (which only produces crisp partitions) and MSFCM (which always finds fuzzy partitions), is the only fuzzy community detection algorithm to date that can find the max-modularity partition, fuzzy or crisp.

Generalized expectation–maximization approach to LPV process identification with randomly missing output data

This paper considers parameter estimation for linear parameter varying (LPV) systems with randomly missing output data. The multi-model LPV model is adopted and the identification problem is formulated under the scheme of the generalized expectation–maximization (GEM) algorithm. In order to deal with the missing output data, the local models are firstly taken to have the finite impulse response (FIR) model structure. To alleviate potential overparameterization problem, a prior on FIR model coefficients is imposed and the GEM algorithm is modified to derive the maximum a posterior (MAP) estimates of the multi-mode LPV FIR model parameters. Since the FIR model is not suitable for general control applications, a multi-mode LPV output error (OE) model is then identified by applying the GEM algorithm to the same identification data set with parameters initialized based on the estimated FIR models. One simulation example and two experiments are presented to demonstrate the efficiency of the proposed method.

Image Outlier Detection and Feature Extraction via L1-Norm-Based 2D Probabilistic PCA.

This paper introduces an L1-norm-based probabilistic principal component analysis model on 2D data (L1-2DPPCA) based on the assumption of the Laplacian noise model. The Laplacian or L1 density function can be expressed as a superposition of an infinite number of Gaussian distributions. Under this expression, a Bayesian inference can be established based on the variational expectation maximization approach. All the key parameters in the probabilistic model can be learned by the proposed variational algorithm. It has experimentally been demonstrated that the newly introduced hidden variables in the superposition can serve as an effective indicator for data outliers. Experiments on some publicly available databases show that the performance of L1-2DPPCA has largely been improved after identifying and removing sample outliers, resulting in more accurate image reconstruction than the existing PCA-based methods. The performance of feature extraction of the proposed method generally outperforms other existing algorithms in terms of reconstruction errors and classification accuracy.

Integration of cost modelling within the micro-siting design optimisation of tidal turbine arrays

The location of individual turbines within a tidal current turbine array – micro-siting – can have a significant impact on the power that the array may extract from the flow. Due to the infancy of the industry and the challenges of exploiting the resource, the economic costs of realising industrial scale tidal current energy projects are significant and should be considered as one of the key drivers of array design. This paper proposes a framework for the automated design of tidal current turbine arrays in which costs over the lifespan of the array may be modelled and considered as part of the design optimisation process. To demonstrate this approach, the cost of sub-sea cabling is incorporated by implementing a cable-routing algorithm alongside an existing gradient-based array optimisation algorithm. Three idealised test scenarios are used to demonstrate the effects of a financial-return optimising design approach as contrasted with a power maximisation approach.

Semisupervised Pair-Wise Band Selection for Hyperspectral Images

This paper proposes a new approach of band selection for classifying multiple objects in hyperspectral images. Different from traditional algorithms, we construct a semisupervised pair-wise band selection (PWBS) framework for this task, in which an individual band selection process is performed only for each pair of classes. First, the statistical parameters for spectral features of each class, including mean vectors and covariance matrices, are estimated by an expectation maximization approach in a semisupervised learning setting, where both labeled and unlabeled samples are employed for better performance. For each pair of classes, based on the estimated statistical parameters, Bhattacharyya distances between the two classes are calculated to evaluate all possible subsets of bands for classification. Second, as our proposed semisupervised framework, the PWBS followed by a binary classifier can be embedded into the semisupervised expectation maximization process to obtain posterior probabilities of samples on the selected bands. Finally, to evaluate the selected bands, all of the binary decisions obtained with multiple binary classifiers are finally fused together. Comparative experimental results demonstrate the validity of our proposed algorithm. The experimental results also prove that our band selection algorithm can perform well when the training set is very small.

Opportunistic Network Coding Scheme for Two-Way Relay Wireless Networks: A Sum-Rate Maximization Approach

Applying network coding (NC) in the downlink of two-way relay networks can significantly increase the throughput. However, the fading nature of wireless channels usually causes great asymmetry between two downlink channels, which can degrade the performance of NC. Therefore, it is very necessary to perform an opportunistic scheme that selects between broadcast and unicast at the relay node based on channel side information. This paper focuses on the fundamental limit of the sum rate in the downlink. To solve the maximization problem of the sum rate in the downlink, we first introduce an auxiliary variable, known as marginal capacity income of transmit power, and then derive the corresponding power allocation in closed-form expression and present an opportunistic switching selection strategy between broadcast/unicast. Numerical results also show that our proposed scheme achieves a larger downlink sum throughput compared with other existing known schemes.

