Showing papers by "Michael K. Ng published in 2003"

Mathematical analysis of super-resolution methodology

Abstract: The attainment of super resolution (SR) from a sequence of degraded undersampled images could be viewed as reconstruction of the high-resolution (HR) image from a finite set of its projections on a sampling lattice. This can then be formulated as an optimization problem whose solution is obtained by minimizing a cost function. The approaches adopted and their analysis to solve the formulated optimization problem are crucial, The image acquisition scheme is important in the modeling of the degradation process. The need for model accuracy is undeniable in the attainment of SR along with the design of the algorithm whose robust implementation will produce the desired quality in the presence of model parameter uncertainty. To keep the presentation focused and of reasonable size, data acquisition with multisensors instead of, say a video camera is considered.

A Note on K-modes Clustering

Abstract: Recently, Chaturvedi, Green and Carroll (2001) presented a nonparametric approach to deriving clusters from categorical data using a new clustering procedure called K-modes. Huang (1998) proposed the K-modes clustering algorithm. In this note, we demonstrate the equivalence of the two K-modes procedures.

Kronecker Product Approximations for Image Restoration with Reflexive Boundary Conditions

Abstract: Many image processing applications require computing approximate solutions of very large, ill-conditioned linear systems. Physical assumptions of the imaging system usually dictate that the matrices in these linear systems have exploitable structure. The specific structure depends on (usually simplifying) assumptions of the physical model and other considerations such as boundary conditions. When reflexive (Neumann) boundary conditions are used, the coefficient matrix is a combination of Toeplitz and Hankel matrices. Kronecker products also occur, but this structure is not obvious from measured data. In this paper we discuss a scheme for computing a (possibly approximate) Kronecker product decomposition of structured matrices in image processing, which extends previous work by Kamm and Nagy [SIAM J. Matrix Anal. Appl., 22 (2000), pp. 155--172] to a wider class of image restoration problems.

A data cube model for prediction-based web prefetching

Abstract: Reducing the web latency is one of the primary concerns of Internet research. Web caching and web prefetching are two effective techniques to latency reduction. A primary method for intelligent prefetching is to rank potential web documents based on prediction models that are trained on the past web server and proxy server log data, and to prefetch the highly ranked objects. For this method to work well, the prediction model must be updated constantly, and different queries must be answered efficiently. In this paper we present a data-cube model to represent Web access sessions for data mining for supporting the prediction model construction. The cube model organizes session data into three dimensions. With the data cube in place, we apply efficient data mining algorithms for clustering and correlation analysis. As a result of the analysis, the web page clusters can then be used to guide the prefetching system. In this paper, we propose an integrated web-caching and web-prefetching model, where the issues of prefetching aggressiveness, replacement policy and increased network traffic are addressed together in an integrated framework. The core of our integrated solution is a prediction model based on statistical correlation between web objects. This model can be frequently updated by querying the data cube of web server logs. This integrated data cube and prediction based prefetching framework represents a first such effort in our knowledge.

Preconditioners for nonsymmetric block toeplitz-like-plus-diagonal linear systems

Abstract: We consider the system of linear equations Lu=f, where L is a nonsymmetric block Toeplitz-like-plus-diagonal matrix, which arises from the Sinc-Galerkin discretization of differential equations. Our main contribution is to construct effective preconditioners for this structured coefficient matrix and to derive tight bounds for eigenvalues of the preconditioned matrices. Moreover, we use numerical examples to show that the new preconditioners, when applied to the preconditioned GMRES method, are efficient for solving the system of linear equations.

