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Geometrical interpretation and architecture selection of MLP.

A geometrical interpretation of the multilayer perceptron (MLP) is suggested in this paper. Some general guidelines for selecting the architecture of the MLP, i.e., the number of the hidden neurons and the hidden layers, are proposed based upon this interpretation and the controversial issue of whether four-layered MLP is superior to the three-layered MLP is also carefully examined.

Algorithms↗

New adaptive color quantization method based on self-organizing maps.

Color quantization (CQ) is an image processing task popularly used to convert true color images to palletized images for limited color display devices. To minimize the contouring artifacts introduced by the reduction of colors, a new competitive learning (CL) based scheme called the frequency sensitive self-organizing maps (FS-SOMs) is proposed to optimize the color palette design for CQ. FS-SOM harmonically blends the neighborhood adaptation of the well-known self-organizing maps (SOMs) with the neuron dependent frequency sensitive learning model, the global butterfly permutation sequence for input randomization, and the reinitialization of dead neurons to harness effective utilization of neurons. The net effect is an improvement in adaptation, a well-ordered color palette, and the alleviation of underutilization problem, which is the main cause of visually perceivable artifacts of CQ. Extensive simulations have been performed to analyze and compare the learning behavior and performance of FS-SOM against other vector quantization (VQ) algorithms. The results show that the proposed FS-SOM outperforms classical CL, Linde, Buzo, and Gray (LBG), and SOM algorithms. More importantly, FS-SOM achieves its superiority in reconstruction quality and topological ordering with a much greater robustness against variations in network parameters than the current art SOM algorithm for CQ. A most significant bit (MSB) biased encoding scheme is also introduced to reduce the number of parallel processing units. By mapping the pixel values as sign-magnitude numbers and biasing the magnitudes according to their sign bits, eight lattice points in the color space are condensed into one common point density function. Consequently, the same processing element can be used to map several color clusters and the entire FS-SOM network can be substantially scaled down without severely scarifying the quality of the displayed image. The drawback of this encoding scheme is the additional storage overhead, which can be cut down by leveraging on existing encoder in an overall lossy compression scheme.

Algorithms↗

Rigorous proof of termination of SMO algorithm for support vector machines.

Sequential minimal optimization (SMO) algorithm is one of the simplest decomposition methods for learning of support vector machines (SVMs). Keerthi and Gilbert have recently studied the convergence property of SMO algorithm and given a proof that SMO algorithm always stops within a finite number of iterations. In this letter, we point out the incompleteness of their proof and give a more rigorous proof.

Algorithms↗

Accuracy/diversity and ensemble MLP classifier design.

The difficulties of tuning parameters of multilayer perceptrons (MLP) classifiers are well known. In this paper, a measure is described that is capable of predicting the number of classifier training epochs for achieving optimal performance in an ensemble of MLP classifiers. The measure is computed between pairs of patterns on the training data and is based on a spectral representation of a Boolean function. This representation characterizes the mapping from classifier decisions to target label and allows accuracy and diversity to be incorporated within a single measure. Results on many benchmark problems, including the Olivetti Research Laboratory (ORL) face database demonstrate that the measure is well correlated with base-classifier test error, and may be used to predict the optimal number of training epochs. While correlation with ensemble test error is not quite as strong, it is shown in this paper that the measure may be used to predict number of epochs for optimal ensemble performance. Although the technique is only applicable to two-class problems, it is extended here to multiclass through output coding. For the output-coding technique, a random code matrix is shown to give better performance than one-per-class code, even when the base classifier is well-tuned.

Algorithms↗

Global exponential stability of multitime scale competitive neural networks with nonsmooth functions.

In this paper, we study the global exponential stability of a multitime scale competitive neural network model with nonsmooth functions, which models a literally inhibited neural network with unsupervised Hebbian learning. The network has two types of state variables, one corresponds to the fast neural activity and another to the slow unsupervised modification of connection weights. Based on the nonsmooth analysis techniques, we prove the existence and uniqueness of equilibrium for the system and establish some new theoretical conditions ensuring global exponential stability of the unique equilibrium of the neural network. Numerical simulations are conducted to illustrate the effectiveness of the derived conditions in characterizing stability regions of the neural network.

Algorithms↗

Feature selection using a piecewise linear network.

We present an efficient feature selection algorithm for the general regression problem, which utilizes a piecewise linear orthonormal least squares (OLS) procedure. The algorithm 1) determines an appropriate piecewise linear network (PLN) model for the given data set, 2) applies the OLS procedure to the PLN model, and 3) searches for useful feature subsets using a floating search algorithm. The floating search prevents the "nesting effect." The proposed algorithm is computationally very efficient because only one data pass is required. Several examples are given to demonstrate the effectiveness of the proposed algorithm.

Algorithms↗

Multiperiodicity of discrete-time delayed neural networks evoked by periodic external inputs.

