Bayesian semiparametric customer base segmentation of mobile phone users based on longitudinal traffic data

Customer segmentation is one of the most important purposes of customer base analysis for telecommunication companies. Because companies accumulate very large amounts of data on customer behavior, segmentation is typically achieved by profiling and clustering traffic behavior jointly with demographic data and contracts characteristics. Unfortunately, most algorithms and models used for segmentation do not take into account the longitudinal characteristics of data. In particular, in telecommunication traffic analysis, the importance of decreasing patterns of traffic in customers' lives is well known, and it is relevant to aggregate all clients with such a pattern, while other unknown clusters may be of interest for the marketing manager. Our approach to address this problem is based on specifying the distribution of functions as a mixture of a parametric hierarchical model describing the decreasing pattern segment and a nonparametric contamination that allows unanticipated curve shapes in subjects' traffic. The parametric component is chosen based on prior knowledge, while the contamination is characterized as a functional Dirichlet process. Copyright © 2014 John Wiley & Sons, Ltd.     

推出冲突避免的机场停机位分配问题

为了科学合理地利用机场停机位资源,克服现有模型对飞机进出机位安全性的考虑不足,研究兼顾运行安全和运行效率的机场停机位分配问题.首先分析了飞机在停机坪中的运行过程,提出以主动避免方式来解除飞机进出机位过程中的冲突,从而将具有潜在冲突的飞机对的机位分配作为约束条件,建立了一类推出冲突避免的停机位分配模型.然后对目标函数和约束条件进行分析和简化,将模型转化为线性模型来求解.算例仿真结果验证了该模型的有效性,表明所提出的主动避免冲突方法是能兼顾运行安全和效率的一种有效方法.     

Principal Component Analysis of Two-Dimensional Functional Data

This article presents and compares two approaches of principal component (PC) analysis for two-dimensional functional data on a possibly irregular domain. The first approach applies the singular value decomposition of the data matrix obtained from a fine discretization of the two-dimensional functions. When the functions are only observed at discrete points that are possibly sparse and may differ from function to function, this approach incorporates an initial smoothing step prior to the singular value decomposition. The second approach employs a mixed effects model that specifies the PC functions as bivariate splines on triangulations and the PC scores as random effects. We apply the thin-plate penalty for regularizing the function estimation and develop an effective expectation–maximization algorithm for calculating the penalized likelihood estimates of the parameters. The mixed effects model-based approach integrates scatterplot smoothing and functional PC analysis in a unified framework and is shown in a simulation study to be more efficient than the two-step approach that separately performs smoothing and PC analysis. The proposed methods are applied to analyze the temperature variation in Texas using 100 years of temperature data recorded by Texas weather stations. Supplementary materials for this article are available online.     

Modeling Very Oscillating Signals. Application to Image Processing

This article is a companion paper of a previous work where we have developed the numerical analysis of a variational model first introduced by Rudin et al. and revisited by Meyer for removing the noise and capturing textures in an image. The basic idea in this model is to decompose an image f into two components (u + v) and then to search for (u,v) as a minimizer of an energy functional. The first component u belongs to BV and contains geometrical information, while the second one v is sought in a space G which contains signals with large oscillations, i.e. noise and textures. In Meyer carried out his study in the whole ² and his approach is rather built on harmonic analysis tools. We place ourselves in the case of a bounded set of ² which is the proper setting for image processing and our approach is based upon functional analysis arguments. We define in this context the space G, give some of its properties, and then study in this continuous setting the energy functional which allows us to recover the components u and v. We present some numerical experiments to show the relevance of the model for image decomposition and for image denoising.     

Performance analysis of distributed solution approaches in simulation-based optimization

Applying computationally expensive simulations in design or process optimization results in long-running solution processes even when using a state-of-the-art distributed algorithm and hardware. Within these simulation-based optimization problems the optimizer has to treat the simulation systems as black-boxes. The distributed solution of this kind of optimization problem demands efficient utilization of resources (i.e. processors) and evaluation of the solution quality. Analyzing the parallel performance is therefore an important task in the development of adequate distributed approaches taking into account the numerical algorithm, its implementation, and the used hardware architecture. In this paper, simulation-based optimization problems are characterized and a distributed solution algorithm is presented. Different performance analysis techniques (e.g. scalability analysis, computational complexity) are discussed and a new approach integrating parallel performance and solution quality is developed. This approach combines a priori and a posteriori techniques and can be applied in early stages of the solution process. The feasibility of the approach is demonstrated by applying it to three different classes of simulation-based optimization problems from groundwater management.     

