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Sensitivity analysis in neural net solutions
Abstract
Neural networks have been shown to have promise for solving
certain types of optimization problems. A particular example is the
classic NP-complete problem of the traveling salesman (TSP) in which a
minimum distance tour of n cities is to be found. J.J. Hopfield
and D.W. Tank (1985) presented a simulation of a neural network that was
able to produce good, if not optimal, tours. However, little information
was given concerning the validity and quality of the network solutions
in general. In the present study, a more detailed analysis of the TSP
network is given. In particular, a sensitivity analysis is performed
with respect to the bias-input and intercity-distance contributions to
the network energy function. The results indicate that a statistical
approach is needed to specify the performance of the network.
Additionally, the behavior of the network is studied across a range in
numbers of cities (10 through 30). An analysis of TSPs for 10, 15, 20,
25 and 30 cities indicated that the practical maximum number of cities
that can be analyzed with the permutation-matrix network configuration
is about 50 cities
... If ρ k ≥ η 1 , then ∆ k+1 = γ 2 ∆ k and replace y − ∈ Y by x + = x k + s k , where y − is defined in (43). If ρ k < η 1 and the interpolation set Y is inadequate, then for every y i ∈ Y find y i pr by (18), y − by (17) and replace y − with a point y + in the trust-region to improve ∂(Y ) in (9). If ρ k < η 1 but the interpolation set Y is adequate, then ∆ k+1 = γ 1 ∆ k . ...
... If ρ k ≥ η 1 , then ∆ k+1 = γ 2 ∆ k and replace y − ∈ Y = S ∪ T by x + = x k + s k , where y − is defined in (43). If ρ k < η 1 and the interpolation set Y is inadequate, then for every y i ∈ Y find y i pr by (18), y − by (17) and replace y − with a point y + in the trust-region and sample more interpolation points, which means n w = ⌊θ 1 n w ⌋ and n b = ⌊θ ′ 1 n b ⌋. ...
In this paper (part 1), we describe a derivative-free trust-region method for solving unconstrained optimization problems. In this new approach, we use artificial neural-network to approximate a model of the objective function within the trust-region, and then through back-propagation, the sub-problem solution can be calculated.
... Beyond simply applying machine learning methods and assessing models using the confusion matrix, it's imperative to provide a detailed explanation of the model and validate its precision while considering potential biases and previously unrecognized patterns. Sensitivity analysis emerges as a potent instrument at this juncture, empowering researchers to quantify the correlation between input and output variables, pinpoint the key factors that substantially influence the model's predictive capacity, and validate its accuracy (Davis, 1989). In the realm of machine learning, sensitivity analysis can be perceived as an experimental procedure wherein each input variable is systematically eliminated from the model to assess the resulting effect on its predictive capabilities. ...
Vaccination is seen as the most promising one among the efforts to stop COVID-19 and the U.S. government has given great importance to vaccination. However, which states have performed well in administering COVID-19 vaccines and which have not is an open significant question. Another important question is what makes a state more successful than others when evaluating vaccination performance. To answer both of these questions, we proposed a hybrid method that consists of Data Envelopment Analysis and Ensemble ML Methods. DEA was employed to find the vaccine efficiency of the states using the data aggregated from counties. ML techniques are then applied for the vaccine efficiency prediction and understanding the significance of the variables in the prediction. Our findings revealed that there are considerable differences between U.S. States’ performance and only 16 of the states were efficient in terms of their vaccination performance. Furthermore, Light GBM, Random Forest and XGBoost models provided the best results among the five ensemble machine learning methods that were applied. Therefore, an information fusion-based sensitivity analysis method was used to combine the results of each ML technique and ascertain the relative significance of the factors in the prediction of the efficiency. As the findings for factors affecting vaccination performance, percentage of vaccine doses delivered and COVID-19 deaths were found to be the major influential factors on the prediction of the efficiency and percentage of fully vaccinated people, the number of healthcare employees and human development index followed these variables.
... Once a common structure and configuration were defined, a comparative analysis of these models was carried out. First, the contribution of each input to the model output was assessed using a sensitivity analysis [114,118,119]. The 5th, 25th, 50th, 75th and 95th percentiles were used to run the sensitivity analysis for each input, while fixing the rest on their means. ...
In the last decades, urban climate researchers have highlighted the need for a reliable provision of meteorological data in the local urban context. Several efforts have been made in this direction using Artificial Neural Networks (ANN), demonstrating that they are an accurate alternative to numerical approaches when modelling large time series. However, existing approaches are varied, and it is unclear how much data are needed to train them. This study explores whether the need for training data can be reduced without overly compromising model accuracy, and if model reliability can be increased by selecting the UHI intensity as the main model output instead of air temperature. These two approaches were compared using a common ANN configuration and under different data availability scenarios. Results show that reducing the training dataset from 12 to 9 or even 6 months would still produce reliable results, particularly if the UHI intensity is used. The latter proved to be more effective than the temperature approach under most training scenarios, with an average RMSE improvement of 16.4% when using only 3 months of data. These findings have important implications for urban climate research as they can potentially reduce the duration and cost of field measurement campaigns.
... As mentioned before, we cannot directly explain the learning process of classifiers in the 'black box'. In case that the overfitting issue occurs in this procedure, the sensitivity analysis is conducted to minimize this effect as well as test the algorithm robustness under uncertainty [53]. One of the conventional approaches of sensitivity analysis is moving input variables one-at-a-time and checking the impact of the rest of the input variables on the performance (one-vs-one method) [54]. ...
Machine learning algorithms aim to improve the power of predictors over conventional regression models. This study aims to tap the predictive potential of crash mechanism-related variables using ensemble machine learning models. The results demonstrate selected models can predict severity at a high level of accuracy. The stacking model with a linear blender is preferred for the designed ensemble combination. Most bagging, boosting, and stacking algorithms perform well, indicating ensemble models are capable of improving upon individual models.
... In order to overcome this problem, several numerical methods have been developed to interpret the contribution of each variable to the result of an ANN model (Fish & Blodgett, 2003;Fish & Segall, 2004). SA is a method that allows us to obtain the relative importance of each dependent variable to the model outcome (Davis, 1989). In other words, SA evaluates how sensitive a dependent variable to the changes in the independent variables. ...
