In deep-learning-based process monitoring, obtaining an effective feature representation is a critical step in constructing a reliable deep-learning monitoring model. Conventional deep-learning methods like stacked auto-encoders (SAEs) capture feature representation by minimizing the data reconstruction errors, which lack the expression of essential information and ultimately lead to degradation of the monitoring performance. To solve this problem, variational discriminative SAE (VDSAE) is proposed in this article. First, a variational generative discriminative structure is designed to obtain a reliable prelearned discriminator. Based on this new variational discriminator, the authenticity of the reconstructed data is evaluated as an important criterion for feature learning. Then, an SAE incorporating the prelearned discriminator is trained by both minimizing the reconstruction error and maximizing the data authenticity. In this way, the prelearned discriminator makes the network effectively capture the essential expression of the reconstructed data. The proposed approach enables SAE to learn a better feature representation owing to the excellent reconstruction performance. Finally, the feature representation and fault detection performance of VDSAE are verified in two cases. The results show that the average fault detection rates (FDRs) of the multiphase flow facility and the waste-water treatment process (WWTP) can be improved to 72% and 97%, respectively, compared with the other fault detection methods.

As a successful application of machine learning in remote sensing and natural language processing, image captioning of remote-sensing images has been promoted and developed. Remote sensing images are large in width, complex in features, and contain abundant information. It is a difficult task to extract available visual features based domain knowledge behind sufficiently and to utilize extracted feature for image captioning generation sufficiently. In order to overcome this difficulty, we propose a novel model based “encoder-decoder” framework, termed remote sensing image captioning with sequential attention and flexible word correlation (SA-FWC). In the encoder, we fuse features of different layers in VGG16 to extract global and local information. In the decoder, we propose sequential attention and flexible word correlation (SA-FWC) to utilize extracted visual information to generate accurate image captioning sufficiently. Specially, to utilize visual features from the encoding layer sufficiently, highlight important information and reduce redundant information, long short-term memory (LSTM) in SA-FWC is used for obtaining better feature representations. Feature fusion strategy and self-attention mechanism to utilize visual features sufficiently. Additionally, we provide a data augmentation strategy based minimal training sample pairs. In the experiments, four evaluation metrics are used to evaluate the experimental results, and the effects of various parameters on the experimental results are discussed. The experimental results (BELU-0.72, ROUGE-0.65, METEOR-0.37, and CIDEr-2.83) show that the proposed method is effective and outperforms other network structures.

Deep learning networks have achieved great success in many areas, such as in large-scale image processing. They usually need large computing resources and time and process easy and hard samples inefficiently in the same way. Another undesirable problem is that the network generally needs to be retrained to learn new incoming data. Efforts have been made to reduce the computing resources and realize incremental learning by adjusting architectures, such as scalable effort classifiers, multi-grained cascade forest (gcForest), conditional deep learning (CDL), tree CNN, decision tree structure with knowledge transfer (ERDK), forest of decision trees with radial basis function (RBF) networks, and knowledge transfer (FDRK). In this article, a parallel multistage wide neural network (PMWNN) is presented. It is composed of multiple stages to classify different parts of data. First, a wide radial basis function (WRBF) network is designed to learn features efficiently in the wide direction. It can work on both vector and image instances and can be trained in one epoch using subsampling and least squares (LS). Second, successive stages of WRBF networks are combined to make up the PMWNN. Each stage focuses on the misclassified samples of the previous stage. It can stop growing at an early stage, and a stage can be added incrementally when new training data are acquired. Finally, the stages of the PMWNN can be tested in parallel, thus speeding up the testing process. To sum up, the proposed PMWNN network has the advantages of: 1) optimized computing resources; 2) incremental learning; and 3) parallel testing with stages. The experimental results with the MNIST data, a number of large hyperspectral remote sensing data, and different types of data in different application areas, including many image and nonimage datasets, show that the WRBF and PMWNN can work well on both image and nonimage data and have very competitive accuracy compared to learning models, such as stacked autoencoders, deep belief nets, support vector machine (SVM), multilayer perceptron (MLP), LeNet-5, RBF network, recently proposed CDL, broad learning, gcForest, ERDK, and FDRK.