In this paper, the multiperiodicity of a general class of discrete-time delayed neural networks (DTDNNs) is formulated and studied. Several sufficient conditions are obtained to ensure n-neuron DTDNNs can have 2n periodic orbits and these periodic orbits are locally attractive. In addition, we give the conditions for a periodic orbit to be locally or globally attractive when the periodic orbit locates in a designated region. As two typical representatives, the Hopfield neural network and the cellular neural network are examined in detail. These conditions improve and extend the existing stability results in the literature. Simulations results are also discussed in three illustrative examples.

Algorithms↗

The hierarchical fair competition (HFC) framework for sustainable evolutionary algorithms.

Many current Evolutionary Algorithms (EAs) suffer from a tendency to converge prematurely or stagnate without progress for complex problems. This may be due to the loss of or failure to discover certain valuable genetic material or the loss of the capability to discover new genetic material before convergence has limited the algorithm's ability to search widely. In this paper, the Hierarchical Fair Competition (HFC) model, including several variants, is proposed as a generic framework for sustainable evolutionary search by transforming the convergent nature of the current EA framework into a non-convergent search process. That is, the structure of HFC does not allow the convergence of the population to the vicinity of any set of optimal or locally optimal solutions. The sustainable search capability of HFC is achieved by ensuring a continuous supply and the incorporation of genetic material in a hierarchical manner, and by culturing and maintaining, but continually renewing, populations of individuals of intermediate fitness levels. HFC employs an assembly-line structure in which subpopulations are hierarchically organized into different fitness levels, reducing the selection pressure within each subpopulation while maintaining the global selection pressure to help ensure the exploitation of the good genetic material found. Three EAs based on the HFC principle are tested - two on the even-10-parity genetic programming benchmark problem and a real-world analog circuit synthesis problem, and another on the HIFF genetic algorithm (GA) benchmark problem. The significant gain in robustness, scalability and efficiency by HFC, with little additional computing effort, and its tolerance of small population sizes, demonstrates its effectiveness on these problems and shows promise of its potential for improving other existing EAs for difficult problems. A paradigm shift from that of most EAs is proposed: rather than trying to escape from local optima or delay convergence at a local optimum, HFC allows the emergence of new optima continually in a bottom-up manner, maintaining low local selection pressure at all fitness levels, while fostering exploitation of high-fitness individuals through promotion to higher levels.

Algorithms↗

Medical image informatics infrastructure design and applications.

Picture archiving and communication systems (PACS) is a system integration of multimodality images and health information systems designed for improving the operation of a radiology department. As it evolves, PACS becomes a hospital image document management system with a voluminous image and related data file repository. A medical image informatics infrastructure can be designed to take advantage of existing data, providing PACS with add-on value for health care service, research, and education. A medical image informatics infrastructure (MIII) consists of the following components: medical images and associated data (including PACS database), image processing, data/knowledge base management, visualization, graphic user interface, communication networking, and application oriented software. This paper describes these components and their logical connection, and illustrates some applications based on the concept of the MIII.

Age Determination by Skeleton↗

A data mining approach for analyzing density maps representing macromolecular structures.

Results of electron microscopy-based three-dimensional reconstructions of macromolecules or their complexes are usually stored as density maps. Each point ("voxel") in the map represents a density value and one approach for studying details of the map is to display an isosurface enclosing areas of interest. We have taken a data mining approach not only focusing on the areas of immediate interest but determining all possible separate entities ("blobs") from a density map. After the entire density map is analyzed with our mining program BLOBBER, properties of all detected blobs can be browsed and sets of blobs can be visualized using our VIZBLOB program. Since BLOBBER analyzes density maps using only density information and relates it to spatial relationships, BLOBBER can be used to analyze symmetrical or asymmetrical density maps from any source. To test our program we have analyzed published bacteriophage PRD1 reconstructions. We identified various structural details ranging from individual proteins to major complexes such as the whole capsid shell and more elaborate details of possible connections between membrane interfaces. This approach can also be a useful preprocessing tool for visualizing reconstructions.

Bacteriophages↗

High-performance computing and networking as tools for accurate emission computed tomography reconstruction.

It is well known that the quantitative potential of emission computed tomography (ECT) relies on the ability to compensate for resolution, attenuation and scatter effects. Reconstruction algorithms which are able to take these effects into account are highly demanding in terms of computing resources. The reported work aimed to investigate the use of a parallel high-performance computing platform for ECT reconstruction taking into account an accurate model of the acquisition of single-photon emission tomographic (SPET) data. An iterative algorithm with an accurate model of the variable system response was ported on the MIMD (Multiple Instruction Multiple Data) parallel architecture of a 64-node Cray T3D massively parallel computer. The system was organized to make it easily accessible even from low-cost PC-based workstations through standard TCP/IP networking. A complete brain study of 30 (64x64) slices could be reconstructed from a set of 90 (64x64) projections with ten iterations of the conjugate gradients algorithm in 9 s, corresponding to an actual speed-up factor of 135. This work demonstrated the possibility of exploiting remote high-performance computing and networking resources from hospital sites by means of low-cost workstations using standard communication protocols without particular problems for routine use. The achievable speed-up factors allow the assessment of the clinical benefit of advanced reconstruction techniques which require a heavy computational burden for the compensation effects such as variable spatial resolution, scatter and attenuation. The possibility of using the same software on the same hardware platform with data acquired in different laboratories with various kinds of SPET instrumentation is appealing for software quality control and for the evaluation of the clinical impact of the reconstruction methods.