A note on the square root law for urban police travel times

The classical Square Root Law formula for emergency travel times consists of one observable component, the density of patrol coverage, and one unknown component that must be estimated empirically, the effective travel speed. The effective travel speed is typically assumed to be an empirical constant. We test whether this simplifying assumption is justified empirically. We propose a modern machine-learning approach and a Least Absolute Shrinkage and Selection Operator regression to incorporate into a travel speed model various exogenous factors such as call type, incident location, weather conditions and traffic congestion. The value of the proposed analytical approach and some practical implications are demonstrated using operational data from a large urban police jurisdiction based in British Columbia, Canada. Although the analysis is framed within the context of urban emergency police operations, the proposed approach has the potential to be useful for other emergency services or roving business units that deal with unscheduled service calls.     

The discrete-time queue with autoregressive inputs revisited

In this paper, we present an exact queuing analysis of a discrete-time queue whose arrival process is correlated and consists of a discrete autoregressive model of order 1 (DAR(1)). The functional equation describing this DAR(1)/D/1 queuing model, originally derived in Hwang and Sohraby (Queuing Systems 43 (2003)29–41), is manipulated and transformed into a mathematical tractable form. By using simple analytical transform techniques, we show how our proposed approach allows us to derive an equivalent (yet simpler) expression for the steady-state probability generating function (pgf) of the queue length, as originally derived in Hwang and Sohraby (Queuing Systems 43 (2003)29–41). From this pgf, we characterize the distribution of the packet delay. New numerical results related to packet loss ratio and mean delay of the DAR(1)/D/1 queue are also presented. The proposed approach outlines an alternate solution technique and a general framework under which more complex time-series based queuing models can be analyzed. AMS Subject Classifications 60K25     

A new approach for describing glass transition kinetics

We use a functional integral technique generalizing the Keldysh diagram technique to describe glass transition kinetics. We show that the Keldysh functional approach takes the dynamical determinant arising in the glass dynamics into account exactly and generalizes the traditional approach based on using the supersymmetric dynamic generating functional method. In contrast to the supersymmetric method, this approach allows avoiding additional Grassmannian fields and tracking the violation of the fluctuation-dissipation theorem explicitly. We use this method to describe the dynamics of an Edwards-Anderson soft spin-glass-type model near the paramagnet-glass transition. We show that a Vogel-Fulcher-type dynamics arises in the fluctuation region only if the fluctuation-dissipation theorem is violated in the process of dynamical renormalization of the Keldysh action in the replica space.     

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??n this paper, we propose composite quantile regression for functional linear model with dependent data, in which the errors are from a short-range dependent and strictly stationary linear process. The functional principal component analysis is employed to approximate the slope function and the functional predictive variable respectively to construct an estimator of the slope function, and the convergence rate of the estimator is obtained under some regularity conditions. Simulation studies and a real data analysis are presented for illustration of the performance of the proposed estimator.     

Shape functional optimization with restrictions boosted with machine learning techniques

Shape optimization is a widely used technique in the design phase of a product. Current ongoing improvement policies require a product to fulfill a series of conditions from the perspective of mechanical resistance, fatigue, natural frequency, impact resistance, etc. All these conditions are translated into equality or inequality restrictions which must be satisfied during the optimization process that is necessary in order to determine the optimal shape. This article describes a new method for shape optimization that considers any regular shape as a possible shape, thereby improving on traditional methods limited to straight profiles or profiles established a priori. Our focus is based on using functional techniques and this approach is, based on representing the shape of the object by means of functions belonging to a finite-dimension functional space. In order to resolve this problem, the article proposes an optimization method that uses machine learning techniques for functional data in order to represent the perimeter of the set of feasible functions and to speed up the process of evaluating the restrictions in each iteration of the algorithm. The results demonstrate that the functional approach produces better results in the shape optimization process and that speeding up the algorithm using machine learning techniques ensures that this approach does not negatively affect design process response times.     

Time series of functional data with application to yield curves

We develop time series analysis of functional data observed discretely, treating the whole curve as a random realization from a distribution on functions that evolve over time. The method consists of principal components analysis of functional data and subsequently modeling the principal component scores as vector autoregressive moving averag (VARMA) process. We justify the method by showing that an underlying ARMAH structure of the curves leads to a VARMA structure on the principal component scores. We derive asymptotic properties of the estimators, fits, and forecast. For term structures of interest rates, these provide a unified framework for studying the time and maturity components of interest rates under one setup with few parametric assumptions. We apply the method to the yield curves of USA and India. We compare our forecasts to the parametric model that is based on Nelson‐Siegel curves. In another application, we study the dependence of long term interest rate on the short term interest rate using functional regression.     

Composite Quantile Regression for Functional Linear Models with Dependent Errors

n this paper, we propose composite quantile regression for functional linear model with dependent data, in which the errors are from a short-range dependent and strictly stationary linear process. The functional principal component analysis is employed to approximate the slope function and the functional predictive variable respectively to construct an estimator of the slope function, and the convergence rate of the estimator is obtained under some regularity conditions. Simulation studies and a real data analysis are presented for illustration of the performance of the proposed estimator.     

