Submodular Optimization and Data Processing

Thesis (Ph.D.)--University of Washington, 2016-06

Full S matrix calculation via a single real-symmetric Lanczos recursion: The Lanczos artificial boundary inhomogeneity method

We present an efficient and robust method for the calculation of all S matrix elements (elastic, inelastic, and reactive) over an arbitrary energy range from a single real-symmetric Lanczos recursion. Our new method transforms the fundamental equations associated with Light's artificial boundary inhomogeneity approach [J. Chem. Phys. 102, 3262 (1995)] from the primary representation (original grid or basis representation of the Hamiltonian or its function) into a single tridiagonal Lanczos representation, thereby affording an iterative version of the original algorithm with greatly superior scaling properties. The method has important advantages over existing iterative quantum dynamical scattering methods: (a) the numerically intensive matrix propagation proceeds with real symmetric algebra, which is inherently more stable than its complex symmetric counterpart; (b) no complex absorbing potential or real damping operator is required, saving much of the exterior grid space which is commonly needed to support these operators and also removing the associated parameter dependence. Test calculations are presented for the collinear H+H-2 reaction, revealing excellent performance characteristics. (C) 2004 American Institute of Physics.

Processing of English words with fine acoustic contrasts and simple tones: A mismatch negativity study

The purpose of this study was to compare the robustness of the event-related potential (ERP) response, called the mismatch negativity (MMN), when elicited by simple tone stimuli (differing in frequency, duration, or intensity) and speech stimuli (CV nonword contrast /de:/ vs. /ge:/ and CV word contrast /deI/ vs. /geI/). The study was conducted using 30 young adult subjects (Groups A and B; n = 15 each). The speech stimuli were presented to Group A at a stimulus onset asynchrony (SOA) of 610 msec and to Group B at an SOA of 900 msec. The tone stimuli were presented to both groups at an SOA of 610 msec. MMN responses were elicited by the simple tone stimuli (66.7%-96.7% of subjects with MMN "present," or significantly different from zero, p < 0.05) but not the speech stimuli (10% subjects with MMN present for nonwords, 10% for words). The length of the SOA (610 msec or 900 msec) had no effect on the ability to obtain consistent MMN responses to the speech stimuli. The results indicated a lack of robust MMN elicited by speech stimuli with fine acoustic contrasts under carefully controlled methodological conditions. The implications of these results are discussed in relation to conflicting reports in the literature of speech-elicited MMNs, and the importance of appropriate methodological design in MMN studies investigating speech processing in normal and pathological populations.

A tutorial on the cross-entropy method

The cross-entropy (CE) method is a new generic approach to combinatorial and multi-extremal optimization and rare event simulation. The purpose of this tutorial is to give a gentle introduction to the CE method. We present the CE methodology, the basic algorithm and its modifications, and discuss applications in combinatorial optimization and machine learning. combinatorial optimization

Application of the cross-entropy method to the buffer allocation problem in a simulation-based environment

The buffer allocation problem (BAP) is a well-known difficult problem in the design of production lines. We present a stochastic algorithm for solving the BAP, based on the cross-entropy method, a new paradigm for stochastic optimization. The algorithm involves the following iterative steps: (a) the generation of buffer allocations according to a certain random mechanism, followed by (b) the modification of this mechanism on the basis of cross-entropy minimization. Through various numerical experiments we demonstrate the efficiency of the proposed algorithm and show that the method can quickly generate (near-)optimal buffer allocations for fairly large production lines.

Population-based continuous optimization, probabilistic modelling and mean shift

Evolutionary algorithms perform optimization using a population of sample solution points. An interesting development has been to view population-based optimization as the process of evolving an explicit, probabilistic model of the search space. This paper investigates a formal basis for continuous, population-based optimization in terms of a stochastic gradient descent on the Kullback-Leibler divergence between the model probability density and the objective function, represented as an unknown density of assumed form. This leads to an update rule that is related and compared with previous theoretical work, a continuous version of the population-based incremental learning algorithm, and the generalized mean shift clustering framework. Experimental results are presented that demonstrate the dynamics of the new algorithm on a set of simple test problems.

