Hidden Layer Nodes Research Articles

Relating Formulation Variables to in Vitro Dissolution Using an Artificial Neural Network

ABSTRACTThe purpose of this paper was to investigate the effect of several experimental variables on the ability of a neural network to predict in vitro dissolution rate as a function of product formulation changes. Neural network software was trained with sets of hypothetical and experimental data consisting of 4–15 formulations with known in vitro drug dissolution profiles and the ability of the trained model to recognize patterns was validated against similar formations not used to train the neural network. The effect of selected variables, e.g., number of hidden-layer nodes and iterations, as well as the use of replicate or mean data on the accuracy of the predictions was investigated. The importance of optimizing the number of hidden-layer nodes and iterations was demonstrated. The prediction error increased for validation data sets that were outside the range of the training data set. Accurate predictions were obtained with as few as four formulations in the training set, provided the formulations were carefully chosen, and the number of formulation variables were small. Also, limiting the validation set to one formulation was not sufficient to validate the neural network model. Increasing the size of the training set, or replication of the input and output data, also provided more accurate predictions. The neural network accurately predicted in vitro drug release provided the neural network variables were optimized, and the training and validation data sets were appropriately selected.

The impact of gender on car buyer satisfaction and loyalty: A neural network analysis

Women are becoming an increasing force in the car buyer market. Their pattern of car buying differs from that of men, and thus it is proposed that women's expectations of a car, and hence the determinants of satisfaction with car purchase, would differ from those of men. Consumer data, gathered from both male and female car buyers, is analysed, with the aim of investigating in detail the contribution of explanatory variables to degree of satisfaction with last car bought and brand loyalty relating to car purchase. A neural network is used for the analysis, with hidden layer nodes being labelled to represent respondents' less easily articulated attitudes or beliefs. The findings indeed reveal clear differences in attitudes between male and female buyers.

The Hypercube Separation algorithm: A fast and efficient algorithm for on-line handwritten character recognition

This paper introduces a new neural network training algorithm, Hypercube Separation (HCS) algorithm which is very fast and guaranteed to learn. HCS is a simple algorithm suitable for hardware implementation which classifies different input patterns presented to it through the formation of multiple hyperplanes. The performance of the HCS algorithm is compared to that of the Binary Synaptic Weights (BSW) algorithm and to the Backpropagation (BP) algorithm in solving the two spiral problem, which is an almost pathological problem for pattern separation. The HCS algorithm was able to successfully separate the input patterns, requiring three orders of magnitude less training time than the BP algorithm and one order of magnitude less hidden layer nodes than the BSW algorithm. We also present the application of HCS to on-line handwritten character recognition with good results, especially when the simple nature of the algorithm is taken into consideration.

Neural Networks for Readability Analysis

This article describes and reports on the performance of six related artificial neural networks that have been developed for the purpose of readability analysis. Two networks employ counts of linguistic variables that simulate a traditional regression-based approach to readability. The remaining networks determine readability from “visual snapshots” of text. Input text is transformed into a visual pattern representing activation levels for input level nodes and then “blurred” slightly in an effort to promote generalization. Each network included one hidden layer of nodes in addition to input and an output layers. Of the four snapshot readability systems, two are trained to produce grade equivalent output and two depict readability as a distribution of activation values across several grade levels. Results of preliminary trials indicate that the correlation between visual input systems and judgements by experts is low although, in at least one case, comparable to previous correlations reported between readability formulas and teacher judgement. A system using linguistic variables and numerical output correlated perfectly with a regression-based formula within the error tolerance established prior to training. The networks which produce output in the form of a readability distribution suggest a new way of reporting readability that may do greater justice to the concept of readability than traditional grade equivalent scores while, at the same time, addressing concerns that have been voiced about the illusory precision of readability formulas.