Contrary to the popular belief cited in the literature, the proposed data analytics technique shows that multiple linear regression (MLR) can achieve as high a predictive power as some of the black box models when the necessary interventions are implemented pertaining to the regression diagnostic. Such an MLR model can be utilised to design an optimal concrete mix, as it provides the explicit and accurate relationships between the HPC components and the expected compressive strength. Moreover, the proposed study offers a decision support tool incorporating the Extreme Gradient Boosting (XGB) model to bridge the gap between black-box models and practitioners. The tool can be used to make faster, more data-driven, and accurate managerial decisions without having any expertise in the required fields, which would reduce a substantial amount of time, cost, and effort spent on measurement procedures of the compressive strength of HPC. ARTICLE HISTORY
... Sensitivity analysis is employed for determining the variables' significance and also recognized as predictors' importance. Sensitivity analysis of an estimation model is utilized to investigate the cause and effect relationship between the dependent and independent variables (Davis, 1989). The relative significance of each variable when making predictions is known as sensitivity analysis. ...
International trade depends on networking, interaction and in-person meetings which stimulate cross-border travels. The countries are seeking policies to encourage inbound mobility to support bilateral trade, tourism, and foreign direct investments. Some nations have been implementing liberal visa regimes as an important part of facilitating policies in view of security concerns. Turkey has been among the nations introducing liberal visa policies to support trade in the last decade and recorded significant increases in the volumes of exports. In this paper, we employed machine learning methodologies, Support vector machines (SVM) and Neural networks (NN), to investigate the facilitating impact of liberal visa policies on bilateral trade, using the export data from Turkey for the period of 2000-2014. The research disentangled the variables that have the strongest impact on trade utilizing SVM and NN models and exhibited that visa policies have significant impacts on the bilateral trade. More relaxed visa policies are recommended for the countries in the pursuit of increasing exports.
... However, even when a transparent algorithm is used (for example tree structure of the decision tree) cannot always easily be interpreted. In the context of machine learning, sensitivity analysis refers to exclusive experimentation process to establish a possible cause and effect relationship between the input and the output variables [32]. ...
... Sensitivity analysis of a prediction model in machine learning aims to discover the cause and effect relationship between the target variable and the input variables (Davis, 1989). Measuring the importance of predictor variables is often recognized as sensitivity analysis, which is relative to the importance of each variable when making predictions. ...
Purpose
The paper aims to identify and critically analyze the factors influencing cost system functionality (CSF) using several machine learning techniques including decision trees, support vector machines and logistic regression.
Design/methodology/approach
The study employed a self-administered survey method to collect the necessary data from companies conducting business in Turkey. Several prediction models are developed and tested; and a series of sensitivity analyses is performed on the developed prediction models to assess the ranked importance of factors/variables.
Findings
Certain factors/variables influence CSF much more than others. The findings of the study suggest that utilization of management accounting practices require a functional cost system, which is supported by a comprehensive cost data management process (i.e., acquisition, storage and utilization).
Research limitations/implications
The underlying data was collected using a questionnaire survey; thus, it is subjective which reflects the perceptions of the respondents. Ideally, it is expected to reflect the objective of the practices of the firms. Secondly, we have measured CSF it on a “Yes” or “No” basis which does not allow survey respondents reply in between them; thus, it might have limited the choices of the respondents. Thirdly, the Likert scales adopted in the measurement of the other constructs might be limiting the answers of the respondents.
Practical implications
Information technology plays a very important role for the success of CSF practices. That is, successful implementation of a functional cost system relies heavily on a fully-integrated information infrastructure capable of constantly feeding CSF with accurate, relevant and timely data.
Originality/value
In addition to providing evidence regarding the factors underlying CSF based on a broad range of industries interesting finding, this study also illustrates the viability of machine learning methods as a research framework to critically analyze domain specific data.
... The objective of sensitivity analysis is to measure the importance of predictor variables. Davis [15] stated that the "Cause and effect" relationship between the dependent (output) and independent (input) variables of a prediction model is determined by "sensitivity analysis" in machine learning algorithms. It is commonly used to identify and focus on the more important variables and to ignore or drop the least important ones. ...
... Since neural network (NN) models (Bayesian neural networks for this current case of USM) are considered to be Bblack-box^models (Davis 1989), understanding and making inferences from the results of NNs can be realized to some extent by determining the relative importance ranking of each of the latent variables. This is measured by using the sensitivity analysis (Principe et al. 2000). ...
Mobile banking (MB) has emerged as a strategic differentiator for financial institutions. This study explores the limitations associated with using subjective measures in MB studies that solely rely on survey-based approaches and traditional structural analysis models. We incorporate an objective data analytic approach into measuring usage experiences in MB to overcome potential limitations and to provide further insight for practitioners. We first utilize a multi-phase path analytical approach to validate the UTAUT model in order to reveal critical factors determining the success of MB use and disclose any nonlinearities within those factors. Proposed data analytics approach also identifies non-hypothesized paths and interaction effects. Our sample is collected from computer-recorded log data and self-reported data of 472 bank customers in the northeastern region of USA. We have analyzed the data using the conventional structural equation modeling (SEM) and the Bayesian neural networks-based universal structural modeling (USM). This holistic approach reveals non-trivial, implicit, previously unknown, and potentially useful results. To exemplify, effort expectancy is found to relate positively (but nonlinearly) with behavioral intention and is also ranked as the most important driving factor in UTAUT affecting the MB system usage. Theoretical and practical implications are discussed and presented in terms of both academic and industry-based perspectives.
... It is also known as the variable importance. Sensitivity analysis of a prediction model is used to examine the cause and effect association between the target variable and the input variables (Davis, 1989). Measuring the importance of C. Kuzey et al. ...
Facilitating mobility is important for creating tourism demand and is legislated by the visa policies of nations. Most countries implement visa regulations aimed at homeland security which also deter genuine travellers hindering domestic economy by means of tourism, trade, science and knowledge exchange. Turkey, on the other hand, has been implementing liberal visa policies in recent decades in order to boost the number of visiting travellers and thereby support tourism. In this paper, we used a decision tree approach to decipher the hampering impact of restrictive visa regimes on tourism demand, employing the inbound tourism data from eighty-four countries to Turkey in the period of 2000-13. We discovered the predictors that have the strongest impact on tourism demand using the Chi-square Automatic Interaction Detector (CHAID), Exhaustive-CHAID, Classification and Regression Trees, and Random Tree algorithms, and found that visa restrictions are as prognostic via the information fusion based sensitivity analysis. We recommend policy-makers describing liberal visa policies to the greatest extent in view of immigration issues and security threats they pose in order to improve the mobility across nations
... Moreover, putting independent variables in rank order in terms of their importance in prediction is also critical. In Artificial Neural Networks, sensitivity analysis is the technique to do so for a trained ANN model (Davis 1989). Through the sensitivity analysis, the learning algorithm of the ANN model is disabled after the learning is accomplished so that the network weights are not affected. ...