Polynomial spline estimation for partial functional linear regression models

Because of its orthogonality, interpretability and best representation, functional principal component analysis approach has been extensively used to estimate the slope function in the functional linear model. However, as a very popular smooth technique in nonparametric/semiparametric regression, polynomial spline method has received little attention in the functional data case. In this paper, we propose the polynomial spline method to estimate a partial functional linear model. Some asymptotic results are established, including asymptotic normality for the parameter vector and the global rate of convergence for the slope function. Finally, we evaluate the performance of our estimation method by some simulation studies.     

Principal Nested Spheres for Time-Warped Functional Data Analysis

There are often two important types of variation in functional data: the horizontal (or phase) variation and the vertical (or amplitude) variation. These two types of variation have been appropriately separated and modeled through a domain warping method (or curve registration) based on the Fisher–Rao metric. This article focuses on the analysis of the horizontal variation, captured by the domain warping functions. The square-root velocity function representation transforms the manifold of the warping functions to a Hilbert sphere. Motivated by recent results on manifold analogs of principal component analysis, we propose to analyze the horizontal variation via a principal nested spheres approach. Compared with earlier approaches, such as approximating tangent plane principal component analysis, this is seen to be an efficient and interpretable approach to decompose the horizontal variation in both simulated and real data examples.     

Experiences during development of a dynamic crash response automobile model

A finite element automobile model for use in crash safety studies was developed through reverse engineering. The model was designed for calculating the response of the automobile structure during full frontal, offset frontal, or side impacts. The reverse engineering process involves the digitization of component surfaces as the vehicle is dismantled, the meshing and reassembly of these components into a complete finite element model, and the measurement of stiffness properties for structural materials. Quasi-static component tests and full-vehicle crash tests were used to validate the model, which will become part of a finite element vehicle fleet.     

Using matrices to link conflict evolution and resolution in a graph model

The graph model for conflict resolution provides a convenient and effective means to model and analyze a strategic conflict. Standard practice is to carry out a stability analysis of a graph model, and then to follow up with a post-stability analysis, an important component of which is status quo analysis. A graph model can be viewed as an edge-colored graph, but the fundamental problem of status quo analysis – to find a shortest colored path from the status quo node to a desired equilibrium – is different from the well-known network analysis problem of finding the shortest path between two nodes. The only matrix method that has been proposed cannot track all aspects of the evolution of a conflict from the status quo state. Our explicit algebraic approach is convenient for computer implementation and, as demonstrated with a real world case study, easy to use. It provides new insights into a graph model, not only identifying all equilibria reachable from the status quo, but also how to reach them. Moreover, this approach bridges the gap between stability analysis and status quo analysis in the graph model for conflict resolution.     

Bond graph modelling of marine power systems

The main motivation for writing this article is to develop a model library for an All-Electric Ship that gives an opportunity to simulate both existing and new machinery systems without having to remodel the entire system each time. The model library should support the process of modelling and reuse, while also emphasizing openness to brace the modeller during the development and refinement phase. The bond graph approach is good when it comes to the physical modelling of systems and is a good tool for combining different energy domains to better help in understanding the system. In addition, a bond graph is a powerful method to find dependencies between various components. Using a causal analysis, any problems in the model, for example, algebraic constrains or dependent system variables, will be detected, and the necessary remodelling may be performed to handle such problems. The bond graph approach is therefore used when developing the component library. The component library consists of selected power producers such as diesel and gas engines, fuel cell and synchronous generator and power consumers such as asynchronous motor with a voltage source converter in addition to a generic load used for hotel and auxiliary loads. The library also consists of a ship model and propeller models.     

基于B样条和聚类分析的非参数轮廓监控方法研究

在轮廓监控中,产品或过程的质量特征可以由一种特定的函数关系表示。如果轮廓的函数形式是已知的,则可以使用参数化方法来监控轮廓。然而,当轮廓形态复杂时,继续使用参数方法则可能导致由于模型设定不准确而无法正确识别异常轮廓的问题。因此本文提出了一种基于非参数回归的新方法以解决制造过程中常见的复杂轮廓监控问题。所提方法将基于非参数回归的B样条与迭代的聚类分析过程相结合,在应用过程中不需要对轮廓的形式进行限制性假设。仿真研究评估了该监控方法在不同变异情况下的性能,并且通过与现有方法的比较分析,验证了该方法的有效性和优越性。最后通过轮廓监控领域的一个经典案例说明了新方法的实际应用效果。     

A mixture model-based approach to the clustering of exponential repeated data

The analysis of finite mixture models for exponential repeated data is considered. The mixture components correspond to different unknown groups of the statistical units. Dependency and variability of repeated data are taken into account through random effects. For each component, an exponential mixed model is thus defined. When considering parameter estimation in this mixture of exponential mixed models, the EM-algorithm cannot be directly used since the marginal distribution of each mixture component cannot be analytically derived. In this paper, we propose two parameter estimation methods. The first one uses a linearisation specific to the exponential distribution hypothesis within each component. The second approach uses a Metropolis–Hastings algorithm as a building block of a general MCEM-algorithm.