A model-independent approach for efficient influence maximization in social networks

The well-known influence maximization problem (Kempe et al., in proceedings of the 9th SIGKDD international conference on knowledge discovery and data mining (KDD), pp 137–146, 2003) (or viral marketing through social networks) deals with selecting a few influential initial seeds to maximize the awareness of product(s) over the social network. As it is computationally hard (Kempe et al., in proceedings of the 9th SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD), pp 137–146, 2003), a greedy approximation algorithm is designed to address the influence maximization problem. However, the major drawback of this greedy algorithm is that it runs extremely slow even on network datasets consisting of a few thousand nodes and edges (Leskovec et al., in proceedings of the 13th SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD), pp 420–429, 2007; Checn et al., in proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD), pp 937–944, 2009). Several efficient heuristics have been proposed in the literature (Checn et al., in proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD), pp 937–944, 2009) to alleviate this computational difficulty; however, these heuristics are designed for specific influence propagation models such as linear threshold model and independent cascade model. This motivates the strong need to design an approach that not only works with any influence propagation model, but also efficiently solves the influence maximization problem. In this paper, we precisely address this problem by proposing a new framework which fuses both link and interaction data to come up with a backbone for a given social network, which can further be used for efficient influence maximization. We then conduct thorough experimentation with several real-life social network datasets such as DBLP, Epinions, Digg, and Slashdot and show that the proposed approach is efficient as well as scalable.

A Linear Quadratic Gaussian Approach for Power Transfer Maximization of a Point Absorber Wave Energy Converter

This article studies the problem of maximizing the take-off power from a buoy-type point absorber of a wave energy converter. The article offers a solution framework for the above-mentioned problem under the linear quadratic Gaussian control approach. The standard Kalman estimator technique is used to estimate the position and velocity of the two-body wave energy system. The optimal power take-off force is computed, and hence, the maximum output power is achieved. A comparison with a conventional approach reflects the superiority of this framework even under different values of a mooring constant.

A Two-Component $K$–Lognormal Mixture Model and Its Parameter Estimation Method

Statistical models are used for describing the synthetic aperture radar (SAR) image data and are the basis of SAR image interpretations. Appropriate statistical models that can accurately describe the SAR image data are essential for the performances of SAR image interpretations. A statistical model, which is a mixture of $K$ distribution and lognormal distribution, is proposed in this paper. This mixture model is able to model the clutter data, the target data, or the mixed data of clutter and target. This mixture model is also able to describe the proportions of clutter region and target region in a scene as well as the statistical properties of the clutter data and target data in the scene. A maximum likelihood method using the expectation–maximization approach is derived for estimating the parameters of the mixture model. Experiments have been conducted to demonstrate the effectiveness of the mixture model (together with the proposed parameter estimation method) for modeling the SAR data.

Copula Gaussian graphical models with penalized ascent Monte Carlo EM algorithm

Typical data that arise from surveys, experiments, and observational studies include continuous and discrete variables. In this article, we study the interdependence among a mixed (continuous, count, ordered categorical, and binary) set of variables via graphical models. We propose an ℓ1‐penalized extended rank likelihood with an ascent Monte Carlo expectation maximization approach for the copula Gaussian graphical models and establish near conditional independence relations and zero elements of a precision matrix. In particular, we focus on high‐dimensional inference where the number of observations are in the same order or less than the number of variables under consideration. To illustrate how to infer networks for mixed variables through conditional independence, we consider two datasets: one in the area of sports and the other concerning breast cancer.

Adaptive Interaction: A Utility Maximization Approach to Understanding Human Interaction with Technology by Stephen J.Payne and AndrewHowes. San Rafael, CA: Morgan & Claypool Publishers, 2013. 111 pp. Paperback. $35.00USD. (ISBN: 978‐1628458387).

Adaptive Interaction: A Utility Maximization Approach to Understanding Human Interaction with Technology by Stephen J.Payne and AndrewHowes. San Rafael, CA: Morgan & Claypool Publishers, 2013. 111 pp. Paperback. $35.00USD. (ISBN: 978‐1628458387).

Analysing bicycle-sharing system user destination choice preferences: Chicago’s Divvy system

In recent years, there has been increasing attention on bicycle-sharing systems (BSS) as a viable and sustainable mode of transportation for short trips. However, due to the relatively recent adoption of BSS, there is very little research exploring how people consider these systems within existing transportation options. Given recent BSS growth around the world, there is substantial interest in identifying contributing factors that encourage individuals to use these systems. The current study contributes to this growing literature by examining BSS behavior at the trip level to analyze bicyclists’ destination preferences. Specifically, we study the decision process involved in identifying destination locations after picking up a bicycle at a BSS station, using a random utility maximization approach in the form of a multinomial logit model (MNL). The quantitative frameworks developed have been estimated using 2013 data from the Chicago’s Divvy system. In our modeling effort, we distinguish between BSS users with annual membership and short-term customers with daily passes. The developed model should allow bicycle-sharing system operators to plan services more effectively by examining the impact of travel distance, land use, built environment, and access to public transportation infrastructure on users’ destination preferences. Using the estimated model, we generated utility profiles as a function of distance and various other attributes, allowing us to represent visually the trade-offs that individuals make in the decision process. To illustrate further the applicability of the proposed framework for planning purposes, destination station-choice probability prediction is undertaken.