This study aims to assist marketing managers in identifying locations in which to host peer-to-peer educational events for healthcare professionals (HCPs) throughout the country using data analytics. These events would allow physicians and other HCPs to engage with their peers and learn about the most up-to-date clinical data and research from worldwide known Key Opinion Leaders. Decision making power in the healthcare industry is beginning to grow and fragment into numerous drivers. There are increasingly more variables, which affect marketing initiatives, and hence marketing managers are challenged to find the right methodology to place large investments and resources in the correct market segment. 3400 observations were collected from several sources including: The National Institute of Infant Nutrition monthly survey, Nielsen Consumer Behavior Data Reports, Congressional Budget Office Core Based Statistical Areas, US Census 2010 SF2 File, ZCTA Population and account information from the sales force. There were 17 input variables considered in this current analysis. The variables included; Return on Investment rank, total dollars of distribution margin, hospital influence rate, mother’s decision rate, healthcare professional decision rate, total investment, and competitive market share. The results from the data analytic models indicate that the most accurate classifier was the support vector machines followed by artificial neural networks and decision trees respectively. Marketing managers can flexibly utilize the proposed data analytic methodology proposed here to assist in identifying their target market. With the deployment of data analytics, marketing managers may now begin to sort through the large and complex data they gather and enhance their analyses of key target markets.
... First, it can suggest the underlying casual factors for any of the prediction models. This is particularly important in understanding and communicating the results of ANNs [48] which are still considered by many to be black box models [49]. A second major reason for the importance of sensitivity analysis is it provides us with a framework to capture the importance of independent variables across different models. ...
Predicting the survival of heart transplant patients is an important, yet challenging problem since it plays a crucial role in understanding the matching procedure between a donor and a recipient. Data mining models can be used to effectively analyze and extract novel information from large/complex transplantation datasets. The objective of this study is to predict the 1-, 5-, and 9-year patient's graft survival following a heart transplant surgery via the deployment of analytical models that are based on four powerful classification algorithms (i.e. decision trees, artificial neural networks, support vector machines, and logistic regression). Since the datasets used in this study has a much larger number of survival cases than deaths for 1- and 5-year survival analysis and vice versa for 9-year survival analysis, random under sampling (RUS) and synthetic minority over-sampling (SMOTE) are employed to overcome the data-imbalance problems. The results indicate that logistic regression combined with SMOTE achieves the best classification for the 1-, 5-, and 9-year outcome prediction, with area-under-the-curve (AUC) values of 0.624, 0.676, and 0.838, respectively. By applying sensitivity analysis to the data analytical models, the most important predictors and their associated contribution for the 1-, 5-, and 9-year graft survival of heart transplant patients are identified. By doing so, variables, whose importance changes over time, are differentiated. Not only this proposed hybrid approach gives superior results over the literature but also the models and identification of the variables present important retrospective findings, which can be the basis for a prospective medical study.
... Moreover, putting independent variables in rank order in terms of their importance in prediction is also critical. In ANNs, sensitivity analysis is the technique to do so for a trained ANN model (Davis, 1989). Through the sensitivity analysis, the learning algorithm of the ANN model is disabled after the learning is accomplished so that the network weights are not affected. ...
Purpose
The prediction of graduation rates of college students has become increasingly important to colleges and universities across the USA and the world. Graduation rates, also referred to as completion rates, directly impact university rankings and represent a measurement of institutional performance and student success. In recent years, there has been a concerted effort by federal and state governments to increase the transparency and accountability of institutions, making “graduation rates” an important and challenging university goal. In line with this, the main purpose of this paper is to propose a hybrid data analytic approach which can be flexibly implemented not only in the USA but also at various colleges across the world which would help predict the graduation status of undergraduate students due to its generic nature. It is also aimed at providing a means of determining and ranking the critical factors of graduation status.
Design/methodology/approach
This study focuses on developing a novel hybrid data analytic approach to predict the degree completion of undergraduate students at a four-year public university in the USA. Via the deployment of the proposed methodology, the data were analyzed using three popular data mining classifications methods (i.e. decision trees, artificial neural networks, and support vector machines) to develop predictive degree completion models. Finally, a sensitivity analysis is performed to identify the relative importance of each predictor factor driving the graduation.
Findings
The sensitivity analysis of the most critical factors in predicting graduation rates is determined to be fall-term grade-point average, housing status (on campus or commuter), and which high school the student attended. The least influential factors of graduation status are ethnicity, whether or not a student had work study, and whether or not a student applied for financial aid. All three data analytic models yielded high accuracies ranging from 71.56 to 77.61 percent, which validates the proposed model.
Originality/value
This study presents uniqueness in that it presents an unbiased means of determining the driving factors of college graduation status with a flexible and powerful hybrid methodology to be implemented at other similar decision-making settings.
... First, it can suggest the underlying casual factors for any of the prediction models. This is particularly important in understanding and communicating the results of ANNs (Davis 1989) which are still considered by many to be black-box models. A second major reason for the importance of sensitivity analysis is it provides us with a framework to capture the importance of independent variables across different models. ...
This study is aimed at determining the future share net inflows and outflows of Exchange Traded Funds (ETFs). The relationship between net flows is closely related to investor perception of the future and past performance of mutual funds. The net flows for Exchange Traded Funds are expected to be less related to overall fund performance, but rather based on the characteristics of the fund that make it attractive to an individual investor. In order to explore the relationship between investor’s perception of ETFs and subsequent net flows, this study is designed to shed light on the multifaceted linkages between fund characteristics and net flows. A meta-classification predictive modeling approach is designed for the use of large data sets. Then its implementation and results are discussed. A thorough selection of fifteen attributes from each fund, which are the most likely contributors to fund inflows and outflows, is deployed in the analyses. The large data set calls for the use of a robust systematic approach to identifying the attributes of the funds that best predict future inflows and outflows of the fund. The predictive performance of the proposed decision analytic methodology was assessed via the 10-fold cross validation, which yielded very promising results.
... Sensitivity analysis (SA) is a method to reveal the cause and effect relationship between the inputs and outputs of a trained model in machine learning algorithms (Davis 1989). After obtaining the performance of the prediction models based on the above-mentioned performance criteria, the importance of the independent variables is determined using the SA. ...