A higher-order Markov model for the Newsboy's problem

Abstract: Markov models are commonly used in modelling many practical systems such as telecommunication systems, manufacturing systems and inventory systems However, higher-order Markov models are not commonly used in practice because of their huge number of states and parameters that lead to computational difficulties In this paper, we propose a higher-order Markov model whose number of states and parameters are linear with respect to the order of the model We also develop efficient estimation methods for the model parameters We then apply the model and method to solve the generalised Newsboy's problem Numerical examples with applications to production planning are given to illustrate the power of our proposed model

Block {ω}-circulant preconditioners¶for the systems of differential equations

Abstract: The numerical solution of large and sparse nonsymmetric linear systems of algebraic equations is usually the most time consuming part of time-step integrators for differential equations based on implicit formulas. Preconditioned Krylov subspace methods using Strang block circulant preconditioners have been employed to solve such linear systems. However, it has been observed that these block circulant preconditioners can be very ill-conditioned or singular even when the underlying nonpreconditioned matrix is well-conditioned. In this paper we propose the more general class of the block { ω }-circulant preconditioners. For the underlying problems, ω can be chosen so that the condition number of these preconditioners is much smaller than that of the Strang block circulant preconditioner (which belongs to the same class with ω =1) and the related iterations can converge very quickly.

Higher-Order Hidden Markov Models with Applications to DNA Sequences

Abstract: Hidden Markov models (HMMs) have been applied to many real-world applications. Very often HMMs only deal with the first order transition probability distribution among the hidden states. In this paper we develop higher-order HMMs. We study the evaluation of the probability of a sequence of observations based on higher-order HMMs and determination of a best sequence of model states.

A Superresolution Framework for fMRI Sequences and Its Impact on Resulting Activation Maps

Abstract: This paper investigates the benefits of using a superresolution approach for fMRI sequences in order to obtain high-quality activation maps based on low-resolution acquisitions. We propose a protocol to acquire low-resolution images, shifted in the slice direction, so that they can be used to generate superresolution images. Adopting a variational framework, the superresolution images are defiend as the minimizers of objective functions. We focus on edge preserving regularized objective functions because of their ability to preserve details and edges. We show that applying regularization only in the slice direction leads more pertinent solutions than 3-dimensional regularization. Moreover, it leads to a considerably easier optimization problem. The latter point is crucial since we have to process long fMRI sequences. The solutions—the sought high resoltion images—are calculated based on a half-quadratic reformulation of the objective function which allows fast minimization schemes to be implemented. Our acquisition protocol and processing technique are tested both on simulated and real functional MRI datasets.

Band-toeplitz preconditioned gmres iterations for time-dependent pdes ∗

Abstract: Nonsymmetric linear systems of algebraic equations which are small rank perturbations of block band-Toeplitz matrices from discretization of time-dependent PDEs are considered. With a combination of analytical and experimental results, we examine the convergence characteristics of the GMRES method with circulant-like block preconditioning for solving these systems.

Advances in Data Mining and Modeling

Abstract: Selected papers presented at the workshop: Advances in Data Mining and Modeling, Hong Kong, 27 – 28 June 2002

A highly-usable projected clustering algorithm for gene expression profiles

Abstract: Projected clustering has become a hot research topic due to its ability to cluster high-dimensional data. However, most existing projected clustering algorithms depend on some critical user parameters in determining the relevant attributes of each cluster. In case wrong parameter values are used, the clustering performance will be seriously degraded. Unfortunately, correct parameter values are rarely known in real datasets. In this paper, we propose a projected clustering algorithm that does not depend on user inputs in determining relevant attributes. It responds to the clustering status and adjusts the internal thresholds dynamically. From experimental results, our algorithm shows a much higher usability than the other projected clustering algorithms used in our comparison study. It also works well with a gene expression dataset for studying lymphoma. The high usability of the algorithm and the encouraging results suggest that projected clustering can be a practical tool for analyzing gene expression profiles.

A graph-based optimization algorithm for website topology using interesting association rules

Abstract: The Web serves as a global information service center that contains vast amount of data. The Website structure should be designed effectively so that users can efficiently find their information. The main contribution of this paper is to propose a graph-based optimization algorithm to modify Website topology using interesting association rules. The interestingness of an association rule A ⇒ B is defined based on the probability measure between two sets of Web pages A and B in the Website. If the probability measure between A and B is low (high), then the association rule A ⇒ B has high (low) interest. The hyperlinks in the Website can be modified to adapt user access patterns according to association rules with high interest. We present experimental results and demonstrate that our method is effective.