Multidimensional embedding is a technique useful for characterizing spectral signature relations in hyperspectral images. However, such images consist of disjoint similar spectral classes that are spatially sensitive, thus presenting challenges to existing graph embedding tools. Robust parameter estimation is often difficult when the image pixels contain several hundreds of bands. In addition, finding a corresponding high-quality lower dimensional coordinate system to map signature relations remains an open research question. We answer positively on these challenges by first proposing a combined kernel function of spatial and spectral information in computing neighborhood graphs. We further adapt a force field intuition from mechanics to develop a unifying nonlinear graph embedding framework. The generalized framework leads to novel unsupervised multidimensional artificial field embedding techniques that rely on the simple additive assumption of pair-dependent attraction and repulsion functions. The formulations capture long-range- and short-range-distance-related effects often associated with living organisms and help to establish algorithmic properties that mimic mutual behavior for the purpose of dimensionality reduction. In its application, the framework reveals strong relations to existing embedding techniques, and also highlights sources of weaknesses in such techniques. As part of evaluation, visualization, gradient field trajectories, and semisupervised classification experiments are conducted for image scenes acquired by multiple sensors at various spatial resolutions over different types of objects. The results demonstrate the superiority of the proposed embedding framework over various widely used methods.

The extended space forest is a new method for decision tree construction in which training is done with input vectors including all the original features and their random combinations. The combinations are generated with a difference operator applied to random pairs of original features. The experimental results show that extended space versions of ensemble algorithms have better performance than the original ensemble algorithms. To investigate the success dynamics of the extended space forest, the individual accuracy and diversity creation powers of ensemble algorithms are compared. The Extended Space Forest creates more diversity when it uses all the input features than Bagging and Rotation Forest. It also results in more individual accuracy when it uses random selection of the features than Random Subspace and Random Forest methods. It needs more training time because of using more features than the original algorithms. But its testing time is lower than the others because it generates less complex base learners.

Graph embedding techniques are useful to characterize spectral signature relations for hyperspectral images. However, such images consists of disjoint classes due to spatial details that are often ignored by existing graph computing tools. Robust parameter estimation is a challenge for kernel functions that compute such graphs. Finding a corresponding high quality coordinate system to map signature relations remains an open research question. We answer positively on these challenges by proposing a kernel function of spatial and spectral information in computing neighborhood graphs. Furthermore, a multidimensional artificial field graph embedding technique that relies on simple additive assumptions of pair-dependent attraction and repulsion functions is proposed. High quality visualizations and improved classification performance demonstrate the benefits of the approach.

In hyperspectral imagery, low-dimensional representations are sought in order to explain well the nonlinear characteristics that are hidden in high-dimensional spectral channels. While many algorithms have been proposed for dimension reduction and manifold learning in Euclidean spaces, very few attempts have focused on non-Euclidean spaces. Here, we propose a novel approach that embeds hyperspectral data, transformed into bilateral probability similarities, onto a nonlinear unit norm coordinate system. By seeking a unitl2-norm nonlinear manifold, we encode similarity representations onto a space in which important regularities in data are easily captured. In its general application, the technique addresses problems related to dimension reduction and visualization of hyperspectral images. Unlike methods such as multidimensional scaling and spherical embeddings, which are based on the notion of pairwise distance computations, our approach is based on a stochastic objective function of spherical coordinates. This allows the use of an Exit probability distribution to discover the nonlinear characteristics that are inherent in hyperspectral data. In addition, the method directly learns the probability distribution over neighboring pixel maps while computing for the optimal embedding coordinates. As part of evaluation, classification experiments were conducted on the manifold spaces for hyperspectral data acquired by multiple sensors at various spatial resolutions over different types of land cover. Various visualization and classification comparisons to five existing techniques demonstrated the strength of the proposed approach while its algorithmic nature is guaranteed to converge to meaningful factors underlying the data.