This article addresses the determination of velocity profile in small streams by employing powerful machine learning algorithms that include artificial neural networks (ANNs), support vector machine (SVMs), and k-nearest neighbor algorithms (k-NN). Therefore, this study also aims to present a reliable and low-cost method for predicting velocity profile. The data set used in this study was achieved by field measurements performed by using the acoustic Doppler velocimeter (ADV) between 2005 and 2010, in Central Turkey. The eight observational variables and calculated non-dimensional parameters were used as inputs to the models for predicting the target values, u (point velocity in measured verticals). Performances of prediction methods were determined via 10-fold cross-validation approach. The comparative results revealed that k-NN algorithms outperformed the other two machine learning models, with the R value of 0.98 ± 0.0069 and the MAE value of 0.053 ± 0.0075, while ANNs and SVMs models have the R values of 0.95 ± 0.0085 and 0.89 ± 0.0046, the MAE values of 0.085 ± 0.0077 and 0.099 ± 0.0117, respectively. Importance of the predictor variables for ANNs and SVMs models were also presented by using sensitivity analysis.
... El problema de la selección óptima de los parámetros no es trivial. Al aumentar el tamaño del problema, se reduce el rango de valores de los parámetros que permiten obtener soluciones factibles [29], y existe un pequeño rango de combinaciones de parámetros que generan soluciones estables para el TSP [30]- [31]. Se han aplicado técnicas muy variadas para intentar generar valores adecuados para los parámetros, obteniendo los mejores resultados al aplicar algoritmos genéticos [32]. ...
El Problema del Viajante de Comercio es un problema de optimización combinatoria de tipo NP-completo al que se han intentado aplicar numerosas técnicas de solución. Este trabajo se centra en la descripción de varias técnicas novedosas, inspiradas en sistemas presentes en la naturaleza formados por agentes muy simples que cooperan para la resolución de problemas complejos. Se ha demostrado que tales técnicas permiten obtener soluciones muy buenas en tiempo reducido, lo que permite aplicarlas a problemas grandes.
... The objective of sensitivity analysis is to measure the importance of predictor variables. Davis [15] stated that the "Cause and effect" relationship between the dependent (output) and independent (input) variables of a prediction model is determined by "sensitivity analysis" in machine learning algorithms. It is commonly used to identify and focus on the more important variables and to ignore or drop the least important ones. ...
... One major problem with such solutions is scaleability. With increasing problem size two things happen: first, the network becomes so big that simulation times are excessively long; and second, finding good parameters becomes increasingly hard that either the network converges to invalid solutions, or the quality of the solutions is poor [14], [2]. ...
This paper proposes a mean field neural network for the two-dimensional module placement problem. An efficient coding scheme with only 0(N log N) neu-rons is employed where N is the number of modules. The neurons are evolved in groups of N in log TV iteration steps such that the circuit is recursively parti-tioned in alternating vertical and horizontal directions. In our simulations, the network was able to find optimal solutions to all test problems with up to 128 modules.
... In addition, determining the rank order of independent variables in terms of their importance in prediction is also critical. In artificial neural networks, sensitivity analysis is the technique to do so for a trained ANN model (Davis, 1989). Through the sensitivity analysis, the learning algorithm of the ANN model is disabled after the learning is accomplished so that the network weights remain unaffected. ...
The purpose of this paper is to develop an early warning system to predict currency crises. In this study, a data set covering the period of January 1992–December 2011 of Turkish economy is used, and an early warning system is developed with artificial neural networks (ANN), decision trees, and logistic regression models. Financial Pressure Index (FPI) is an aggregated value, composed of the percentage changes in dollar exchange rate, gross foreign exchange reserves of the Central Bank, and overnight interest rate. In this study, FPI is the dependent variable, and thirty-two macroeconomic indicators are the independent variables. Three models, which are tested in Turkish crisis cases, have given clear signals that predicted the 1994 and 2001 crises 12 months earlier. Considering all three prediction model results, Turkey’s economy is not expected to have a currency crisis (ceteris paribus) until the end of 2012. This study presents uniqueness in that decision support model developed in this study uses basic macroeconomic indicators to predict crises up to a year before they actually happened with an accuracy rate of approximately 95%. It also ranks the leading factors of currency crisis with regard to their importance in predicting the crisis.
... "Cause and effect" relationship between the dependent (output) and independent (input) variables of a prediction model is often determined by "sensitivity analysis" in machine learning algorithms [25]. Sensitivity analysis aims to measure the importance of predictor variables. ...
... On the other hand, after determining which prediction models pass the threshold values based on the performance criteria as explained in Section 3.2.1, it is required to determine the rank order for the importance of the independent variables. In artificial neural networks, sensitivity analysis is a method for extracting the cause and effect relationship between the inputs and outputs of a trained ANN model [16,18]. In the process of performing sensitivity analysis, after the model is trained; the ANN learning is disabled so that the network weights are not affected. ...
The research presented in this paper proposes a new machine learning-based evaluation method for assessing the usability of eLearning systems. Three machine learning methods (support vector machines, neural networks and decision trees) along with multiple linear regression are used to develop prediction models in order to discover the underlying relationship between the overall eLearning system usability and its predictor factors. A subsequent sensitivity analysis is conducted to determine the rank-order importance of the predictors. Using both sensitivity values along with the usability scores, a metric (called severity index) is devised. By applying a Pareto-like analysis, the severity index values are ranked and the most important usability character-istics are identified. The case study results show that the proposed methodology enhances the determination of eLearning system problems by identifying the most pertinent usability factors. The proposed method could provide an invaluable guidance to the usability experts as to what measures should be improved in order to max-imize the system usability for a targeted group of end-users of an eLearning system.
... In addition, the rank order for the importance of the independent variables needs to be determined. In ANNs, the sensitivity analysis is a method for extracting the cause and effect relationship between the inputs and outputs of a trained ANN model (Davis, 1989). In the process of performing a sensitivity analysis after the model is trained, the ANN learning is disabled so that the network weights are not affected. ...
Predicting the performance of planned organ transplantation has proved to be a critical problem to solve. The purpose of this study is to present a data mining-based model for variable filtering and selection in order to predict the performance of thoracic transplantation via the graft survivability after the transplant. To this end, 10-fold cross-validated information fusion-based sensitivity analyses on machine learning models are conducted to receive an unbiased predictor variable ranking to be used in a subsequent Cox survival analysis. The study is unique in that it provides a mathematical means for medical experts to deal with thoracic recipients more efficiently and effectively.
... Sensitivity analysis is a method for extracting the cause and effect relationship between the inputs and outputs of a trained neural network model (Davis 1989). In the process of performing sensitivity analysis, the neural network learning is disabled so that its weights are not affected. ...