Seizure detection algorithm for neonates based on wave-sequence analysis

Objective: The description and evaluation of the performance of a new real-time seizure detection algorithm in the newborn infant. Methods: The algorithm includes parallel fragmentation of EEG signal into waves; wave-feature extraction and averaging; elementary, preliminary and final detection. The algorithm detects EEG waves with heightened regularity, using wave intervals, amplitudes and shapes. The performance of the algorithm was assessed with the use of event-based and liberal and conservative time-based approaches and compared with the performance of Gotman's and Liu's algorithms. Results: The algorithm was assessed on multi-channel EEG records of 55 neonates including 17 with seizures. The algorithm showed sensitivities ranging 83-95% with positive predictive values (PPV) 48-77%. There were 2.0 false positive detections per hour. In comparison, Gotman's algorithm (with 30 s gap-closing procedure) displayed sensitivities of 45-88% and PPV 29-56%; with 7.4 false positives per hour and Liu's algorithm displayed sensitivities of 96-99%, and PPV 10-25%; with 15.7 false positives per hour. Conclusions: The wave-sequence analysis based algorithm displayed higher sensitivity, higher PPV and a substantially lower level of false positives than two previously published algorithms. Significance: The proposed algorithm provides a basis for major improvements in neonatal seizure detection and monitoring. Published by Elsevier Ireland Ltd. on behalf of International Federation of Clinical Neurophysiology.

Biomechanics of the rostrum in crocodilians: A comparative analysis using finite-element modeling

This article reports the use of simple beam and finite-element models to investigate the relationship between rostral shape and biomechanical performance in living crocodilians under a range of loading conditions. Load cases corresponded to simple biting, lateral head shaking, and twist feeding behaviors. The six specimens were chosen to reflect, as far as possible, the full range of rostral shape in living crocodilians: a juvenile Caiman crocodilus, subadult Alligator mississippiensis and Crocodylus johnstoni, and adult Caiman crocodilus, Melanosuchus niger, and Paleosuchus palpebrosus. The simple beam models were generated using morphometric landmarks from each specimen. Three of the finite-element models, the A. mississippiensis, juvenile Caiman crocodilus, and the Crocodylus johnstoni, were based on CT scan data from respective specimens, but these data were not available for the other models and so these-the adult Caiman crocodilus, M. niger, and P. palpebrosus-were generated by morphing the juvenile Caiman crocodilus mesh with reference to three-dimensional linear distance measured from specimens. Comparison of the mechanical performance of the six finite-element models essentially matched results of the simple beam models: relatively tall skulls performed best under vertical loading and tall and wide skulls performed best under torsional loading. The widely held assumption that the platyrostral (dorsoventrally flattened) crocodilian skull is optimized for torsional loading was not supported by either simple beam theory models or finite-element modeling. Rather than being purely optimized against loads encountered while subduing and processing food, the shape of the crocodilian rostrum may be significantly affected by the hydrodynamic constraints of catching agile aquatic prey. This observation has important implications for our understanding of biomechanics in crocodilians and other aquatic reptiles.

Heuristic algorithm for computing reversal distance with multigene families via binary integer programming

Hannenhalli and Pevzner developed the first polynomial-time algorithm for the combinatorial problem of sorting of signed genomic data. Their algorithm solves the minimum number of reversals required for rearranging a genome to another when gene duplication is nonexisting. In this paper, we show how to extend the Hannenhalli-Pevzner approach to genomes with multigene families. We propose a new heuristic algorithm to compute the reversal distance between two genomes with multigene families via the concept of binary integer programming without removing gene duplicates. The experimental results on simulated and real biological data demonstrate that the proposed algorithm is able to find the reversal distance accurately. ©2005 IEEE

Improvements in the data partitioning approach for frequent itemsets mining

Frequent Itemsets mining is well explored for various data types, and its computational complexity is well understood. There are methods to deal effectively with computational problems. This paper shows another approach to further performance enhancements of frequent items sets computation. We have made a series of observations that led us to inventing data pre-processing methods such that the final step of the Partition algorithm, where a combination of all local candidate sets must be processed, is executed on substantially smaller input data. The paper shows results from several experiments that confirmed our general and formally presented observations.

