Speeding up the EM algorithm for mixture model-based segmentation of magnetic resonance images

Mixture models implemented via the expectation-maximization (EM) algorithm are being increasingly used in a wide range of problems in pattern recognition such as image segmentation. However, the EM algorithm requires considerable computational time in its application to huge data sets such as a three-dimensional magnetic resonance (MR) image of over 10 million voxels. Recently, it was shown that a sparse, incremental version of the EM algorithm could improve its rate of convergence. In this paper, we show how this modified EM algorithm can be speeded up further by adopting a multiresolution kd-tree structure in performing the E-step. The proposed algorithm outperforms some other variants of the EM algorithm for segmenting MR images of the human brain. (C) 2004 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.

An Incremental EM-based Learning Approach for On-Line Prediction of Hospital Resource Utilization

Objective: Inpatient length of stay (LOS) is an important measure of hospital activity, health care resource consumption, and patient acuity. This research work aims at developing an incremental expectation maximization (EM) based learning approach on mixture of experts (ME) system for on-line prediction of LOS. The use of a batchmode learning process in most existing artificial neural networks to predict LOS is unrealistic, as the data become available over time and their pattern change dynamically. In contrast, an on-line process is capable of providing an output whenever a new datum becomes available. This on-the-spot information is therefore more useful and practical for making decisions, especially when one deals with a tremendous amount of data. Methods and material: The proposed approach is illustrated using a real example of gastroenteritis LOS data. The data set was extracted from a retrospective cohort study on all infants born in 1995-1997 and their subsequent admissions for gastroenteritis. The total number of admissions in this data set was n = 692. Linked hospitalization records of the cohort were retrieved retrospectively to derive the outcome measure, patient demographics, and associated co-morbidities information. A comparative study of the incremental learning and the batch-mode learning algorithms is considered. The performances of the learning algorithms are compared based on the mean absolute difference (MAD) between the predictions and the actual LOS, and the proportion of predictions with MAD < 1 day (Prop(MAD < 1)). The significance of the comparison is assessed through a regression analysis. Results: The incremental learning algorithm provides better on-line prediction of LOS when the system has gained sufficient training from more examples (MAD = 1.77 days and Prop(MAD < 1) = 54.3%), compared to that using the batch-mode learning. The regression analysis indicates a significant decrease of MAD (p-value = 0.063) and a significant (p-value = 0.044) increase of Prop(MAD

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.

An augmented Lanczos algorithm for the efficient computation of a dot-product of a function of a large sparse symmetric matrix

The Lanczos algorithm is appreciated in many situations due to its speed. and economy of storage. However, the advantage that the Lanczos basis vectors need not be kept is lost when the algorithm is used to compute the action of a matrix function on a vector. Either the basis vectors need to be kept, or the Lanczos process needs to be applied twice. In this study we describe an augmented Lanczos algorithm to compute a dot product relative to a function of a large sparse symmetric matrix, without keeping the basis vectors.

Incremental parsing in language-based editors: user needs and how to meet them

Incremental parsing has long been recognized as a technique of great utility in the construction of language-based editors, and correspondingly, the area currently enjoys a mature theory. Unfortunately, many practical considerations have been largely overlooked in previously published algorithms. Many user requirements for an editing system necessarily impact on the design of its incremental parser, but most approaches focus only on one: response time. This paper details an incremental parser based on LR parsing techniques and designed for use in a modeless syntax recognition editor. The nature of this editor places significant demands on the structure and quality of the document representation it uses, and hence, on the parser. The strategy presented here is novel in that both the parser and the representation it constructs are tolerant of the inevitable and frequent syntax errors that arise during editing. This is achieved by a method that differs from conventional error repair techniques, and that is more appropriate for use in an interactive context. Furthermore, the parser aims to minimize disturbance to this representation, not only to ensure other system components can operate incrementally, but also to avoid unfortunate consequences for certain user-oriented services. The algorithm is augmented with a limited form of predictive tree-building, and a technique is presented for the determination of valid symbols for menu-based insertion. Copyright (C) 2001 John Wiley & Sons, Ltd.

QRT: A Qr-based tridiagonalization algorithm for nonsymmetric matrices

The stable similarity reduction of a nonsymmetric square matrix to tridiagonal form has been a long-standing problem in numerical linear algebra. The biorthogonal Lanczos process is in principle a candidate method for this task, but in practice it is confined to sparse matrices and is restarted periodically because roundoff errors affect its three-term recurrence scheme and degrade the biorthogonality after a few steps. This adds to its vulnerability to serious breakdowns or near-breakdowns, the handling of which involves recovery strategies such as the look-ahead technique, which needs a careful implementation to produce a block-tridiagonal form with unpredictable block sizes. Other candidate methods, geared generally towards full matrices, rely on elementary similarity transformations that are prone to numerical instabilities. Such concomitant difficulties have hampered finding a satisfactory solution to the problem for either sparse or full matrices. This study focuses primarily on full matrices. After outlining earlier tridiagonalization algorithms from within a general framework, we present a new elimination technique combining orthogonal similarity transformations that are stable. We also discuss heuristics to circumvent breakdowns. Applications of this study include eigenvalue calculation and the approximation of matrix functions.