The purpose of this study is to test the efficacy of three popular data-mining methods (artificial neural networks, decision trees, and rough sets) by comparing and contrasting them using gambling ballot data that were collected for tourism policy purposes. Sixty unique prediction models were built for this comparative study. The findings of the study suggest that the rough-set algorithm was the best forecasting tool (among the three) with a cross-validation predictive accuracy of 83.8%, followed by artificial neural networks (79.4%) and decision trees (76.7%). Although the political utility of this study remains to be established, there is sufficient evidence to indicate the efficacy of rough sets in fore-casting gaming ballot outcomes. Policy makers, politicians, investors, and public service administrators can potentially use the results of these contemporary forecasting methods in their decision-making processes. Implications of the findings are discussed within the context of data mining and gambling literature.
... The use of derivatives of the prediction with respect to the input data, sometimes called sensitivity analysis, is not new (Deif, 1986;Davis, 1989). Since a neural network model is parametric (with possibly a large parameter space), a discussion of the derivatives of the function is meaningful (Hornik et al., 1990(Hornik et al., , 1993. ...
Artificial neural networks (ANN) seem very promising for regression and classification, especially for large covariate spaces. Yet, their usefulness for medical and social research is limited because they present only prediction results and do not present features of the underlying process relating the inputs to the output. ANNs approximate a non-linear function by a composition of low-dimensional ridge functions, and therefore appear to be less sensitive to the dimensionality of the covariate space. However, due to non-uniqueness of a global minimum and the existence of (possibly) many local minima, the model revealed by the network is non-stable. We introduce a method that demonstrates the effects of inputs on output of ANNs by using novel robustification techniques. Simulated data from known models are used to demonstrate the interpretability results of the ANNs. Graphical tools are used for studying the interpretation results, and for detecting interactions between covariates. The effects of different regularization methods on the robustness of the interpretation are discussed; in particular we note that ANNs must include skip layer connections. An application to an ANN model predicting 5-yr mortality following breast cancer diagnosis is presented. We conclude that neural networks estimated with sufficient regularization can be reliably interpreted using the method presented in this paper.
... Sensitivity analysis is a method for extracting the cause and effect relationship between the inputs and outputs of a trained neural network model (Davis 1989 ). In the process of performing sensitivity analysis , the neural network learning is disabled so that its weights are not affected. ...
*The purpose of this paper is to develop and test models to predict community support or lack thereof for commercial gaming using an artificial neural network. The findings reveal that there is a significant relationship between abolition of certain prohibitionary laws for gaming and sociodemographic and geographic variables. Specifically, increased proportion of minority populations within a geographical space, proximity to population centers, and church membership growth within the general public were variables found to be sensitive to changes in voting behavior toward gaming. Practical and theoretical implications are discussed within the framework of political science theory and commercial gaming.Résumé*La prévision des referendums sur le Jeu. L’objectif de cet article est de développer et tester des modèles pour prédire le soutien ou l’opposition de la communauté en ce qui concerne le Jeu commercial en utilisant un réseau neural artificiel. Les résultats montrent qu’il y a un rapport significatif entre l’abolition de certaines lois prohibitives au sujet du Jeu et des variables sociodémographiques et géographiques. En particulier, on a trouvé que les changements dans le comportement de vote au sujet du Jeu dépendaient des variables de la croissance de la proportion des populations minoritaires dans un espace géographique, la proximité des agglomérations et la croissance d’appartenance à une église parmi le grand public. On discute des implications theoriques et pratiques dans le cadre des théories de sciences politiques et du Jeu commercial.
... Examining the eigenvalues of the Jacobian matrix of the H-T energy function, they found conditions for the parameters under which a valid tour would be stable. Extensive studies by Davis [45] confirmed their analysis, which showed that there are only a very narrow range of parameter combinations that result in valid and stable solutions to the TSP-explaining the disappointing percentage of valid tours generated by many using the H-T formulation of the TSP. Despite these theoretical results, many researchers continue the search for methods of optimally selecting the penalty parameters. ...
It has been over a decade since neural networks were first applied to solve combinatorial optimization problems. During this period, enthusiasm has been erratic as new approaches are developed and (sometimes years later) their limitations are re- alized. This article briefly summarizes the work that has been done and presents the current standing of neural networks for combinatorial optimization by considering each of the major classes of combinatorial optimization problems. Areas which have not yet been studied are identified for future research.
... The higher the regression coefficient, the more important the input variable is. In neural networks, sensitivity analysis is a method for extracting the cause-and-effect relationship between the inputs and outputs of a trained neural network model (Davis, 1989). In the process of performing sensitivity analysis, after the model is trained the NN learning is disabled so that the network weights are not affected. ...
In this study, a decision support system (DSS) for usability assessment and design of web-based information systems (WIS) is proposed. It employs three machine learning methods (support vector machines, neural networks, and decision trees) and a statistical technique (multiple linear regression) to reveal the underlying relationships between the overall WIS usability and its determinative factors. A sensitivity analysis on the predictive models is performed and a new metric, criticality index, is devised to identify the importance ranking of the determinative factors. Checklist items with the highest and the lowest contribution to the usability performance of the WIS are specified by means of the criticality index. The most important usability problems for the WIS are determined with the help of a pseudo-Pareto analysis. A case study through a student information system at Fatih University is carried out to validate the proposed DSS. The proposed DSS can be used to decide which usability problems to focus on so as to improve the usability and quality of WIS.
... In machine learning, sensitivity analysis is a method for extracting the cause and effect relationship between the inputs and outputs of a trained prediction model [8]. Sensitivity analysis is similar to feature selection in that they both try to find the relative importance of the independent variables (features) as they relate to the output variable. ...
Demand for high-quality, affordable healthcare services increasing with the aging population in the US. In order to cope with this situation, decision makers in healthcare (managerial, administrative and/or clinical) need to be increasingly more effective and efficient at what they do. Along with expertise, information and knowledge are the other key sources for better decisions. Data mining techniques are becoming a popular tool for extracting information/knowledge hidden deep into large healthcare databases. In this study, using a large, feature-rich, nationwide inpatient databases along with four popular machine learning techniques, we developed predictive models; and using an information fusion based sensitivity analysis on these models, we explained the surgical outcome of a patient undergoing a coronary artery bypass grafting. In this study, support vector machines produced the best prediction results (87.74%) followed by decision trees and neural networks. Studies like this illustrate the fact that accurate prediction and better understanding of such complex medical interventions can potentially lead to more favorable outcomes and optimal use of limited healthcare resources.
... In machine learning, sensitivity analysis is used for identifying the ''cause-and-effect" relationship between the inputs and outputs of a prediction model [53]. Sensitivity measures the importance of predictor values based on the change in modeling performance that occurs if a predictor value is not included in the inputs. ...