As the number of feature increases, classification accuracy may decrease. Additionally, computational overload increases with a large number of features. For effective classification performance and shortened the training time, the redundant features should be eliminated before the classification process. In this paper, a new HDMR-based feature selection approach is presented, sorting the features with respect to their sensitivity coefficient calculated by HDMR sensitivity analysis. With the experiments conducted, the HDMR-based feature selection approach is competitive with sequential forward feature selection method and faster in terms of computational time, especially when dealing with datasets having a large number of features.

Classification of nonlinearly separable data by nonlinear support vector machines (SVMs) is often a difficult task, particularly due to the necessity of choosing a convenient kernel type. Moreover, in order to get the optimum classification performance with the nonlinear SVM, a kernel and its parameters should be determined in advance. In this paper, we propose a new classification method called support vector selection and adaptation (SVSA) which is applicable to both linearly and nonlinearly separable data without choosing any kernel type. The method consists of two steps: selection and adaptation. In the selection step, first, the support vectors are obtained by a linear SVM. Then, these support vectors are classified by using the$K$-nearest neighbor method, and some of them are rejected if they are misclassified. In the adaptation step, the remaining support vectors are iteratively adapted with respect to the training data to generate the reference vectors. Afterward, classification of the test data is carried out by 1-nearest neighbor with the reference vectors. The SVSA method was applied to some synthetic data, multisource Colorado data, post-earthquake remote sensing data, and hyperspectral data. The experimental results showed that the SVSA is competitive with the traditional SVM with both linearly and nonlinearly separable data.

A linear support vector machine (LSVM) is based on determining an optimum hyperplane that separates the data into two classes with the maximum margin. The LSVM typically has high classification accuracy for linearly separable data. However, for nonlinearly separable data, it usually has poor performance. For this type of data, the Support Vector Selection and Adaptation (SVSA) method was developed, but its classification accuracy is not very high for linearly separable data in comparison to LSVM. In this paper, we present a new classifier that combines the LSVM with the SVSA, to be called the Hybrid SVM and SVSA method (HSVSA), for classification of both linearly and nonlinearly separable data and remote sensing images as well. The experimental results show that the HSVSA has higher classification accuracy than the traditional LSVM, the nonlinear SVM (NSVM) with the radial basis kernel, and the previous SVSA.

In this paper, we propose a new machine learning algorithm that we named Support Vector Selection and Adaptation (SVSA). Our aim is to achieve the classification performance of the nonlinear support vector machines (SVM) by using only the support vectors of the linear SVM. The proposed method does not require any type of kernels, and requires less computation time compared to the nonlinear SVM. The SVSA algorithm has two steps: selection and adaptation. In the first step, some of the support vectors obtained from linear SVM are selected. Then the selected support vectors are adapted iteratively in the traning algorithm. The proposed method are compared against the linear and nonlinear SVM on sythetic and real remote sensing data. The results show that the proposed SVSA algorithm achieves very close performance to nonlinear SVM without any kernels in less computation time.

Establishment of the Kamal Ewida Earth Observatory (KEEO) has been funded by the North Atlantic Treaty Organization (NATO) Science for Peace Program. KEEO is a joint initiative of two of Egypt's largest and most venerable institutions of higher learning, Cairo University and Al Azhar University, both based in Cairo, Egypt, in collaboration with established environmental observatories in two NATO countries, Turkey and the USA. Specifically, the Egyptian partners, based in their Departments of Meteorology and Astronomy, Faculty of Science, at the two Egyptian Universities, are engaging in applications development, research and instructional collaboration with partnering resources from Bogaziçi University's Kandilli Observatory and Earthquake Research Institute (Istanbul, Turkey), with expertise in disaster mitigation, and Purdue University's Rosen Center for Advanced Computing's Purdue Terrestrial Observatory (West Lafayette, Indiana, USA), with expertise in real-time remote sensing and multi-disciplinary applications of satellite data. The KEEO project provides an interdisciplinary approach to effective disaster management and facilitates collaborative research and decision support, within the Egyptian context, for disaster mitigation.