Efficient spatial clustering algorithm using binary tree

In this paper we present an efficient k-Means clustering algorithm for two dimensional data. The proposed algorithm re-organizes dataset into a form of nested binary tree*. Data items are compared at each node with only two nearest means with respect to each dimension and assigned to the one that has the closer mean. The main intuition of our research is as follows: We build the nested binary tree. Then we scan the data in raster order by in-order traversal of the tree. Lastly we compare data item at each node to the only two nearest means to assign the value to the intendant cluster. In this way we are able to save the computational cost significantly by reducing the number of comparisons with means and also by the least use to Euclidian distance formula. Our results showed that our method can perform clustering operation much faster than the classical ones. © Springer-Verlag Berlin Heidelberg 2005

An empirical study of Hoelfding Racing for model selction in K-nearest neighbor classification

Racing algorithms have recently been proposed as a general-purpose method for performing model selection in machine teaming algorithms. In this paper, we present an empirical study of the Hoeffding racing algorithm for selecting the k parameter in a simple k-nearest neighbor classifier. Fifteen widely-used classification datasets from UCI are used and experiments conducted across different confidence levels for racing. The results reveal a significant amount of sensitivity of the k-nn classifier to its model parameter value. The Hoeffding racing algorithm also varies widely in its performance, in terms of the computational savings gained over an exhaustive evaluation. While in some cases the savings gained are quite small, the racing algorithm proved to be highly robust to the possibility of erroneously eliminating the optimal models. All results were strongly dependent on the datasets used.

An efficient algorithm for partitioning parameterized polygons into rectangles

In this paper, we propose an algorithm for partitioning parameterized orthogonal polygons into rectangles. The algorithm is based on the plane-sweep technique and can be used for partitioning polygons which contain holes. The input to the algorithm consists of the contour of a parameterized polygon to be partitioned and the constraints for those parameters which reside in the contour. The algorithm uses horizontal cuts only and generates a minimum number of rectangles whose union is the original orthogonal polygon. The proposed algorithm can be used as the basis to build corner stitching data structure for parameterized VLSI layouts and has been implemented in Java programming language. Copyright © 2010 ACM, Inc.

Towards a Modeling Environment for Earth Systems Simulations

The developments of models in Earth Sciences, e.g. for earthquake prediction and for the simulation of mantel convection, are fare from being finalized. Therefore there is a need for a modelling environment that allows scientist to implement and test new models in an easy but flexible way. After been verified, the models should be easy to apply within its scope, typically by setting input parameters through a GUI or web services. It should be possible to link certain parameters to external data sources, such as databases and other simulation codes. Moreover, as typically large-scale meshes have to be used to achieve appropriate resolutions, the computational efficiency of the underlying numerical methods is important. Conceptional this leads to a software system with three major layers: the application layer, the mathematical layer, and the numerical algorithm layer. The latter is implemented as a C/C++ library to solve a basic, computational intensive linear problem, such as a linear partial differential equation. The mathematical layer allows the model developer to define his model and to implement high level solution algorithms (e.g. Newton-Raphson scheme, Crank-Nicholson scheme) or choose these algorithms form an algorithm library. The kernels of the model are generic, typically linear, solvers provided through the numerical algorithm layer. Finally, to provide an easy-to-use application environment, a web interface is (semi-automatically) built to edit the XML input file for the modelling code. In the talk, we will discuss the advantages and disadvantages of this concept in more details. We will also present the modelling environment escript which is a prototype implementation toward such a software system in Python (see www.python.org). Key components of escript are the Data class and the PDE class. Objects of the Data class allow generating, holding, accessing, and manipulating data, in such a way that the actual, in the particular context best, representation is transparent to the user. They are also the key to establish connections with external data sources. PDE class objects are describing (linear) partial differential equation objects to be solved by a numerical library. The current implementation of escript has been linked to the finite element code Finley to solve general linear partial differential equations. We will give a few simple examples which will illustrate the usage escript. Moreover, we show the usage of escript together with Finley for the modelling of interacting fault systems and for the simulation of mantel convection.

Curvature-driven smoothing: a learning algorithm for feed-forward networks

The performance of feed-forward neural networks in real applications can be often be improved significantly if use is made of a-priori information. For interpolation problems this prior knowledge frequently includes smoothness requirements on the network mapping, and can be imposed by the addition to the error function of suitable regularization terms. The new error function, however, now depends on the derivatives of the network mapping, and so the standard back-propagation algorithm cannot be applied. In this paper, we derive a computationally efficient learning algorithm, for a feed-forward network of arbitrary topology, which can be used to minimize the new error function. Networks having a single hidden layer, for which the learning algorithm simplifies, are treated as a special case.