This research investigates the impact of connecting building characteristics and designs with its performance by data mining techniques, hence the appropriateness of a room in relation to energy efficiency. Mining models are developed by the use of comparable analytical methods. Performance of prediction models is estimated by cross validation consisting of holding a fraction of observations out as a test set. The derived results show the high accuracy and reliability of these techniques in predicting low-energy comfortable rooms. The results are extended to show the benefits of these techniques in optimizing a building's four basic elements (structure, systems, services and management) and the interrelationships between them. These techniques extend and enhance, current methodologies, to simplify modeling interior daylight and thermal comfort, to further assist building energy management decision-making.
... After selecting the best prediction model based on the performance criteria as explained in Section 2.2.1, it is required to determine the importance of the independent variables. In machine learning algorithms, sensitivity analysis is a method for extracting the cause and effect relationship between the inputs and outputs of a trained model [36]. In the process of performing sensitivity analysis, after the model is trained the learning is disabled so that the network weights are not affected. ...
Objective:
The prediction of survival time after organ transplantations and prognosis analysis of different risk groups of transplant patients are not only clinically important but also technically challenging. The current studies, which are mostly linear modeling-based statistical analyses, have focused on small sets of disparate predictive factors where many potentially important variables are neglected in their analyses. Data mining methods, such as machine learning-based approaches, are capable of providing an effective way of overcoming these limitations by utilizing sufficiently large data sets with many predictive factors to identify not only linear associations but also highly complex, non-linear relationships. Therefore, this study is aimed at exploring risk groups of thoracic recipients through machine learning-based methods.
Methods and material:
A large, feature-rich, nation-wide thoracic transplantation dataset (obtained from the United Network for Organ Sharing-UNOS) is used to develop predictive models for the survival time estimation. The predictive factors that are most relevant to the survival time identified via, (1) conducting sensitivity analysis on models developed by the machine learning methods, (2) extraction of variables from the published literature, and (3) eliciting variables from the medical experts and other domain specific knowledge bases. A unified set of predictors is then used to develop a Cox regression model and the related prognosis indices. A comparison of clustering algorithm-based and conventional risk grouping techniques is conducted based on the outcome of the Cox regression model in order to identify optimal number of risk groups of thoracic recipients. Finally, the Kaplan-Meier survival analysis is performed to validate the discrimination among the identified various risk groups.
Results:
The machine learning models performed very effectively in predicting the survival time: the support vector machine model with a radial basis Kernel function produced the best fit with an R(2) value of 0.879, the artificial neural network (multilayer perceptron-MLP-model) came the second with an R(2) value of 0.847, and the M5 algorithm-based regression tree model came last with an R(2) value of 0.785. Following the proposed method, a consolidated set of predictive variables are determined and used to build the Cox survival model. Using the prognosis indices revealed by the Cox survival model along with a k-means clustering algorithm, an optimal number of "three" risk groups is identified. The significance of differences among these risk groups are also validated using the Kaplan-Meier survival analysis.
Conclusions:
This study demonstrated that the integrated machine learning method to select the predictor variables is more effective in developing the Cox survival models than the traditional methods commonly found in the literature. The significant distinction among the risk groups of thoracic patients also validates the effectiveness of the methodology proposed herein. We anticipate that this study (and other AI based analytic studies like this one) will lead to more effective analyses of thoracic transplant procedures to better understand the prognosis of thoracic organ recipients. It would potentially lead to new medical and biological advances and more effective allocation policies in the field of organ transplantation.
Earthquakes are challenging disasters that pose a huge threat to the urbanized world. In particular, the majority of the existing reinforced concrete (RC) building stock in developing countries such as Turkey is under huge seismic risk. These structures are at risk of partial or complete collapse under the effects of strong ground motions, due to some deficiencies in the structures. Therefore, seismic evaluation of existing buildings with a predominantly RC structural system is vital to reduce the potential seismic risk. In this study, machine learning (ML) techniques have been used for the prediction of the existing RC buildings’ performance against earthquake. The k-fold cross-validation has been employed to check the accuracy of the ML techniques. Random Forest (RF) provided the highest performance among the other ML techniques used. Sensitivity analysis has also been performed to determine the most significant factors in the prediction of the performance of the buildings. The results show that the building age, concrete compression strength, maximum column stirrup distance, steel yield strength, and the existence of corrosion have a high impact on the assessment of building performance.
Steep increases in air temperatures and CO2 emissions have been associated with the global demand for energy. This is coupled with population growth and improved living standards that encourages the reliance on mechanical acclimatization. Lighting energy alone is responsible for a large portion of total energy consumption in office buildings; and the demand for artificial light is expected to grow in the next years. One of sustainable approaches to enhance energy-efficiency is to incorporate daylighting strategies, which entail the controlled use of daylight inside buildings. Daylight simulation is an active area of research that offers accurate estimations, yet requires a complex set of inputs. Even with today’s computers, simulations are computationally expensive and time-consuming, hindering to acquire accelerated preliminary approximations in acceptable timeframes, especially for the iterative design alternatives. Alternatively, predictive models that build on machine learning algorithms have granted much interest from the building design community due to their ability to handle such complex non-linear problems, acting as proxies to heavy simulations. This research presents a review on the growing directions that exploit machine learning to rapidly predict daylighting performance inside buildings, putting a particular focus on scopes of prediction, used algorithms, data sources and sizes, besides evaluation metrics. This work should improve architects’ decision-making and increase the applicability to predict daylighting. Another implication is to point towards knowledge gaps and missing opportunities in the related research domain, revealing future trends that allow for such innovative approaches to be exploited more commonly in Architectural practice.
Accurate prediction of no-show patients plays a crucial role as it enables researchers to increase the efficiency of their scheduling systems. The purpose of the current study is to formulate a novel hybrid data mining-based methodology to a) accurately predict the no-show patients, b) build a parsimonious model by employing a comprehensive variable selection procedure, c) build a model that does not suffer due to data imbalance, and d) provide healthcare agencies with a patient-specific risk level. Our study suggests that an Artificial Neural Network (ANN) model should be employed as a classification algorithm in predicting patient no-shows by using the variable set that is commonly selected by a Genetic Algorithm (GA) and Simulated Annealing (SA). In addition, we used Random Under Sampling (RUS) to improve the performance of the model in predicting the minority group (no-show) patients. The patient-specific risk scores were justified by applying a threshold sensitivity analysis. Also, the web-based decision support tool that can be adopted by clinics is developed. The clinics can incorporate their own intuition/incentive to make the final decision on the cases where the model is not confident enough (i.e. when the estimated probabilities fall near the decision boundary). These insights enable health care professionals to improve clinic utilization and patient outcomes.