A new family of algorithm called Cline that provides a number of methods to construct and use multivariate decision trees is presented. We report experimental results for two types of data: synthetic data to visualize the behavior of the algorithms and publicly available eight data sets. The new methods have been tested against 23 other decision-tree construction algorithms based on benchmark data sets. Empirical results indicate that our approach achieves better classification accuracy compared to other algorithms.

Information technology (IT) has been the driver of increased productivity in the manufacturing and service sectors, bringing real-time information to decision makers and process owners to improve process behavior and performance. Thus, organizations have invested heavily in training their employees to use IT in a disciplined, scientific way to make process improvements. This has spawned such popular initiatives as Six Sigma, yielding significant returns, but at considerable investment in training in statistical-analysis and decision-making tools. Can aspects of the decision-making process be automated, letting humans do what they do best (create, define, and measure) and machines (e.g., learning machines) do what they do best (analyze)? We propose an automated intelligent manufacturing system (AIMS) for analysis and decision making that mines real-time or historical data, and uses statistical and computational-intelligence algorithms to model and optimize enterprise processes. The algorithms employed involve a regression support vector machine (SVM) for model construction and a genetic algorithm (GA) for model optimization. Performance of AIMS was compared to Six-Sigma-trained teams employing statistical methodologies, such as design of experiments (DOE), to improve a simulated manufacturing operation, a three-stage TV-manufacturing process, where the objectives were to maximize yield, minimize cycle time and its variation, and minimize manufacturing costs, which were affected by conflicting defects and their causes. AIMS generally outperformed the teams on the above criteria, required relatively little data and time to train the SVM, and was easy to use. AIMS could serve as a productivity springboard for enterprises in existing and emergent technologies, such as nanotechnology and biotechnology/life sciences, where environment and miniaturization may make human monitoring and intervention difficult or infeasible.

Effective partitioning of the feature space for high classification accuracy with due attention to rare class members is often a difficult task. In this paper, the border vector detection and adaptation (BVDA) algorithm is proposed for this purpose. The BVDA consists of two parts. In the first part of the algorithm, some specially selected training samples are assigned as initial reference vectors called border vectors. In the second part of the algorithm, the border vectors are adapted by moving them toward the decision boundaries. At the end of the adaptation process, the border vectors are finalized. The method next uses the minimum distance to border vector rule for classification. In supervised learning, the training process should be unbiased to reach more accurate results in testing. In the BVDA, decision region borders are related to the initialization of the border vectors and the input ordering of the training samples. Consensus strategy can be applied with cross validation to reduce these dependencies. The performance of the BVDA and consensual BVDA were studied in comparison to other classification algorithms including neural network with backpropagation learning, support vector machines, and some statistical classification techniques.

Consensual and hierarchical approaches are developed for the classification of remotely sensed multispectral images. The proposed method consists of preprocessing of input patterns, generating multiple classification results by hierarchical neural networks, and a combining scheme to generate a consensus of multiple classification results. Transformations of input patterns by random matrices and nonlinear filtering are used for preprocessing. By varying the input patterns, the multiple classification results are generated with sufficiently independent errors by using a single type of classifier. This helps to improve classification performance when the multiple classification results are combined. Hierarchical neural networks involve the use of successive classifiers which are tuned to reduce the remaining errors to increase the classification performance. This structure includes detection schemes to decide whether successive classifiers are utilized for each input. Consensual and hierarchical approaches generate more reliable and accurate results based on group decision.