ARTIFICIAL NEURAL NETWORK BASED CLASSIFICATION OF MAMMOGRAPHIC MICROCALCIFICATIONS USING IMAGE STRUCTURE FEATURES

Mammography associated with clinical breast examination and breast self-examination is the only effective and viable method for mass breast screening. Most of the minimal breast cancers are detected by the presence of microcalcifications. It is however difficult to distinguish between benign and malignant microcalcifications associated with breast cancer. Most of the techniques used in the computerized analysis of mammographic microcalcifications segment the digitized grey-level image into regions representing microcalcifications. Since mammographic images usually suffer from poorly defined microcalcification features, the extraction of microcalcification features based on segmentation process is not reliable and accurate. We present a second-order grey-level histogram based feature extraction approach which does not require the segmentation of microcalcifications into binary regions to extract features to be used in classification. The image structure features, computed from the second-order grey-level histogram statistics, are used for classification of microcalcifications. Several image structure features were computed for 100 cases of “difficult to diagnose” microcalcification cases with known biopsy results. These features were analyzed in a correlation study which provided a set of five best image structure features. A feedforward backpropagation neural network was used to classify mammographic microcalcifications using the image structure features. Four networks were trained for different combinations of training and test cases, and number of nodes in hidden layers. False Positive (FP) and True Positive (TP) rates for microcalcification classification were computed to compare the performance of the trained networks. The results of the neural network based classification were compared with those obtained using multivariate Baye’s classifiers, and the k-nearest neighbor classifier. The neural network yielded good results for classification of “difficult-to-diagnose” micro-calcifications into benign and malignant categories using the selected image structure features.

Wave‐net: a multiresolution, hierarchical neural network with localized learning

AbstractA Wave‐Net is an artificial neural network with one hidden layer of nodes, whose basis functions are drawn from a family of orthonormal wavelets. The good localization characteristics of the basis functions, both in the input and frequency domains, allow hierarchical, multiresolution learning of input‐output maps from experimental data. Furthermore, Wave‐Nets allow explicit estimation for global and local prediction error‐bounds, and thus lend themselves to a rigorous and explicit design of the network. This article presents the mathematical framework for the development of Wave‐Nets and discusses the various aspects of their practical implementation. Computational complexity arguments prove that the training and adaptation efficiency of Wave‐Nets is at least an order of magnitude better than other networks. In addition, it presents two examples on the application of Wave‐Nets; (a) the prediction of a chaotic time‐series, representing population dynamics, and (b) the classification of experimental data for process fault diagnosis.

Some analytical solutions to the general approximation problem for feedforward neural networks

The general approximation problem of interest to the area of feedforward neural networks is stated. Solutions for some special cases are given, which include an upper bound on the number of nodes in hidden layer(s) and the weights for that configuration. Analytical solutions to the general feedforward neural network problem in one-dimensional cases requiring an infinite number of nodes are presented. The practical solutions (not requiring an infinite number of nodes) in one-dimensional cases are derived under piecewise constant approximations with constant width partitions, under piecewise constant approximations with variable width partitions, and under piecewise linear approximations using ramps instead of sigmoids. A four layer solution to the general feedforward neural network problem in the n-dimensional case is presented. A three layer solution to the general feedforward neural network problem in the n-dimensional case with piecewise constant approximation requires the use of the corner function as the activation function. The corner function, a special case of n dimensional sigmoid function, is found to have desirable characteristics, and can be used to approximate functions with much weaker requirements (only boundedness and piecewise continuity. ) Concave regions can be formed with a single layer of nodes with the corner function.

A code in the nodes

Four two-layer associative networks (one layer of hidden nodes) were trained to classify spectra extracted from naturally produced vowels of one talker, using the hack-propagation learning algorithm [Rumelhart et al., Nature 323, 533–536 (1986)]. The inputs to the networks were either LPC spectra or “perceptual” spectra, obtained by convolving the Bark-transformed spectrum with an asymmetric filter. The networks trained on LPC input classified test vowels more accurately than the networks trained on the perceptually based spectra. The networks' solutions were examined to determine (a) whether it was possible to characterize the features underlying the solutions and (b) whether the input spectral representation affected the nature of the solutions. Principal components analyses of the activation patterns of the hidden units showed that three dimensions accounted for over 80% of the variance for all networks. For networks trained on “perceptual” spectra, the first three dimensions were highly correlated with F2/F1 ratio, F3/F2 ratio, and F3, respectively. For LPC input, the first three dimensions correlated with F1, F3/F2 ratio, and F2/F1 ratio. Thus these networks classified the vowels using features related to the formant space.