Deconvolution of positron annihilation coincidence Doppler broadening spectra using an iterative projected Newton method with non-negativity constraints

Abstract: A generalized least-square method with Tikonov–Miller regularization and non-negativity constraints has been developed for deconvoluting two-dimensional coincidence Doppler broadening spectroscopy (CDBS) spectra. A projected Newton algorithm is employed to solve the generalized least-square problem. The algorithm has been tested on Monte Carlo generated spectra to find the best regularization parameters for different simulated experimental conditions. Good retrieval of the underlying positron–electron momentum distributions in the low momentum region is demonstrated. The algorithm has been successfully used to deconvolute experimental CDBS data from aluminum.

A parallel tabu search heuristic for clustering data sets

Abstract: Clustering methods partition a set of objects into clusters such that objects in the same cluster are more similar to each other than objects in different clusters according to some defined criteria. In this paper, a parallel tabu search heuristic for solving this problem is developed and implemented on a cluster of PCs. We observe that parallelization does not affect the quality of clustering results, but provides a large saving of the computational times in practice.

Statistical models for time sequences data mining

Abstract: In this paper, we present an adaptive modelling technique for studying past behaviors of objects and predicting the near future events. Our approach is to define a sliding window (of different window sizes) over a time sequence and build autoregression models from subsequences in different windows. The models are representations of past behaviors of the sequence objects. We can use the AR coefficients as features to index subsequences to facilitate the query of subsequences with similar behaviors. We can use a clustering algorithm to group time sequences on their similarity in the feature space. We can also use the AR models for prediction within different windows. Our experiments show that the adaptive model can give better prediction than non-adaptive models.

Advances in Data Mining and Modeling: Hong Kong 27 - 28 June 2002

Abstract: Data Mining: Algorithms for Mining Frequent Sequences (B Kao & M-H Zhang) Cluster Analysis Using Unidimensional Scaling (P-L Leung et al.) From Associated Implication Networks to Intermarket Analysis (P C-W Tse & J-M Liu) Automating Technical Analysis (P L-H Yu et al.) Data Modeling: Learning Sunspot Series Dynamics by Recurrent Neural Networks (L-K Li) Bond Risk and Return in the SSE (L-Z Fan) Mining Loyal Customers: A Practical Use of the Repeat Buying Theory (H-P Lo et al.) and other papers.

Superresolution image reconstruction from blurred observations by multisensors

Abstract: Superresolution image reconstruction refers to obtaining an image at a resolution higher than that of the camera (sensor) used in recording the image. In this article, we present a joint minimization model with an objective function setup that comprises three terms: the data-fitting term (DFT), the regularization term for the reconstructed image, and the observed low-resolution images. An alternating minimization iterative algorithm is presented to reconstruct the image. We also analyze the alternating minimization iterative algorithm and show that it converges globally for H1-norm or total-variation regularization that are functional for the reconstructed image. Numeric examples are given to illustrate the effectiveness of the joint minimization model and the efficiency of the algorithm. © 2003 Wiley Periodicals, Inc. Int J Imaging Syst Technol 13, 153–160, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.10053

Super-resolution images from blurred observations

Abstract: In this paper, we present a technique for generating a high- resolution image from a blurred image sequence. The image sequence consists of decimated, blurred and noisy versions of the high- resolution image. The high-resolution image is modeled as a Markov random field, and a maximum a posteriori estimation technique is used for image restoration. A fast algorithm based on Fast Fourier Transforms (FFTs) is derived to solve the resulting linear system. Numerical examples are given to illustrate the effectiveness of the method.

Higher-order hidden Markov models with applications to DNA sequences

Abstract: Hidden Markov models (HMMs) have been applied to many real-world applications. Very often HMMs only deal with the first order transition probability distribution among the hidden states. In this paper we develop higher-order HMMs. We study the evaluation of the probability of a sequence of observations based on higher-order HMMs and determination of a best sequence of model states.