https://doi.org/10.1109/igarss.2005.1526650

A new learning system called a statistical self-organizing learning system (SSOLS), combining functional-link neural networks, statistical hypothesis testing, and self-organization of a number of enhancement nodes, is introduced for remote sensing applications. Its structure consists of two stages, a mapping stage and a learning stage. The input training vectors are initially mapped to the enhancement vectors in the mapping stage by multiplying with a random matrix, followed by pointwise nonlinear transformations. Starting with only one enhancement node, the enhancement layer incrementally adds an extra node in each iteration. The optimum dimension of the enhancement layer is determined by using an efficient leave-one-out cross-validation method. In this way, the number of enhancement nodes is also learned automatically. A t-test algorithm can also be applied to the mapping stage to mitigate the effect of overfitting and to further reduce the number of enhancement nodes required, resulting in a more compact network. In the learning stage, both the input vectors and the enhancement vectors are fed into a least squares learning module to obtain the estimated output vectors. This is made possible by choosing the output layer linear. In addition, several SSOLSs can be trained independently in parallel to form a consensual SSOLS, whose final output is a linear combination of the outputs of each SSOLS module. The SSOLS is simple, fast to compute, and suitable for remote sensing applications, especially with hyperspectral image data of high dimensionality.

Feature extraction of SAR data based on eigenvector of texture samples tries to find the principle components of the distribution of training sets. These eigenvectors can be considered as a set of features, which together characterize the variations between training samples for each class. Defining covariance matrix is also an important issue to achieve significant classification accuracy. In this study, classification is performed based on eigenvector of textures and gray level cooccurrence matrix. Both statistical based decision rules and neural networks are applied as a classifier to test the performance of the feature extraction method based on eigenvector of texture samples and cooccurrence matrix.

The recent results of multiple antennas show that a substantial capacity improvement can be achieved. In particular, space-time spreading is a good example combining space-time coding and multiple antennas. To explore this, this paper proposes a multivariable DFE (decision feedback equalizer) which performs ISI (intersymbol interference) rejection by multiple transmit and receive antennas. Different multiple channels and paths are assumed between different transmit and receive antennas. Using the expression of multivariable DFE in a MIMO (multi-input multi-output) channel, we investigate the performance of multivariable DFE according to the number of Tx and Rx antennas by the effective average SNR in the discrete-time multipath channels.

MOTIVATION: Many problems in molecular biology as well as other areas involve detection of rare events in unbalanced data. We develop two sample stratification schemes in conjunction with neural networks for rare event detection in such databases. Sample stratification is a technique for making each class in a sample have equal influence on decision making. The first scheme proposed stratifies a sample by adding up the weighted sum of the derivatives during the backward pass of training. The second scheme proposed uses a technique of modified bootstrap aggregating. After training neural networks with multiple sets of bootstrapped examples of the rare event classes and subsampled examples of common event classes, multiple voting for classification is performed. RESULTS: These two schemes make rare event classes have a better chance of being included in the sample used for training neural networks and thus improve the classification accuracy for rare event detection. The experimental performance of the two schemes using two sets of human DNA sequences as well as another set of Gaussian data indicates that proposed schemes have the potential of significantly improving accuracy of neural networks to recognize rare events.

A neural network architecture, the parallel self-organizing consensus neural net (PSCNN), is developed to improve performance and speed of such networks. The architecture has all the advantages of previous models such as self-organization and possesses new or superior characteristics such as input parallelism and decision making based on consensus. Due to the parallel properties of this network its parallel implementation on an N-cube machine was also studied. The architecture self organizes its modules to maximize performance. Since the system is completely parallel, both recall and learning procedures are very fast. The performance of the network was compared to backpropagation networks in problems of language perception remote sensing and binary logic (Exclusive-Or). PSCNN showed superior performance in all cases studied. In the research reported in the paper, we demonstrate and test the development of the PSCNN's architecture as well as its training rules. In addition, the performance of this new PSCNN system is compared to the performance of backpropagation models.