Breeding is of particular importance in recent years due to its economic value and value. One of the important issues in the shrimp supply chain is producing the right size for export because it costs storage costs if the supply chain is inappropriate. On the other hand, if the farmer has an accurate estimate of the size of the end period, the manufacturer will be able to plan for sales of different sizes that will lead to more profit in the chain. Many research has been done in the past years to improve growth. Hence, in this research, firstly, the parameters affecting shrimp growth and their ranking are considered important, and then estimation of shrimp weight for estimation of the product using data mining approaches has been studied. In this research, parameters such as age, food, density, temperature, salinity and pH of water were identified as factors influencing shrimp growth by sensitivity analysis. In this study, the Ensemble Neural Network model was used to estimate the weight of shrimp and it was shown that the model with accuracy of 84.6% was able to predict the size of shrimp. It also evaluated this model with other data mining approaches including linear regression Artificial Neural Network , Support Vector Regression, Decision Tree.
Investigation of the risk factors that contribute to the injury severity in motor vehicle crashes has proved to be a thought-provoking and challenging problem. The results of such investigation can help better understand and potentially mitigate the severe injury risks involved in automobile crashes and thereby advance the well-being of people involved in these traffic accidents. Many factors were found to have an impact on the severity of injury sustained by occupants in the event of an automobile accident. In this analytics study we used a large and feature-rich crash dataset along with a number of predictive analytics algorithms to model the complex relationships between varying levels of injury severity and the crash related risk factors. Applying a systematic series of information fusion-based sensitivity analysis on the trained predictive models we identified the relative importance of the crash related risk factors. The results provided invaluable insights for the use of predictive analytics in this domain and exposed the relative importance of crash related risk factors with the changing levels of injury severity.
This chapter treating a deterministic, continuous, linear, time-invariant system (DCLTIS), advances analytical expressions for sensitivity functions with distinctions between analysis for system-structural parameters (Definition 2.2-10) and that of system-physical parameters (Definition 2.2-11), followed by sensitivity functions generation in the frequency domain Special distinction between sensitivity functions of open-loop and closed-loop systems, as well as reconstructible and unreconstructible systems should be cited. The concept of low-order sensitivity functions and that of complete simultaneity properties (for higher-order sensitivity functions) are discussed. Additionally, the concept of total-sensitivity functions (TSF) is introduced. The details of a system model are also included, and in the last part of this chapter sensitivity invariance is presented.
Forecasting stock market returns is a challenging task due to the complex nature of the data. This study develops a generic methodology to predict daily stock price movements by deploying and integrating three data analytical prediction models: adaptive neuro-fuzzy inference systems, artificial neural networks, and support vector machines. The proposed approach is tested on the Borsa Istanbul BIST 100 Index over an eight year period from 2007 to 2014, using accuracy, sensitivity, and specificity as metrics to evaluate each model. Using a ten-fold stratified cross-validation to minimize the bias of random sampling, the case study demonstrates that the support vector machine outperforms the other models. For all three predictive models, accuracy in predicting down movements in the index outweighs accuracy in predicting the up movements. This study yields more accurate forecasts with fever input factors compared to prior studies of forecasts for securities trading on Borsa Istanbul. This efficient yet also effective data analytic approach can easily be applied to other emerging market stock return series.
In this paper we propose Resultant Projection Neural Networks, based on the idea of orthogonal projections onto convex sets for solving optimization problems under inequality constraints. The proposed network is capable of solving optimization problems with inequality constraints which cannot be solved directly using a Hopfield network. The effect of various network parameters on the optimization process are theoretically analyzed. A probabilistic analysis of the expected performance of the network has been carried out for the 0-1 knapsack problem. Simulation results for the 0-1 knapsack, multidimensional 0-1 knapsack and job processing with deadlines are also shown. The average performance (mean and median) of the network compare quite well with optimal and suboptimal solutions obtained using standard techniques in conventional computers. However, there are some instances which do produce bad solutions.
Most business students in universities across the United States find the quantitatively oriented courses challenging to comprehend the course material to a degree necessary to develop capability and confidence level to solve business problems. A determination of critical factors that influence performance in such courses is critical to designing class instructions. Instructors teaching these classes agonize over the fact that these courses are amongst the most difficult to teach as they encompass relatively harder concepts transformed into analytical skill sets with real applications to business operations that students struggle to grasp. This study employs a machine learning-based approach to determine critical success factors by analyzing the dataset of a focus course and provides some guidelines to educators for improving their teaching effectiveness. Information fusionbased sensitivity analyses on the data mining models provide an unbiased weighting scheme for the rank order of the variables that help predict the students' comprehension level.
The automated guided vehicle (AGV)system is emerging as the dominant technology to maximize the flexibility of material handling, while increasing the overall productivity of manufacturing operations. This paper presents a new way of finding the shortest flow path for an AGV system on a specific routing structure. An optimal solution of the system is determined by using an approach based on the Hopfield neural network with the simulated annealing (SA) procedure. In other words, the proposed approach reduces the total cost of an AGV delivery path from one workstation to another on the shop floor. By changing the temperature of the two-stage SA, a solution can be found that avoids potential collisions between AGVs. Both the flow path and the potential collision, which are major problems in AGV systems, may be solved simultaneously by the proposed neural network approach. Other advantages offered by the proposed method are its simplicity compared with operations research (OR)methods and a decreased number of needed AGVs. The performance of the approach is also investigated.
This paper investigates a method for allocating production resources to manufacturing tasks. The method is discussed with the help of a dynamic travelling salesman problem (DTSP), which has been formulated in order to model the conditions encountered in the manufacturing environment. The method approaches the DTSP using a decision-making procedure which can be adjusted with a number of decision parameters. The decision parameters affect the quality of the solution as well as the computational burden required for the procedure. The effect of these parameters is explained using a probability analysis. In addition, the paper investigates how to select proper values for the decision parameters with the aid of statistically designed experiments
In this Chapter, we review the virtues and limitations of the Hopfield neural network for tackling NP-hard combinatorial optimization
problems (COPs). Then we discuss two new neural network models based on the noisy chaotic neural network, and applied the
two methods to solving two different NP-hard COPs in communication networks. The simulation results show that our methods
are superior to previous methods in solution quality. We also point out several future challenges and possible directions
in this domain.
A quadrisectioning based neural network algorithm for the
placement problem in VLSI layout synthesis is presented. The mean field
theory neural network with graded neurons proposed by Peterson and
Soderberg is used. It is renamed normalized mean field net. The problem
is solved by recursive quadrisectioning where, at each step, all neurons
in the network evolve simultaneously, maintaining a level of globality.