Enhanced detection-guided NLMS estimation of sparse FIR-modeled signal channels

In various signal-channel-estimation problems, the channel being estimated may be well approximated by a discrete finite impulse response (FIR) model with sparsely separated active or nonzero taps. A common approach to estimating such channels involves a discrete normalized least-mean-square (NLMS) adaptive FIR filter, every tap of which is adapted at each sample interval. Such an approach suffers from slow convergence rates and poor tracking when the required FIR filter is "long." Recently, NLMS-based algorithms have been proposed that employ least-squares-based structural detection techniques to exploit possible sparse channel structure and subsequently provide improved estimation performance. However, these algorithms perform poorly when there is a large dynamic range amongst the active taps. In this paper, we propose two modifications to the previous algorithms, which essentially remove this limitation. The modifications also significantly improve the applicability of the detection technique to structurally time varying channels. Importantly, for sparse channels, the computational cost of the newly proposed detection-guided NLMS estimator is only marginally greater than that of the standard NLMS estimator. Simulations demonstrate the favourable performance of the newly proposed algorithm. © 2006 IEEE.

Incremental learning for interactive e-mail filtering

In this article, we propose a framework, namely, Prediction-Learning-Distillation (PLD) for interactive document classification and distilling misclassified documents. Whenever a user points out misclassified documents, the PLD learns from the mistakes and identifies the same mistakes from all other classified documents. The PLD then enforces this learning for future classifications. If the classifier fails to accept relevant documents or reject irrelevant documents on certain categories, then PLD will assign those documents as new positive/negative training instances. The classifier can then strengthen its weakness by learning from these new training instances. Our experiments’ results have demonstrated that the proposed algorithm can learn from user-identified misclassified documents, and then distil the rest successfully.

Incremental derivation of abstraction relations for data refinements

Data refinements are refinement steps in which a program’s local data structures are changed. Data refinement proof obligations require the software designer to find an abstraction relation that relates the states of the original and new program. In this paper we describe an algorithm that helps a designer find an abstraction relation for a proposed refinement. Given sufficient time and space, the algorithm can find a minimal abstraction relation, and thus show that the refinement holds. As it executes, the algorithm displays mappings that cannot be in any abstraction relation. When the algorithm is not given sufficient resources to terminate, these mappings can help the designer find a suitable abstraction relation. The same algorithm can be used to test an abstraction relation supplied by the designer.

An improved seeded region growing algorithm

Recently Adams and Bischof (1994) proposed a novel region growing algorithm for segmenting intensity images. The inputs to the algorithm are the intensity image and a set of seeds - individual points or connected components - that identify the individual regions to be segmented. The algorithm grows these seed regions until all of the image pixels have been assimilated. Unfortunately the algorithm is inherently dependent on the order of pixel processing. This means, for example, that raster order processing and anti-raster order processing do not, in general, lead to the same tessellation. In this paper we propose an improved seeded region growing algorithm that retains the advantages of the Adams and Bischof algorithm fast execution, robust segmentation, and no tuning parameters - but is pixel order independent. (C) 1997 Elsevier Science B.V.

Prediction of MHC class II-binding peptides using an evolutionary algorithm and artificial neural network

Motivation: Prediction methods for identifying binding peptides could minimize the number of peptides required to be synthesized and assayed, and thereby facilitate the identification of potential T-cell epitopes. We developed a bioinformatic method for the prediction of peptide binding to MHC class II molecules. Results: Experimental binding data and expert knowledge of anchor positions and binding motifs were combined with an evolutionary algorithm (EA) and an artificial neural network (ANN): binding data extraction --> peptide alignment --> ANN training and classification. This method, termed PERUN, was implemented for the prediction of peptides that bind to HLA-DR4(B1*0401). The respective positive predictive values of PERUN predictions of high-, moderate-, low- and zero-affinity binder-a were assessed as 0.8, 0.7, 0.5 and 0.8 by cross-validation, and 1.0, 0.8, 0.3 and 0.7 by experimental binding. This illustrates the synergy between experimentation and computer modeling, and its application to the identification of potential immunotheraaeutic peptides.

A numerical study of large sparse matrix exponentials arising in Markov chains

Krylov subspace techniques have been shown to yield robust methods for the numerical computation of large sparse matrix exponentials and especially the transient solutions of Markov Chains. The attractiveness of these methods results from the fact that they allow us to compute the action of a matrix exponential operator on an operand vector without having to compute, explicitly, the matrix exponential in isolation. In this paper we compare a Krylov-based method with some of the current approaches used for computing transient solutions of Markov chains. After a brief synthesis of the features of the methods used, wide-ranging numerical comparisons are performed on a power challenge array supercomputer on three different models. (C) 1999 Elsevier Science B.V. All rights reserved.AMS Classification: 65F99; 65L05; 65U05.

A consistent point-searching algorithm for solution interpolation in unstructured meshes consisting of 4-node bilinear quadrilateral elements

To translate and transfer solution data between two totally different meshes (i.e. mesh 1 and mesh 2), a consistent point-searching algorithm for solution interpolation in unstructured meshes consisting of 4-node bilinear quadrilateral elements is presented in this paper. The proposed algorithm has the following significant advantages: (1) The use of a point-searching strategy allows a point in one mesh to be accurately related to an element (containing this point) in another mesh. Thus, to translate/transfer the solution of any particular point from mesh 2 td mesh 1, only one element in mesh 2 needs to be inversely mapped. This certainly minimizes the number of elements, to which the inverse mapping is applied. In this regard, the present algorithm is very effective and efficient. (2) Analytical solutions to the local co ordinates of any point in a four-node quadrilateral element, which are derived in a rigorous mathematical manner in the context of this paper, make it possible to carry out an inverse mapping process very effectively and efficiently. (3) The use of consistent interpolation enables the interpolated solution to be compatible with an original solution and, therefore guarantees the interpolated solution of extremely high accuracy. After the mathematical formulations of the algorithm are presented, the algorithm is tested and validated through a challenging problem. The related results from the test problem have demonstrated the generality, accuracy, effectiveness, efficiency and robustness of the proposed consistent point-searching algorithm. Copyright (C) 1999 John Wiley & Sons, Ltd.