Statistical methods are preferred for reconstruction of images from projections when the signal-to-noise ratio is low or data is sparse. Likelihoods resulting from statistical formulation are usually nonlinear. Simultaneous iterative methods such as the conjugate gradient (CG), and point iterative methods such as Gauss-Seidel (GS) have been the most popular methods used for maximization of likelihoods. Simultaneous and point iterative methods are special cases of group iterative methods (GIM) with trivial block choices. It has been shown for similar problems that GIMs with nontrivial block choices may provide faster convergence, however, an optimal block selection rule has not been presented. We propose an optimal block-size selection method for GIMs, and demonstrate its usefulness on a positron emission tomography (PET) image reconstruction application.

Classification accuracy improvement of neural network classifiers using unlabeled testing data is presented. In order to increase the classification accuracy without increasing the number of training data, the network makes use of testing data along with training data for learning. It is shown that including the unlabled samples from underrepresented classes in the training set improves the classification accuracy of some of the classes during supervised-unsupervised learning.

A new type of a neural-network architecture, the parallel consensual neural network (PCNN), is introduced and applied in classification/data fusion of multisource remote sensing and geographic data. The PCNN architecture is based on statistical consensus theory and involves using stage neural networks with transformed input data. The input data are transformed several times and the different transformed data are used as if they were independent inputs. The independent inputs are first classified using the stage neural networks. The output responses from the stage networks are then weighted and combined to make a consensual decision. In this paper, optimization methods are used in order to weight the outputs from the stage networks. Two approaches are proposed to compute the data transforms for the PCNN, one for binary data and another for analog data. The analog approach uses wavelet packets. The experimental results obtained with the proposed approach show that the PCNN outperforms both a conjugate-gradient backpropagation neural network and conventional statistical methods in terms of overall classification accuracy of test data.

Direct Bayesian segmentation of PET emission images gives more satisfactory results compared to the segmentation methods relying only on reconstructions by CBP or deterministic iterative methods, when the data is sparse and noisy. The objective function for Bayesian segmentation is nonconvex and nondifferentiable. Therefore, gradient based techniques cannot be used. A Gauss-Seidel type method has been proposed before. In this paper, we propose a block-iterative approach which finds a higher maximum of the likelihood function than other techniques with local search strategy.

Parallel, self-organizing, hierarchical neural networks (PSHNN's) are multistage networks in which stages operate in parallel rather than in series during testing. Each stage can be any particular type of network. Previous PSHNN's assume quantized, say, binary outputs. A new type of PSHNN is discussed such that the outputs are allowed to be continuous-valued. The performance of the resulting networks is tested in the problem of predicting speech signal samples from past samples. Three types of networks in which the stages are learned by the delta rule, sequential least-squares, and the backpropagation (BP) algorithm, respectively, are described. In all cases studied, the new networks achieve better performance than linear prediction. A revised BP algorithm is discussed for learning input nonlinearities. When the BP algorithm is to be used, better performance is achieved when a single BP network is replaced by a PSHNN of equal complexity in which each stage is a BP network of smaller complexity than the single BP network.

The PNS module is discussed as the building block for the synthesis of parallel, self-organizing, hierarchical, neural networks (PSHNN). The P- and NS-units are fractile in nature, meaning that each such unit may itself consist of a number of parallel PNS modules. Through a mechanism of statistical acceptance or rejection of input vectors for classification, the sample space is divided into a number of subspaces. The input vectors belonging to each subspace are classified by a dedicated set of PNS modules. This strategy results in considerably higher accuracy of classification and better generalization as compared to previous neural network models.>

Major continuous-time, discrete-time, and discrete Fourier-related transforms as well as Fourier-related series are discussed both with real and complex kernels. The complex Fourier transforms, Fourier series, cosine, sine, Hartley, Mellin, Laplace transforms, and z-transforms are covered on a comparative basis. Generalizations of the Fourier transform kernel lead to a number of novel transforms, in particular, special discrete cosine, discrete sine, and real discrete Fourier transforms, which have already found use in a number of applications. The fast algorithms for the real discrete Fourier transform provide a unified approach for the optimal fast computation of all discrete Fourier-related transforms. The short-time Fourier-related transforms are discussed for applications involving nonstationary signals. The one-dimensional transforms discussed are also extended to the two-dimensional transforms.>