In the authors' simulations, the network is able to find optimal
solutions to all hand constructed test problems with up to 256 modules
A neural-network-based routing algorithm is presented which
demonstrates the ability to take into account simultaneously the
shortest path and the channel capacity in computer communication
networks. A Hopfield-type of neural-network architecture is proposed to
provide the necessary connections and weights, and it is considered as a
massively parallel distributed processing system with the ability to
reconfigure a route through dynamic learning. This provides an optimum
transmission path from the source node to the destination node. The
traffic conditions measured throughout the system have been
investigated. No congestion occurs in this network because it adjusts to
the changes in the status of weights and provides a dynamic response
according to the input traffic load. Simulation of a ten-node
communication network shows not only the efficiency but also the
capability of generating a route if broken links occur or the channels
are saturated
To reduce cost, this paper proposes a system architecture to simulate and assess the multivariate of equipment properties. The architecture integrates the Monte Carlo simulation, the neural network model and the sensitivity analysis to construct a virtual metrology system. By assuming the property's probability distribution, the architecture generates the extreme input data to supplement the actual data for enhancing the model accuracy and estimating the property trend. An industrial case applied to validate the proposed system architecture
Student retention is an essential part of many enrollment management systems. It affects university rankings, school reputation, and financial wellbeing. Student retention has become one of the most important priorities for decision makers in higher education institutions. Improving student retention starts with a thorough understanding of the reasons behind the attrition. Such an understanding is the basis for accurately predicting at-risk students and appropriately intervening to retain them. In this study, using five years of institutional data along with several data mining techniques (both individuals as well as ensembles), we developed analytical models to predict and to explain the reasons behind freshmen student attrition. The comparative analyses results showed that the ensembles performed better than individual models, while the balanced dataset produced better prediction results than the unbalanced dataset. The sensitivity analysis of the models revealed that the educational and financial variables are among the most important predictors of the phenomenon.
The studies on interpretability of neural networks have been playing an important role in understanding the knowledge developed through their learning and promoting the use of neurocomputing in practical problems. The rule-based setting in which neural networks are interpreted provides a convenient way of expressing knowledge in a transparent and modular manner and at a desired level of granularity (specificity). In this study, we formulate a certain engineering-based style of interpretation in which a given neural network is represented as a collection of local linear models where such models are developed around a collection of linearization nodes. The notion of multi-linearization of neural networks captures the essence of the proposed interpretation. We formulate the problem as an optimization of (i) a collection of linearization nodes around which individual linear models are formed and (ii) aggregation of the individual linearizations, where the linearization fields are subject to optimization. Given the non-differentiable character of the problem, we consider the use of population-based optimization of Particle Swarm Optimization (PSO). Numeric experiments are provided to illustrate the main aspects of the multi-linearization of neural networks.
Thesis (Ph. D.)--University of Washington, 2001 This dissertation investigates several modifications and extensions of conventional neural networks for application to the problem of optimally choosing the adjustable parameters in a sonar system. In general, neural networks offer several key advantages over other technologies that might be used for this task, including the ability to learn from examples and the ability to extract information about the underlying system through neural network inversion. One aspect of this work is the use of a neural network for emulating a computationally intensive acoustic model. A novel neural network training technique for varying output node dimension is developed, allowing a single neural network to be used for different output topologies. Step size modification for this training technique is also introduced to improve accuracy, convergence time, and the smoothness of the weight space, eventually providing better generalization. Inversion of neural networks is also investigated in order to solve for the optimal control parameters given a requested level of sonar performance. In order to improve inversion accuracy, modular neural networks are designed using adaptive resonance theory for pre-clustering. In addition, sensitivity of the feed forward layered perceptron neural network is derived in this work. Sensitivity information (i.e., how small changes in input layer neurons affect output layer neurons) can be very useful in both the inversion process and system performance analysis. Finally, the multiple sonar ping optimization problem is addressed using an evolutionary computation algorithm applied to the results of properly trained neural networks. It searches for the combination of control parameters over multiple independent sonar pings that maximizes the combined sonar coverage.
Highly-interconnected networks of nonlinear analog neurons are shown to be extremely effective in computing. The networks can rapidly provide a collectively-computed solution (a digital output) to a problem on the basis of analog input information. The problems to be solved must be formulated in terms of desired optima, often subject to constraints. The general principles involved in constructing networks to solve specific problems are discussed. Results of computer simulations of a network designed to solve a difficult but well-defined optimization problem--the Traveling-Salesman Problem--are presented and used to illustrate the computational power of the networks. Good solutions to this problem are collectively computed within an elapsed time of only a few neural time constants. The effectiveness of the computation involves both the nonlinear analog response of the neurons and the large connectivity among them. Dedicated networks of biological or microelectronic neurons could provide the computational capabilities described for a wide class of problems having combinatorial complexity. The power and speed naturally displayed by such collective networks may contribute to the effectiveness of biological information processing.
A model for a large network of "neurons" with a graded response (or sigmoid input-output relation) is studied. This deterministic system has collective properties in very close correspondence with the earlier stochastic model based on McCulloch - Pitts neurons. The content- addressable memory and other emergent collective properties of the original model also are present in the graded response model. The idea that such collective properties are used in biological systems is given added credence by the continued presence of such properties for more nearly biological "neurons." Collective analog electrical circuits of the kind described will certainly function. The collective states of the two models have a simple correspondence. The original model will continue to be useful for simulations, because its connection to graded response systems is established. Equations that include the effect of action potentials in the graded response system are also developed.
From the Publisher:
A comprehensive look at feedback control. Physical systems are customarily represented by models consisting of idealized components which can be precisely defined mathematically. This book discusses a number of ways to utilize these mathematical characteristics or models.
The model of the catfish retina (Siminoff, in press) has been extended to the turtle retina with incorporation of color-coding. The turtle retina contains 6 types of cones of which 4 are red-sensitive and the other 2 are green- and blue-sensitive, respectively. The cone-horizontal circuit incorporates negative feedback from the L-HC to all the cones having input to the L-HC. By use of systems analysis, Laplace transforms and the convolution theorem, impulse responses, that give information as to gain and phase, for the cone-types and L-HC were simulated. As with the catfish retina, negative feedback gain was proportional to the dc level of the L-HC and therefore, the mean illuminance level. It was shown that this mechanism can be an important factor in chromatic adaptation, since the gains of the various cone-types are preferentially altered dependent on mean illuminance level and wavelength of the background light.