New global optimization algorithms for model-based clustering

The Expectation-Maximization (EM) algorithm is a very popular optimization tool for mixture problems and in particular for model-based clustering problems. However, while the algorithm is convenient to implement and numerically very stable, it only produces local solutions. Thus, it may not achieve the globally optimal solution in problems that have a large number of local optima. This paper introduces several new algorithms designed to produce global solutions in model-based clustering. The building blocks for these algorithms are methods from the operations research literature, namely the Cross-Entropy (CE) method and Model Reference Adaptive Search (MRAS). One problem with applying these methods directly is the efficient simulation of positive definite covariance matrices. We propose several new solutions to this problem. One solution is to apply the principles of Expectation-Maximization updating, which leads to two new algorithms, CE-EM and MRAS-EM. We also propose two additional algorithms, CE-CD and MRAS-CD, which rely on the Cholesky decomposition. We conduct numerical experiments of varying complexity to evaluate the effectiveness of the proposed algorithms in comparison to classical EM. We find that although a single run of the new algorithms is slower than a single run of EM, all have the potential for producing significantly better solutions. We also find that although repeat application of EM may achieve similar results, our algorithms provide automated, data-driven decision rules which may significantly reduce the burden of searching for the global optimum.     

Sorting by Short Block-Moves

Sorting permutations by operations such as reversals and block-moves has received much interest because of its applications in the study of genome rearrangements and in the design of interconnection networks. A short block-move is an operation on a permutation that moves an element at most two positions away from its original position. This paper investigates the problem of finding a minimum-length sorting sequence of short block-moves for a given permutation. A 4/3 -approximation algorithm for this problem is presented. Woven double-strip permutations are defined and a polynomial-time algorithm for this class of permutations is devised that employs graph matching techniques. A linear-time maximum matching algorithm for a special class of grid graphs improves the time complexity of the algorithm for woven double-strip permutations. Received June 1, 1997; revised July 25, 1998.     

How Will We Interact with the Web of Data?

The Web is currently evolving from an information space of linked documents, to a Web of linked, machine-readable data. Perhaps counter-intuitively, this shift to publishing data for machine consumption raises many challenges for human-computer interaction. In this article I will discuss some of the implications of this trend for how we interact with the Web of data and consider how familiar tools such as the Web browser may need to develop.     

Collaborative Semantic Authoring

In the context of the semantic Web, notions of collaboration, interoperability, and reuse are intrinsically interrelated: interoperability implies reuse, which in turn is a form of collaboration. If we adopt this viewpoint, the semantic Web becomes essentially a medium for knowledge exchange, in which the knowledge produced by one agent is consumed by another agent, possibly to create new knowledge. A collaboration-centric perspective on the semantic Web introduces both challenges and interesting research directions. Clearly, it's no longer desirable that the process of authoring semantic content necessarily take place in a room full of experts and ontologists. Indeed, as we move from classic Web 2.0 technologies to scenarios in which semantic content is created, our technologies need to change so that it becomes possible to create and exchange knowledge transparently, in accordance with the medium's openness and the knowledge producers' various goals and skill levels. In this article, we examine three modalities for collaborative semantic authoring based on selecting and reusing external, open semantic resources. These three ways of creating semantic content correspond to three levels of interaction between the user and the created resources. We illustrate each level by describing a tool we designed in the context of our research on semantic Web applications at the Knowledge Media Institute.     

Factorization of multipliers in passivity and IQC analysis

Multipliers are often used to find conditions for the absolute stability of Lur’e systems. They can be used either in conjunction with passivity theory or within the more recent framework of integral quadratic constraints (IQCs). We compare the use of multipliers in both approaches. Passivity theory requires that the multipliers have a canonical factorization and it has been suggested in the literature that this represents an advantage of the IQC theory. We consider sufficient conditions on the nonlinearity class for the associated multipliers to have a canonical factorization.     

Preoperative radiotherapy for adenocarcinoma of the rectosigmoid

Ninety-seven patients with adenocarcinoma of the rectosigmoid have been treated with high dose (5000-6000 rad) preoperative irradiation from 1960 through 1972 at the University of Oregon Health Sciences Center. Fifty-seven were initially clinically resectable and 40 were initially inoperable. Forty of the 57 initially clinically resectable patients had "curative" resections and are at risk for more than 5 years. An increase in 5-year survival (from 38% to 53%) and an absence of pelvic recurrence have occurred in those patients receiving preoperative irradiation and "curative" resection. Four of the 40 initially inoperable patients are alive without tumor. Three of the four survivors had irradiation and surgery; one had irradiation only. An additional four patients had no evidence of tumor at death. Tumor was totally sterilized by irradiation and nine patients and reduced to microfocal extent in an additional three of the 97 patients. Incidence of complications was no greater than has been reported in a surgical series from the same institution.     

Channel Adaptive Quantization for Limited Feedback MIMO Beamforming Systems

Multiple-input multiple-output (MIMO) wireless systems can achieve significant diversity and array gain by using transmit beamforming and receive combining techniques. In the absence of full channel knowledge at the transmitter, the transmit beamforming vector can be quantized at the receiver and sent to the transmitter using a low-rate feedback channel. In the literature, quantization algorithms for the beamforming vector are designed and optimized for a particular channel distribution, commonly the uncorrelated Rayleigh distribution. When the channel is not uncorrelated Rayleigh, however, these quantization strategies result in a degradation of the receive signal-to-noise ratio (SNR). In this paper, switched codebook quantization is proposed where the codebook is dynamically chosen based on the channel distribution. The codebook adaptation enables the quantization to exploit the spatial and temporal correlation inherent in the channel. The convergence properties of the codebook selection algorithm are studied assuming a block-stationary model for the channel. In the case of a nonstationary channel, it is shown using simulations that the selected codebook tracks the distribution of the channel resulting in improvements in SNR. Simulation results show that in the case of correlated channels, the SNR performance of the link can be significantly improved by adaptation, compared with nonadaptive quantization strategies designed for uncorrelated Rayleigh-fading channels     

Edge-Packing in Planar Graphs

Maximum G Edge-Packing (EPack _G ) is the problem of finding the maximum number of edge-disjoint isomorphic copies of a fixed guest graph G in a host graph H . This paper investigates the computational complexity of edge-packing for planar guests and planar hosts. Edge-packing is solvable in polynomial time when both G and H are trees. Edge-packing is solvable in linear time when H is outerplanar and G is either a 3-cycle or a k -star (a graph isomorphic to K _1,k ). Edge-packing is NP-complete when H is planar and G is either a cycle or a tree with edges. A strategy for developing polynomial-time approximation algorithms for planar hosts is exemplified by a linear-time approximation algorithm that finds a k -star edge-packing of size at least half the optimal. Received May 1995, and in revised form November 1995, and in final form December 1997.     

Normalizing Behavior of Unsaturated Granular Pavement Materials

One of the important components of a flexible pavement structure is granular material layers. Unsaturated granular pavement materials (UGPMs) in these layers influence stresses and strains throughout the pavement structure, and have a large effect on asphalt concrete fatigue and pavement rutting (two of the primary failure mechanisms for flexible pavements). The behavior of UGPMs is dependent on water content, but this effect has been traditionally difficult to quantify using either empirical or mechanistic methods. This paper presents a practical mechanistic framework for determining the behavior of UGPMs within the range of water contents, densities, and stress states likely to be encountered under field conditions. Both soil suction and generated pore pressures are determined and compared to confinement under typical field loading conditions. The framework utilizes a simple soil suction model that has three density-independent parameters, and can be determined using conventional triaxial equipment that is available in many pavement engineering laboratories.