The discrete cosine-III transform (DC3T) is the same as the discrete symmetric cosine transform (DSCT) with a specific preprocessing of input data. It has less computational complexity than the discrete cosine transform (DCT) in terms of multiplications. The DC3T is also related to the DCT by a weighting matrix. The performance of the DC3T is compared to the DCT when compression is performed by adaptive coding. Experimental results show that a significant improvement in visual performance and mean square reconstruction error can be achieved over what is possible with the DCT. The better performance is attributed to the weighting of the DCT coefficients, which is indirectly achieved at reduced computational cost.>

Adaptive multistage image transform coding is discussed, and an optimal method is introduced for bit allocation. The optimality is in the sense of minimizing the mean square reconstruction error with a given total number of bits and a given number of stages. The statistics of the coefficients in different stages and marginal analysis are used to optimise the division of the total number of bits among the stages. Experimental results indicate that, with two stages, more than 14% improvement for one class and more than 11% improvement for multiple classes are achieved in mean square reconstruction error over one-stage image transform coding. Higher improvements are achieved with three stages. The reconstructed images with multistage coding are subjectively preferable to the reconstructed images with one-stage coding.>

A new neural-network architecture called the parallel, self-organizing, hierarchical neural network (PSHNN) is presented. The new architecture involves a number of stages in which each stage can be a particular neural network (SNN). At the end of each stage, error detection is carried out, and a number of input vectors are rejected. Between two stages there is a nonlinear transformation of input vectors rejected by the previous stage. The new architecture has many desirable properties, such as optimized system complexity (in the sense of minimized self-organizing number of stages), high classification accuracy, minimized learning and recall times, and truly parallel architectures in which all stages operate simultaneously without waiting for data from other stages during testing. The experiments performed indicated the superiority of the new architecture over multilayered networks with back-propagation training.

Two neural network architectures involving nonlinear spectral transformations are described. The first architecture involves generalization of nonlinear matched-filtering techniques, yielding a network that is very fast in learning and recall as well as highly accurate in classification. The second architecture is hierarchical with a number of stages; after each stage, error detection is carried out, followed by nonlinear spectral transformations when the error measure is above threshold.>

Fast algorithms for the computation of the real discrete Fourier transform (RDFT) are discussed. Implementations based on the RDFT are always efficient, whereas the implementations based on the DFT are efficient only when signals to be processed are complex. The fast real Fourier transform (FRFT) algorithms discussed are the radix-2 decimation-in-time (DIT), the radix-4 DIT, the split-radix DIT, the split-radix DIF, the prime factor, and the Winograd FRFT algorithm.>

Speaker and phoneme recognition is investigated based on the discrete rectangular wave transform (DRWT). The DRWT is one of the discrete Fourier preprocessing transforms (DFPTs) which corresponds to the first stage in two-stage algorithms to represent discrete trigonometric transforms such as the discrete Fourier transform (DFT). The DRWT is much faster and easier to implement than the DFT. The recognition experiments performed also show that performance of recognition based on DRWT speech spectrograms is comparable to the performance of recognition based on DFT speech spectrograms.>

A new approach is developed for the fast computation and VLSI implementation of all discrete trigonometric transforms in the least number of operations and pipelining stages. This is achieved in terms of the fast algorithm (FRFT) for the real discrete Fourier transform. FRFT is based upon Givens' plane rotation as the basic unit of computation in contrast to FFT's which are based upon the complex butterfly.

Semisystolic array implementation of circular and linear convolutions in one and multidimensions are discussed. The common feature of the various architectures studied is the broadcasting of the input sequence to the cells of the array. In the case of circular convolutions, there is also circular communication between the cells. A circular convolution of period N can be calculated in N time steps whereas the response time for the computation of N outputs of linear convolution with finite weight and data vectors is also N time steps without initial delay.