Synthesizing modeling of power generation and power limits in energy systems

Applying the common mathematical procedure of thermodynamic optimization the paper offers a synthesizing or generalizing modeling of power production in various energy generators, such as thermal, solar and electrochemical engines (fuel cells). Static and dynamical power systems are investigated. Dynamical models take into account the gradual downgrading of a resource, caused by power delivery. Analytical modeling includes conversion efficiencies expressed in terms of driving fluxes. Products of efficiencies and driving fluxes determine the power yield and power maxima. While optimization of static systems requires using of differential calculus and Lagrange multipliers, dynamic optimization involves variational calculus and dynamic programming. In reacting mixtures balances of mass and energy serve to derive power yield in terms of an active part of chemical affinity. Power maximization approach is also applied to fuel cells treated as flow engines driven by heat flux and fluxes of chemical reagents. The results of power maxima provide limiting indicators for thermal, solar and SOFC generators. They are more exact than classical reversible limits of energy transformation.

Multiple kernel dimensionality reduction via spectral regression and trace ratio maximization

The performance of kernel-based dimensionality reduction heavily relies on the selection of kernel functions. Multiple kernel learning for dimensionality reduction (MKL-DR) has been recently proposed to learn a convex combination from a set of base kernels. But this method relaxes a nonconvex quadratically constrained quadratic programming (QCQP) problem into a semi-definite programming (SDP) problem to specify the kernel weights, which might lead to its performance degradation. Although a trace ratio maximization approach to multiple-kernel based dimensionality reduction (MKL-TR) has been presented to avoid convex relaxation, it has to compute a generalized eigenvalue problem in each iteration of its algorithm, which is expensive in both time and memory. To improve the performance of these methods further, this paper proposes a novel multiple kernel dimensionality reduction method by virtue of spectral regression and trace ratio maximization, termed as MKL-SRTR. The proposed approach aims at learning an appropriate kernel from the multiple base kernels and a transformation into a lower dimensionality space efficiently and effectively. The experimental results demonstrate the effectiveness of the proposed method in benchmark datasets for supervised, unsupervised as well as semi-supervised scenarios.

Throughput Maximization with S-graph Framework using Global Branching Tree

Abstract Majozi and Friedler [3] developed the first approach for throughput maximization, which has no need for the optimal number of time points a-priori. The feasibility of a sequence of subproblems is examined with guided search driven S-graph based approach. Although, the approach has proved to be efficient for several problems [1], it can be developed further to increase the size of addressable cases. In the original approach, a branching tree is generated for each subproblem separately, even though these trees can have significantly large overlaps. The presented approach exploits this redundancy to reduce the computational needs for industrial scale problems.

Quadratic Hedging of Basis Risk

This paper examines a simple basis risk model based on correlated geometric Brownian motions. We apply quadratic criteria to minimize basis risk and hedge in an optimal manner. Initially, we derive the Föllmer–Schweizer decomposition for a European claim. This allows pricing and hedging under the minimal martingale measure, corresponding to the local risk-minimizing strategy. Furthermore, since the mean-variance tradeoff process is deterministic in our setup, the minimal martingale- and variance-optimal martingale measures coincide. Consequently, the mean-variance optimal strategy is easily constructed. Simple pricing and hedging formulae for put and call options are derived in terms of the Black–Scholes formula. Due to market incompleteness, these formulae depend on the drift parameters of the processes. By making a further equilibrium assumption, we derive an approximate hedging formula, which does not require knowledge of these parameters. The hedging strategies are tested using Monte Carlo experiments, and are compared with results achieved using a utility maximization approach.

A Query Approach for Influence Maximization on Specific Users in Social Networks

Influence maximization is introduced to maximize the profit of viral marketing in social networks. The weakness of influence maximization is that it does not distinguish specific users from others, even if some items can be only useful for the specific users. For such items, it is a better strategy to focus on maximizing the influence on the specific users. In this paper, we formulate an influence maximization problem as query processing to distinguish specific users from others. We show that the query processing problem is NP-hard and its objective function is submodular. We propose an expectation model for the value of the objective function and a fast greedy-based approximation method using the expectation model. For the expectation model, we investigate a relationship of paths between users. For the greedy method, we work out an efficient incremental updating of the marginal gain to our objective function. We conduct experiments to evaluate the proposed method with real-life datasets, and compare the results with those of existing methods that are adapted to the problem. From our experimental results, the proposed method is at least an order of magnitude faster than the existing methods in most cases while achieving high accuracy.

Expectation–Maximization Approach to Fault Diagnosis With Missing Data

This paper introduces a data-driven approach for fault diagnosis in the presence of incomplete monitor data. The expectation-maximization (EM) algorithm is applied to handle missing data in order to obtain a maximum-likelihood solution for the discrete (or categorical) distribution. Because of the nature of categorical distributions, the maximization step of the EM algorithm is shown in this paper to have an easily calculated analytical solution, making this method computationally simple. An experimental study on a ball-and-tube system is investigated to demonstrate advantages of the proposed approach.