Algorithms↗

Toward a theory of evolutionary computation.

We outline a theory of evolutionary computation using a formal model of evolutionary computation--the Evolutionary Turing Machine--which is introduced as the extension of the Turing Machine model. Evolutionary Turing Machines provide a better and a more complete model for evolutionary computing than conventional Turing Machines, algorithms, and Markov chains. The convergence and convergence rate are defined and investigated in terms of this new model. The sufficient conditions needed for the completeness and optimality of evolutionary search are investigated. In particular, the notion of the total optimality as an instance of the multiobjective optimization of the Universal Evolutionary Turing Machine is introduced. This provides an automatic way to deal with the intractability of evolutionary search by optimizing the quality of solutions and search costs simultaneously. Based on a new model a very flexible classification of optimization problem hardness for the evolutionary techniques is proposed. The expressiveness of evolutionary computation is investigated. We show that the problem of the best evolutionary algorithm is undecidable independently of whether the fitness function is time dependent or fixed. It is demonstrated that the evolutionary computation paradigm is more expressive than Turing Machines, and thus the conventional computer science based on them. We show that an Evolutionary Turing Machine is able to solve nonalgorithmically the halting problem of the Universal Turing Machine and, asymptotically, the best evolutionary algorithm problem. In other words, the best evolutionary algorithm does not exist, but it can be potentially indefinitely approximated using evolutionary techniques.

Algorithms↗

Simultaneous parallel inclined readout image technique.

Sensitivity-encoded phase undersampling has been combined with simultaneous slice excitation to produce a parallel MRI method with a high volumetric acquisition acceleration factor without the need for auxiliary stepped field coils. Dual-slice excitation was produced by modulating both spin and gradient echo sequences at +/-6 kHz. Frequency aliasing of simultaneously excited slices was prevented by using an additional gradient applied along the slice axis during data acquisition. Data were acquired using a four-channel receiver array and x4 sensitivity encoding on a 1.5 T MR system. The simultaneous parallel inclined readout image technique has been successfully demonstrated in both phantoms and volunteers. A multiplicative image acquisition acceleration factor of up to x8 was achieved. Image SNR and resolution was dependent on the ratio of the readout gradient to the additional slice gradient. A ratio of approximately 2:1 produced acceptable image quality. Use of RF pulses with additional excitation bands should enable the technique to be extended to volumetric acquisition acceleration factors in the range of x16-24 without the SNR limitations of pure partially parallel phase reduction methods.

Algorithms↗

Quantization errors of the echoes in ultrasonic pulsed flowmeter employing time domain correlation.

The implementation of Time Domain Correlation Method for blood flow velocity estimation requires the conversion of the reflected ultrasonic signals into digital format in order that the computer can be utilized to investigate the technique. A number of quanitization errors, namely, that the A/D has a finite bit resolution, only a limited number of samples of the waveform may be taken per wavelength and correlation function only exits at discrete points, have an effect on the velocity estimate. This paper discusses the effect of errors associated with A/D conversion process on the accuracy of the velocity estimate. A computer simulation was performed to achieve this goal. A band passed white Gaussian noise segment was used to simulate the reflected ultrasonic signal. The jitters of the velocity estimates corresponding various A/D resolutions were calculated and plotted. Effects of interpolating the correlation function rather than determining the complete function were presented.

Algorithms↗

Inferring qualitative relations in genetic networks and metabolic pathways.

MOTIVATION: Inferring genetic network architecture from time series data of gene expression patterns is an important topic in bioinformatics. Although inference algorithms based on the Boolean network were proposed, the Boolean network was not sufficient as a model of a genetic network. RESULTS: First, a Boolean network model with noise is proposed, together with an inference algorithm for it. Next, a qualitative network model is proposed, in which regulation rules are represented as qualitative rules and embedded in the network structure. Algorithms are also presented for inferring qualitative relations from time series data. Then, an algorithm for inferring S-systems (synergistic and saturable systems) from time series data is presented, where S-systems are based on a particular kind of nonlinear differential equation and have been applied to the analysis of various biological systems. Theoretical results are shown for Boolean networks with noises and simple qualitative networks. Computational results are shown for Boolean networks with noises and S-systems, where real data are not used because the proposed models are still conceptual and the quantity and quality of currently available data are not enough for the application of the proposed methods.

Algorithms↗